Game Theory in the AHCA

Game Theory in the headlines:

It is Friday. Speaker Ryan comes to Trump to tell him he lacks the votes to pass the AHCA. The Freedom Caucus is still a no and, with all of the compromises to them in the "fixed up" version of the bill, the Tuesday Club. (GOP moderates) are now also likely a no.

The question is whether to hold a vote, even knowing that it will lose, to force each Rep to publicly take a stand, or to pull the bill.

This is a classic Game Theory question. We have an IGoUGo game where Trump has the first move, pull the bill or not, and then the Congress has the second, casting a vote. The votes will affect both Trump's payoff as well as the individual Reps themselves.

What should Trump do, force a vote or pull the bill?

Trump reasons (aloud) thusly: a vote will "smoke out the disloyal", so I'll know where I stand with each Rep. Hence, going for the vote is optimal.

Speaker Ryan counters that, while that might have been true of the original bill, it no longer holds because of the massive concessions made to the hard right. Reading between the lines, he is saying that the consummate dealmaker, Tump, has managed to fashion a bill that will lose BOTH the Freedom Caucus and the Tuesday Club.

He goes on by noting that forcing the Tuesdays to cast a no vote will hurt their chances of being re elected whereas forcing the Freedom Caucus to cast a no vote will have no effect.

In essence he is saying this: Mr. President, you already know the Freedom Caucus is disloyal. Forcing them to make an easy public vote does nothing. On the other hand, the Tuesdays are your natural allies, but the strategy you propose is very likely to see these allies removed from the chess board in the near future.

Trump reluctantly agrees to pull the bill. But his chief strategy advisor, Steve Bannon still insists on a vote and is overruled.

It seems to me that Ryan is 100% right in his analysis and Trump's loyalty argument rather silly. If the bill had come to the floor unamended, in the form exactly as the Speaker and President agreed, you could cast the vote as one of party loyalty. But once it is altered to concede to a specific side, it loses this status. The speaker sees this, the President and, worse yet, his chief strategist, do not.

Paid versus Unpaid Work: A Bedtime Story

Let me tell you a story:

Once upon a time in a faraway land, there lived two girls, Anna and Bess. Each was a single mom with a one-year old to care for. Their pregnancies were such that their families deeply disapproved and banished them. Instead, both relied on a government program that gave single moms $10k/year. It was a hard life, but they were just able to scrape along. The 10k program was the only form of support in this land.

Moreover, this was a world of big data---everything was measured very carefully. One day, a social worker visited each woman and measured her mothering output thanks to a new gadget, the Workatron 6000. When looking after her own child, the Workatron showed that each woman produced 2 units of mothering. The social worker then had them swap--when looking after the other's child, the Workatron showed that each mom was less effective, producing only one unit of mothering when looking after the other's child. Finally, the social worker studied whether there were economies of scale, having each mom look after both kids for a day. She discovered the opposite--the Workatron showed that each kid received a half a unit of mothering. The social worker wrote her findings down in her notebook and went back to her lab.

Back at the lab, some clever data scientists then examined the effects of mothering on child outcomes. When their findings were reported in the popular press, they were derided as obvious---they found that kids who received more mothering did better in life. Apparently, age 0-4 was when mothering was most important. They computed, using the workatron, that each child produced an additional $10,000 per year when receiving an additional unit of mothering. 

One day, a new leader was chosen in the land of Anna and Bess, a leader who believed in the principle: You must earn to receive. The leader made a new rule--only Moms earning 10k in paid work were eligible for the 10k subsidy. Otherwise, Mom and baby would get nothing, starve, and die. This faraway land was very harsh in this way. 

Anna and Bess were scared about the new program. Clearly, they would have to find "real" jobs rather than doing their "fake" job of mothering. Neither had finished high school nor had any skills to speak of. They had no money for day care either. How could they earn $10k in paid work? What would they do to feed their families?

One night, they got together and, over a bottle of cheap wine, worked out a solution. Anna would be a full-time nanny for Bess's daughter and vice-versa. Each would be paid by the other $10k for the work. The money would, of course, come from the subsidy the other mother would receive for her paid work--taking care of the opposite baby. And so they did this for a year. They cleverly "gamed" the system, but their kids received half as much mothering.

But the government in this faraway land hated people who gamed the system and soon found out about their trick. They sent in a social worker to fix the problem.

The clever social worker came to each woman with a wonderful opportunity. Each could work for 12 hours a day cleaning toilets, while the other mom looked after both kids. Moreover, the job perfectly rotated so that when Anna was on duty Bess was off duty and vice-versa. The social worker, and the leader of this faraway place rejoiced. Since toilet cleaning paid each $11k, but they were no longer eligible for the 10k subsidy and thereby saved the state a considerable sum on entitlements. Better yet, Anna and Bess would discover the independence and freedom of true paid work. 

Naturally, Anna and Bess jumped at the chance as both were taught not to burden the state. At the end of the year, their children were less well developed, receiving only half as much mothering than before, but the local penitentiary, where they were working had nice, clean toilets.

Using the Workatron, the social worker determined that the value of clean toilets in the penitentiary was very worthwhile, amounting to a half a unit of mothering to a baby.

And so, my dear friends, we have arrived at a happy ending. Anna and Bess are no longer a burden to the state. Their children are undeniably worse off, society is undeniably worse off. But the state did not have to pay out and their kids, as they struggle through life, can have the happy knowledge that their rarely seen mothers burdened no one else.

The Moral of the Story: It is a choice on the part of society to say that it is better to give kids less mothering than to subsidize maternity leave during early childhood. It is a choice to say that we would prefer than moms send their kids to day care rather than pay for them to stay home and care for the kids themselves.

The parable is also about how arbitrary it is to define work by whether it is paid or not. We should measure the societal benefit of such work and, presumably, incentivize the work yielding the highest social benefit. If we think a new mom's time is better spent cleaning toilets than looking after her child, that is perfectly fine. But let us be open and honest about this judgment rather than saying that, because one activity produces pay and the other doesn't, of necessity the paid activity is more valuable. 

Economics, as well as game theory, says nothing of the sort.

Let me close with an extreme example to illustrate the point. In this faraway land, Charlotte is truly gifted. Were she subsidized by the government, Charlotte could produce world peace lasting forever through her volunteer work. Without a subsidy, the best that Charlotte can do is to spend that time cleaning toilets. It is not a well-paying job, but at least it pays something. 

As a society, we would have to be idiots not to give Charlotte the subsidy--despite the fact that world peace is not paid work while cleaning toilets is.

Clearly the right rule in this faraway land is that government spending should maximize societal benefit. Perhaps, as a rough rule of thumb, insisting on earning to receive benefits is good, but it mustn't be applied dogmatically, as it often is in our world, as well as the faraway land of my story.

The End.

Valuing Life

There are lot of philosophical conundrums dealing with this question. For some reason, most of them involve trains and switches.

Economists have tried to answer this question using a technique called revealed preference. The idea is to look at the risks a person takes and compare the financial gain from the risk against the chance of dying. These measures are all over the place though because, while expected utility theory is beautiful mathematically, it is pretty dreadful at predicting out of sample actions. (In other words, if I see how you behave in deciding about a small risk, I can guess what you might do faced with other small risks. But if I try to guess what you'll do when facing large risks, I'll be miles off.)

Interestingly, states have also dealt with this issue in an interesting way. It turns out that a fair number of people are wrongfully convicted each year. We know that eyewitness testimony is unreliable, but it is often the best evidence we have. Nonetheless, in the fullness of time, with DNA evidence or other sorts of corroboration, many people get out of jail after having been put there despite being innocent.

The question is, how are we to compensate these individuals for the years of their life lost to prison? This is not precisely the value of a human life since an individual in prison is not dead. But from all that I have read, prison is a pretty bad place to go, so it might not be too far off from death. Or, if you believe in heaven, it is perhaps even worse than death. Regardless, it is a question that many states are now contending with.

Much like economist estimates, the legislators solutions to this problem as also all over the place. The modal answer is $70k/year. Many states offer amounts around this value. You might think the answer would vary with the cost of living, but California, a quite expensive state, offers only $36,500/year for those wrongfully convicted. One might also think that blue states would offer more than red. That too turns out to be wrong. Texas gives $80k/year while Wisconsin gives only $5k/year.

And then there are many states, like my old home state of PA, who think very little about the value of life. They offer those wrongfully convicted *absolutely nothing* for their time spent in jail. Perhaps PA jails are especially comfortable or desirable, though I've not heard that from the ex prison guards I talked to. It seems that PA is just plain mean.

A final funny story: During a legislative session in TX, a GOP legislator spoke out against any compensation. He argued that someone who was on welfare would rig a situation so that he or she will be wrongfully convicted of a crime, spend years in jail, and then have an accomplice reveal the wrongful incarceration thereby collecting the reward. While clever, the judge deciding on the validity of the legislation suggested that the congressman must have lost his mind to think that someone would willingly enter Texas jails in exchange for the cash rewards.

So how much is a human life worth? It seems to be about $80k/year if you are at risk of wrongful conviction. An absurdly small amount when one thinks about it.

The Chain Store Paradox of Politics

There is a famous folk tale that game theorists tell their kids before putting them to bed, the story of the Chain Store Paradox. The idea is simple, a large chain faces a finite and known sequence of challengers. It can either give in to them or fight. In each case, fighting is more costly than giving in, but if the chain gives in everywhere, they stand to lose a ton of money.

The reason it is called a paradox is that, on the basis of pure logic (and backward induction), the chain should optimally concede in every case. When told to MBA students, they reject this immediately and vehemently. And they're right--a chain store would be foolish to engage in such a strategy.

Enter clever game theorists to come to the rescue. They amend the story as follows: Suppose there is a small chance of a "tough" chain--one that actually enjoys fighting and prefers it to giving in, even on an individual store basis. Or, at least, suppose that would-be entrants are willing to contemplate such a possibility. Then, if there are enough entrants, the chain store should fight several so as to deter entry from the rest. (Or at least all but the final few.) Moreover, this is credible since a would-be challenger, after seeing several fights, is forced to increase the chance that the chain is tough, which deters entry and profits the chain.

All of the detailed logic aside, this latter conclusion seems sensible and much closer to the mark than the original case. The business lesson: cultivate a reputation for toughness, especially with early challengers.

So what does this have to do with politics?

Everything, actually.

Trump is like the chain store and the GOP legislators the entrants. Trump knows that he will face would be challengers over each of his policies. He also knows that there is a finite endpoint--4 or 8 years most likely---and so, by the end of his term of office, there is little point in fighting, i.e. he will, eventually, be a lame duck. But early on in the game, reputation is critically important--so fighting is called for.

What is key for the chain store in our little parable is that it never show weakness for, once it does, the entrants will conclude that it is not the tough type. They will know it dislikes fighting, and will enter 100% of the time thereafter. In lay terms, once reputation is lost, it is not easily, or perhaps ever, recovered.

But Trump seems to have just flunked game theory 101 with his handling of the AHCA vote.

In supporting the AHCA with all his power, he knew he would face challengers, and he did in the form of the Freedom Caucus. Chain store/game theory logic suggests that, since this is the first big issue on his watch, he has every reason to pretend to be the tough type of President and give little or no ground, even if he would rather concede and compromise. But, as Trump will tell you, he's an instinctive decision maker, and certainly not one to read the cockamamie theories of pointy-headed game theorists or other intellectual types. So he apparently never got the memo about how important it is to create a reputation for toughness.

Instead, he met with the Freedom Caucus guys in secret, and behind the Speaker's back. In this meeting, he offered them many concessions, hoping to get a deal. Smelling blood, the Caucus came back for more...and more...and more.

And so, remarkably, Trump already seems to have squandered a "tough" reputation among favor-seekers in Congress. He'll face a lot more "entrants" in future.

Choosing Auctions

The revenue equivalence theorem identifies conditions where the type of auction is irrelevant to seller revenues. But how should one choose between auction forms when these conditions do not hold?

Open versus Closed

An open auction, an English auction for example, has the property that bidders can adjust their bids to others in a dynamic fashion. In a closed auction, bids are sealed. An open auction is another way to achieve linkage. If bidders' values are correlated, as in the mineral rights model, then, on average, the seller earns more from an open than a closed auction. The reason is that others' bids reveal information, much like an appraisal. This more tightly correlates perceived values and intensifies competition, an effect absent in a closed auction.

So why are closed auctions run? There are several reasons.
1. Cheating: It is easier to engage in bid rigging in an open auction since the bids of others in the ring can be monitored, and countered, if someone decides to deviate.
2. Liquidity: An open auction requires people to participate at a specific time and place. This could reduce the number of bidders attracted to the auction, leaving the auctioneer worse off.

High Bid versus Second Price

A high bid auction is simpler for bidders to understand, even if the equilibrium bidding strategy turns out to be more complex. It is also less subject to the problem of shill bidding, bids made by the auctioneer to boost the price of the item. Second-price auctions invite shill bidding, especially when it is hard to verify who placed what bids.

On the other hand, bidding in the second price auction is simpler, once it is explained. It is more robust to errors on the part of other bidders. Finally, optimal bidding in the first price auction requires knowledge of the number of competing bidders. In the second-price, it does not. For inexperienced bidders, the lack of knowledge about the level of competition, and hence the right amount of bid shading to engage in, represents a serious entry barrier.

The Linkage Principle Revisited

In class, I mentioned that a firm is better off committing to release appraisals of products to be auctioned rather than remaining silent. Here's some more intuition:

Consider a situation where there is a single object of unknown value. God draws the value from some distribution, but keeps it a secret. Instead, everyone, including the auctioneer, gets an unbiased signal about the value. Think of the auctioneer's signal as his appraisal of the value of the object.

(This is sometimes called the mineral rights auction model since it can model a situation where bidders are bidding for a mine with unknown content. The ore extracted from the mine is sold at the same market price regardless of the winning bidder.)

If no appraisal is released, then bidders will bid, accounting for the winner's curse. Bids will of course differ, depending on the signal, and will, in general split the surplus between the bidders and the auctioneer.

To see the linkage principle at work, suppose the appraisal perfectly reveals the true value of the item. Now the perceived value of the item will be identical for all bidders, and everyone will simply bid the value of the item. Bidders will get no surplus and the auctioneer all of the surplus, an ideal situation for the auctioneer.

When the appraisal is an imperfect signal of value, the same basic effect applies: Bidders' perceived value for the item will be more tightly correlated, so competition will be fiercer. This makes the auctioneer better off.

Commitment is important though. If the auctioneer selectively reveals appraisals, displaying them only when they are high and not when they are low, the analysis is no longer so clean because the absence of an appraisal will now affect bidders' perceived valuations as well.

A Brokered GOP Convention?

With the results of yesterday's GOP primaries in FL and the Midwest, Donald Trump is on track to secure a plurality of the national delegates, but not a majority. This matters as the convention rules state that the winning candidate must receive the majority of all votes cast. Thus, even if Trump captures, say, 45% of the delegate votes, alone that will not be enough to secure the nomination. Moreover, if present trends continue, even though highly favorable to Trump, that will be the most likely scenario when the convention comes to order in Cleveland.

So what happens then?

Here is an opportunity to use game theory and outside thinking as a means of guiding our projections.

First, let's get procedures out of the way. Nearly all states have rules requiring that delegates pledged to a given candidate must give that candidate their vote on the first round of voting. In addition to pledged delegates, who make up the bulk of convention voters, there are also so-called "super delegates," high-ranking party officials who are free to vote for whom they wish. If Trump is close to securing a majority, it is possible that these super delegates will vote for him en bloc in an effort to ensure as unified a party as possible. They might reason thusly: Trump, owing to his numbers and intensity of support, is likely to win the nomination in the end. So all that is gained by forcing multiple ballots is disunity and rancor. Since neither of these aspects helps the GOP to win the election, it is better to look forward, reason back and vote for Trump right from the outset.

But Trump looks to fall short of a margin where only a few super delegates will put him over the top. In which case, there will be more than one ballot in all likelihood. In theory, that makes it anyone's election since delegates from many states are free to vote for whom they will after the first ballot. John Kasich recently hired consultants from Reagan's unsuccessful bid to unseat Ford in 1976, in hopes that they will help him to secure the nomination by this second choice route. Kasich faces huge obstacles in this.

The first is Mitt Romney, or rather, Romney's rules. Technically, each convention gets to set its own rules, something done by the powerful Rules Committee. Often, however, these rules are a carryover from the past, and that may help Trump. Romney, in the 2012 race, changed the rules so that, as a pre-condition for nomination, the winning candidate must have won 8 states during the primary race. It looks like only one candidate will meet this hurdle, Trump. Of course, the 2016 Rules Committee could set aside this rule if it wished. But the Rules Committee's membership depends on the delegate count, and here Trump's plurality could be enough. Merely by blocking any change in the status quo, Trump's forces on the Rules Committee can, in effect, create a situation whereby he would be the only candidate eligible for the nomination.

But let's imagine that the other candidates manage to pool their forces to overturn the Romney Rule. Can Kasich now win? The answer is probably not, as even a cursory use of our WITS would suggest. The exact identity of the delegates representing each candidate is determined via statewide caucuses and the like. But these people tend to be among the most committed and passionate for their candidate. Such people do not change their votes easily nor without a good reason. Consider what Kasich must overcome: He must suspend the Romney Rule, stop Trump on the first ballot and then, and then, somehow convince the many, many Trump delegates to shift their votes to Kasich while holding his existing delegates firm.

But what argument can he make to the Trump delegates to get them to switch votes? He cannot argue support from the popular will, for he has lagged badly in most primaries, save for Ohio. He cannot argue that he is the more electable candidate, for the same reasons. He cannot argue that such an outcome is fair or just since, for Trump supporters, it plainly is not.

Simply put, it is hard to imagine any argument more likely to sway Trump voters toward Kasich rather than the reverse. Indeed, it is far easier to conjure up arguments "for the good of the party" that cause non-Trump support to defect than Trump support to defect.

Which leaves only one other path to grasp at--the mysterious "party bigwigs" hijacking the convention and imposing their own preferred candidate. Such a script is undeniably dramatic and interesting, and seems to be the last slender reed at which the anti-Trump forces are grasping, but it does not pay much attention to the strategic motivations of these bigwigs. To impose such a solution, the bigwigs would have to coalesce around their preferred candidate, no easy thing. Then, these same bigwigs would still somehow have to secure the votes of the Trump delegates and suspend the Romney Rule. All of this is very hard, likely impossible.

But what if it were possible? Then would it happen? The answer, even in that case, is probably not. These political bigwigs gained their position by having decent judgment about the electorate, at least within the GOP. So why would they bet their political lives on some anti-Trump candidate like Mitt Romney? Trump might run as a third party in the face of such intrigue, and many would follow his banner. This would almost certainly give the election to the Democrats, hardly worth the massive expenditure of social capital that would be required to hijack Trump. Even if the bigwigs see Trump as unelectable, their own political skins matter a great deal, and those skins are not well served by spurning the Trump branch of the GOP.

Then there is the bigger risk---by "stealing the election" in the eyes of Trump supporters, the fissures within the GOP would be on display for all the world to see. Such fissures are dangerous, especially when dealing with someone as charismatic and unpredictable as Trump. The party bigwigs are only bigwigs so long as their is a powerful GOP. When American parties have disappeared from the scene, as the Whigs did in the 1850s, it occurs because of fracture, not because some new party has appeared fully-fledged. And this, more than anything else, is something the bigwigs do not want.

So while it is fun to think about a convention that is raucous and unpredictable, while it is fun to speculate about dark horse candidates appearing from some unexpected quarter, while it is fun to contemplate a deus ex machina by party elders seeking to restore sanity, it's all very unlikely to come to pass, once one thinks through the strategic possibilities. For better or worse, Donald Trump will be the GOP nominee, probably on the first ballot and even despite not having a majority of delegates.



But these people tend to be among the most committed and passionate of partisans favoring their particular candidate. Indeed,

Wargames

Throughout the semester, I emphasize the importance of outward thinking in identifying and anticipating the key levers available to rivals that might alter the business situation or opportunity. It is often said, mostly truthfully, that no plan survives contact with the enemy. In a business context, there are rarely enemies per se, but there are rivals seeking many of the same customers and opportunities. Thus, properly speaking, Uber and Lyft are not really enemies, but the plans and strategy of one do impinge on the opportunities and profits of the other.

Despite this interactive aspect to the outcomes of business strategy, the process producing that strategy is often mainly introspective rather than adversarial. Moreover, successful planning often requires a flexible approach by the most customer-facing elements of the business. Yet, too often, corporate roadmaps and designation of strategy is rigid, top-down, and its principles insufficiently precisely articulated up and down the hierarchy. The result is to make independent action, and retrenchment if the plan starts failing, difficult.

Such problems with the formulation and articulation of strategy are as old as time, though most often seen in a military context. What can be learned from these experiences?

In my view, one of the most noteworthy, and readily applicable, lessons in strategic planning and formulation that might be drawn from the military is the use of gaming applications. The Prussian General Staff first introduced Kriegspiel in the 19th. At least in part as a result of this, Prussia rapidly achieved rapid victories over Austria and France during this time. Prussia's success was especially surprising in light of its lack of materiel or manpower advantages, especially in relation to France.

While strategic planning using wargames is commonplace in military planning, it is unusual in corporate settings. Instead, most strategy departments create scenarios, explicitly announcing their assumptions. They assign probabilities to various sequences of events, but relying mainly on judgment for the generation of these probabilities.

What is missing from this analysis is human input on the part of the rival or rivals. Obviously, your rivals are not going to tell you their plans nor how they will react to your plans. But in most large firms, a substitute for these rivals is readily available--senior leaders who are ex-employees of your rivals. Wargames as the basis of strategy have two parties, your strategy group and your ersatz rivals, each making decisions and strategic choices that, together, determine outcomes.

A criticism of this type of strategy making approach centers on its practicality--how does one go about building a simulation engine capable of capturing the myriad possible strategies, countermoves, and consumer responses. Such an engine would, if fully fledged, be a daunting proposition. This, however, is to view the purpose of the exercise wrongly--wargaming is not full-fledged simulation. Rather, it is a much simplified model capturing the key big picture elements of the strategic landscape without trying to build from the ground up in capturing all of the particulars. An engineering mindset, strategy as simulation, represents a major hurdle, not logistically but conceptually.

So how do you make such a wargame? The key is the introduction of referees. Referees or umpires should be experts in the industry, possibly outside consultants, who view the strategies proposed by each side through the lens of their expertise and then make an assessment about the likely results. With such individuals in place, it becomes possible to create a rich space without restrictions on strategic options for either side without the impossibility of trying to build a reality engine.

Wargames also matter lower down the chain of leadership--they are central learning devices for developing independent action consistent with the overall plan but flexible enough to take advantage of unforeseen tactical possibilities. Turning back to Prussia, kriegspiel was not merely the province of generals planning campaigns but of sub-lieutenants developing instincts for the best action in the face of a given tactical situation in view of the overarching plans.

The same holds true in business. Wargames, and the umpiring framework, readily extend downstream to the level of product managers, brand managers, and the like. Part of the charge of the strategy group in any organization is in coordinating the actions of these parties in furtherance of the plan. By creating smaller scale wargaming sessions bringing together product managers, for example, there is a chance for spreading deep understanding of the overall strategy, and a manager's role small role in its execution, as well as a chance to infuse passion, and a spirit of friendly competition among these individuals in a way that is far more compelling, and leads to better retention, than the usual sorts of strategy briefs typical of corporate strategy. Returning to the military, the following article offers an interesting and important take on how the British military is using wargames to facilitate independent judgment and decision making prowess among NCO and lieutenants, military equivalents of product managers.

Wargaming: An Overlooked Educational Tool

The lightweight games used in game theory offer a taste for how wargaming can be used to develop outward thinking. But the serious challenge for firms seeking a competitive edge is in incorporating these techniques and ideas into what is, for the most part, an inwardly driven exercise.

Did Trump Win or Lose in Iowa?

The results of the Iowa Caucuses showed Donald Trump in second place, with 24% of the vote, behind Ted Cruz with 28 and just ahead of Marco Rubio with 23%. The difference in terms of numbers, is about 6,000 votes. In other words, if 3000 Iowans would switch their votes from Cruz to Trump, the outcome would have changed. Pundits, and the GOP establishment, seem to view this result as containing the seeds of destruction for the Donald. They point out that part of his campaign persona is that he's a "winner" and yet, in Iowa, he didn't win. What can game theory say about the GOP presidential race?

Coordination and Duverger's Law

Duverger was a French philosopher in the field of politics. He noted that, in winner take all elections (sometimes call first past the post), there is a strong tendency for just two candidates to receive large vote shares. From this, he concluded that such voting rules tend to produce two party systems as in the US and, at the time, the UK. In proportional representation systems, many parties get votes.

Note that the Iowa caucus is actually proportional representation, at least to an extent. Multiple candidates can collect delegates in Iowa,  but there is overrepresentation of delegates among the top vote getters.

Duverger's Law, it turns out, can be understood using game theory. Here's the idea: The main reason that people vote is to help their candidate to get elected. Let's say that there are three candidates, A, B, and C. All voters have rankings over these candidates and, within these rankings, can feel different levels of passion for each. In other words, you and I might both rank the candidates A > B > C, but I feel very strongly for A whereas you are close to indifferent between A and B.

Now for whom should you vote if solely motivated by the outcome of the election? One possible answer is to vote truthfully choosing A if that is your top choice, or B, or C if those are on top. But now suppose a poll has been taken. It shows that C leads narrowly over B while A trails badly behind. Since I rank the candidates ABC this is very bad news. My least favorite candidate is ahead while my candidate trails badly.

So how should I vote? Since I only care about election outcomes, I should switch my vote from A to B. In a very real sense, A is a wasted vote for a voter who cares about outcomes. Of course, all A voters reason in a similar fashion and so A's vote share dwindles ever lower, a death spiral of switching away. Notice that there is a "snowball" nature to this logic very similar to the information cascade--once my candidate's chances grow sufficiently dim, my love for that candidate no longer influences my vote.

So from this, we can conclude that Carly and Jeb and all the others in the single digits in Iowa are effectively doomed. Votes for these candidates will be seen as purely "wasted" and so will dry up.

These votes make up about 15% of the votes in Iowa, probably similar to national rates as well. Where will they go?

Back to the Donald. From his perspective, he benefited from Iowa by strongly affirming what the polls showed--that a vote for the Donald is not a wasted vote. Thus, the missing 15% view him as plausible. But my suspicion is that they mostly will go elsewhere. The Donald is a polarizing figure, you love him or you hate him. He benefits from the passion of his supporters, they provide energy in getting themselves and others out to vote. But this same polarization makes him an unlikely second choice for voters whose first choice was someone else.

Landscaping

Job #1 in strategy is analyzing, and characterizing the business landscape in which the opportunity exists. The use of 5 forces, value net, etc. all represent frameworks for such analysis. Suppose you evaluated the opportunity of an incumbent, small market NBA team seeking to retain a superstar player? You would, of course, examine the rivalry for this all-important asset and sensibly conclude that rivalry is witheringly intense. From here, you would be forced to conclude that the prospects for making profits from such an opportunity are correspondingly small.

Put simply, the intense rivalry of the landscape will compete away all of the "rents" from the superstar player. And, from here, you might also conclude that the overall opportunity of being a small market NBA owner is not worth much in such a landscape.

If, however, you look at the available data, you'll find that teams like the San Antonio Spurs, the Cleveland Cavaliers, and the Indiana Pacers all more or less mint money with their NBA franchises. That is, far from the prediction of our landscape analysis, these are promising opportunities, not poor ones.

The difference is that the analysis presumes that just because rivals can compete all out, they will compete all out, to the detriment of the smaller teams and the overall opportunity. Yet, as we saw in the experiment, competition under the ROFR clause is quite subdued. Rival teams could enter and compete, but they know they won't be successful. Moreover, since competing itself is expensive, there's no point in doing so unless the prospects of success are decent. So, far from the prediction of our models, that unbridled rivalry will destroy value, the reality is more of a "gentleman's" labor market where the incumbent team faces little competition.

On the other hand, take away the ROFR and the labor market becomes as the models predict, brutal and difficult for the small market players. Superstars are retained by the incumbent team only by offering extremely favorable salaries, vastly reducing the quality of the opportunity from owning a small market team.

So the major lesson is one of landscaping. A business landscape may appear unfavorable in pure form, but the details matter. A ROFR clause essentially redoes the landscape of the NBA labor market in a massively important way. An outward thinker is alert to such things in doing strategic analysis of opportunities. The ROFR is an apparently small thing, put in place officially for entirely different reasons than to suppress competition. Yet it and other distortions in the NBA labor market make the opportunity far better than what a simple 5 forces would imply.

How to Think Outwardly

A good exercise in learning to think outwardly is to perform 5 forces or other similar analysis to opportunities of interest as you would in strategy. The twist, though, is to now pay attention to WITS type moments where the implicit assumptions of such analysis get altered, using your outward thinking.

The Interview Game, Choosing by Voting

At its core, the interview game asked you to make a decision of the following form: given a list of m good interviews and n bad interviews, should you hire the person or not. I suggested that the optimal strategy was to follow a voting rule: If the goods outnumbered the bads, then you should hire otherwise you should not. The reason such a simple rule works is that each piece of information conveys exactly the same amount of information.

Photo Credit: Jessica Martinez

Let's do this carefully for the first couple of interviews. In the first interview, a candidate is 50% likely to be competent. In this case, 2/3rds of her interviews are good and 1/3rd bad. Suppose you have a good interview. What is the chance the candidate is competent? Formally, what is:

Pr[Candidate is Good | Interview is Good]

Bayes' rule (Data and Decisions) tells us that

Pr[Candidate is Good | Interview is Good] = Pr[ Interview is Good | Candidate is Good] Pr[Candidate is Good] / Pr [Interview is Good]

The denominator, the chance of a good interview, is just the prior chance of granting a good interview prior to knowing whether the candidate is incompetent or not. This chance is 50-50. Thus,

Pr[Candidate is Good | Interview is Good] = 2/3  1/2 / 1/2 = 2/3

So we draw the obvious conclusion that the first manager should hire the candidate if she interviews well and not if she interviews poorly.

Now let's turn to the second manager. Suppose the candidate was hired by the first manager, but has a bad interview with the second. Then we are interested in:

Pr[Candidate is Good | One good and one bad interview], which I'll now abbreviate as Pr[G | gb]. The capital letters indicate the type of candidate, Good or Bad, and the small letters the type of interview. Again, using Bayes' rule, this amounts to the calculation:

Pr[G| gb] = Pr[ gb | G] Pr[G] / Pr[gb] = Pr[g|G] Pr[b|G] Pr[G] / Pr[gb]

and since Pr[g|G] = 2/3, Pr[b|G] = 1/3 and Pr[gb] = 2/9, we may easily deduce that the chance the candidate is good is 50-50 in this case.

What just happened? Since each piece of information carries the same weight, the bad interview completely cancelled the good one, leaving the second manager in the same position as when she had no information whatever.

But this is exactly like voting--each vote carries the same weight so a Gore vote cancels a Bush vote in Florida in 2000. And, taking the analogy further, we can see that a manager who knew that the candidate had two good interview and no bad ones will never gain enough evidence from her own interview result. If it's good, the vote count is 3-0 in favor of hiring. If bad, the vote count is 2-1. Either way, hire is the better choice.

And so, after only two "votes" have been cast/hire decisions have been made, the resume data completely overwhelms any interview data and we end up in a "cascade." If the candidate experienced initial success, she will be hired by everyone thereafter. If she had no initial success, she is doomed to never be given a chance.

One sees this type of thing all the time with technology platforms--the early success or failure of a platform more of less sets the course of affairs thereafter.

The key take away, and the whole point of performing the experiment, is to illustrate that choice data, what people did in response to information rather than the information itself, may contain very little value. Imagine a job candidate who was hired by the first 100 or the first 1000 managers. One might think it a sure thing that this candidate is competent based on the data. And if the data were non-strategic, you'd be right. But when strategic actors create the data by their actions, this intuition is completely wrong.

In the situation above, the chance the candidate is competent/good is simply

Pr[G | gg] = Pr[gg | G] Pr[G] / Pr[gg]

And this may be readily calculated to be 80%--a long way away from a sure thing.

The situation can be much worse when the data gets noisier. Suppose you are choosing a CEO. CEO talent is notoriously difficult to measure so, when the CEO is good, there is one a p% chance of a good interview. There is the same p% chance of a bad interview, when the CEO is incompetent. Once again, the voting rule describes optimal behavior and, once again, things snowball after a run of only two consecutive identical choices initially.

So suppose our CEO was hired twice initially and then "climbed the ladder" successfully being hired/promoted many times. What is the chance that we end up with a bad CEO? Again, this amounts to

1 - Pr[G | gg] = Pr[gg | G] Pr[G] / Pr[gg]

which we can compute as 1 - p p / ((p p) + (1 - p)(1 - p))

Here is a chart I drew in Excel showing the chance of a bum CEO as a function of p.

What you should notice is that, when the interview/hiring process is noisy, there is a very good chance of being trapped in a "bad" snowball--a situation where the person exhibits a stellar record and then badly underperforms.

Placing excess weight on data subject to this type of "herding" breeds one type of overconfidence, an increasingly common trap as we rely ever more on data driven decisionmaking. The data seem to make the hire a no-brainer, but this is far from the case.

What can you do about it?

If we stopped here, it would be a depressing conclusion--voting is the best decision rule, but it's a lousy decision rule, especially when the data is noisy. So what should you do? The most important thing is to realize you have this potential problem with your data in the first place. Once realized, make a rough estimate of how noisy each piece of data is, and hence the risk of a "bad" snowball outcome. From here, make a cost-benefit assessment of whether new data from other sources is needed before making a decision or not. Also, now being aware of the risk, you might link your decision with various sorts of hedging strategies to try to mitigate this risk.

But the bottom line is this: Without outward thinking, once a record has been established, it looks like no-brainer decision. Those attuned to outward thinking, however, recognize the risk, and incorporate it into their overall portfolio of decisions and forecast outcomes.

Altruistic Bacteria?

Biology student Derrick Grunwald told me about the following tale of the game theory of bacteria. It turns out that certain bacteria come in two varieties, altruistic and selfish. The classification relates to their reaction to emitting a certain molecule. The selfish types emit the molecule and then immediately claim it for themselves using a receptor in another part of the creature. The altruists emit the molecule to the colony and receive the average emissions available, sort of like a public good. Apparently, this process of emitting and receiving creates fitness for the bacteria. Derrick tells me that there is an ideal amount of the molecule to receive, m*. A bacteria exposed to too much is unhealthy as is one exposed to too little.

The puzzle to biologists is how their can be altruistic bacteria. While other-regarding or even eugenic preferences are possible in higher primates, it seems a stretch to consider such motives in bacteria.

So how can we resolve this puzzle using game theory and what does this tell us about the nature of these bacterial colonies? First off, why are there volunteers in the first place? What possible benefit is there from volunteering? When a bacteria emits the molecule, it doesn't get the amount exactly right. Sometimes it emits too much, sometimes too little. On average, it's the correct amount, but individually it is not. Thus, the volunteer bacteria are engaging in a bit of risk pooling. By emitting in general, all of these errors average out in the colony and each individual absorbs just the right amount of the molecule thanks to the magic of the law of large numbers. A colony of selfish bacteria are choosing not to insure. This is obviously less fit than insuring, but does have some advantages of reliability.

Let us study "equilibria" of this game. Suppose that a colony consists entirely of volunteers and it is invaded by a small number of selfish types. The volunteers will still absorb approximately m* of the molecule while the selfish will absorb 2m*--way too much of the molecule. Thus, the selfish are "killed with kindness" by the volunteers. Hence, all volunteers comprises an equilibrium.

What about a colony of all selfish types? While less fit than the volunteers, this colony is also immune to invasion. If a small number of volunteers show up, they hardly affect the absorption of the selfish, which is still approximately m* on average, but the volunteers themselves get almost none of the molecule. Thus, they too die out. So all selfish is an equilibrium despite its inferiority to the insurance scheme worked out by the volunteers.

What about mixed colonies? This is possible, but unstable. If the colony consists of a fraction f of volunteer types, a co-existing equilibrium can arise. In this situation, selfish types are systematically exposed to too much of the molecule since they absorb some of the production of the volunteers. Volunteers systematically have too little of the molecule since the selfish types are "stealing" some. And if the fitness of the two types is approximately equal, they can coexist.

The instability arises from the following problem. If the co-existing colony is invaded by selfish types, this improves the fitness of the selfish, since the emissions of the volunteers are now more diluted by the additional selfish types, but reduces the fitness of volunteers since there are now more selfish types "stealing" the molecule. Hence, such a perturbation would cause the colony to eventually drift to an all-selfish society. By contrast, if the colony is invaded by volunteers, just the opposite occurs--volunteers become more fit while selfish become less fit. Only if invasions of various types are occurring often enough to bring the population back to the equilibrium fraction f, will the colony continue to coexist. This is unlikely if invasions occur randomly, even if both types of invasions are equally likely.

Thus, using game theory, the puzzle of altruistic bacteria may be understood as purely selfish behavior.

If a tree falls in the forest...

There's an old conundrum that asks whether, when a tree falls in the forest, and know one is there to hear it, does it make a sound? Millions of creators of social media must constantly ask themselves the same question. How many thousands of tweets, facebook posts, youtube videos, and blog entries pass through the ether, unheard, unread, and unknown.

In the words of Thomas Gray (Elegy Written in a Country Churchyard)

Full many a flower is born to blush unseen, /And waste its sweetness on the desert air.

 And so it is with social media. How many Ansel Addams' or Auguste Monet's are bound to rest, undisturbed and undiscovered, amidst the detritus of the communication explosion.

At Berkeley-Haas, the Dean's suite often coaxes a reluctant professoriate to embrace the age of social media, to interact with our students outside the classroom in these social spaces. We are advised that the millenials we teach are especially receptive to such bite-sized portions of wisdom, that, in fact, they prefer them to the more traditional long-form of the lecture hall or the textbook. We are advised to turn our classes upside-down, to engage in all possible ways for the ever elusive mindshare.

What we are not offered, however, is evidence. Does any of this flailing outside the classroom matter? Do the students even want it?

I conducted an A/B test to measure this. Before each of my last two Wednesday classes, I wrote a blog entry. I viewed the entries as similarly interesting to my class. If anything, the treatment entry is more interesting. The key treatment was announcing the presence of the entry in one case, and saying nothing in the other.

Here are the results of the experiment:

Blog entry with no announcement: +1, 0 comments, 14 views.
Blog entry with announcement, +1, 0 comments, 14 views.

It takes no statistics to see that awareness that a blog entry has been written makes no difference whatsoever.

What should we make of this experiment? My take is the following: All the hype about social is a bunch of hooey. Individuals want well-produced solid entertainment. There may, at one point, have been novelty value in the power of individuals to create content, but that point has long passed. What millenials want is the same thing that all previous generations want, solid amusement for their out of class hours. So far as I know, this is the first experiment to test the desires of MBA millenials to read the random thoughts of their blogging social professors. Regardless, it's a finding worthy of wider circulation. Simply put, calls to embrace social as an important information stream are, quite simply, nonsense.

It's a sad conclusion, and it won't stop me from writing since I derive joy from the process myself, but it suggests a refocus in pedagogy away from the "flavor of the month" and back toward the heart of the matter, which is providing great experiences for students in the classroom. 

A lovely blog/youtude/facebook/twitter steam is all well and good, but it should be seen for what it is, entirely peripheral and largely wasted motion, at least so far as my sample is representative.

Pregnant MBAs

When most people think of game theory, they think of situations in which two or more individuals compete in some situation or game. Chess is the quintessential example. Yet the thinking underlying formulating a good plan when playing against others is just as important (and useful) when thinking about your own future path.

An episode of Seinfeld captures this idea beautifully when "morning Jerry" curses aloud the bad choices made by "evening Jerry." Evening Jerry stays out too late and indulges too much making life difficult for morning Jerry, who has to pay the piper for this excess. He then muses that morning Jerry does have a punishment available to evening Jerry. Were morning Jerry to lose his job, evening Jerry would be without funds or friends to pursue his wild lifestyle. Not mentioned is that this punishment is also costly to afternoon Jerry, who is likewise in no position to pay the bill at Monk's Cafe for meals with Elaine and George.

While the Seinfeld routine is meant to be funny, for many individuals, the problems of the activities of their many selves are no laughing matter. Anyone struggling with their weight curses their night self or their stressed out self for lack of willpower. That giant piece of cake that stressed-out self saw as deliverance means a week of salads and many extra hours at the gym for the other selves.

I bring this up because we all suffer from the evening Jerry problem, but for MBAs, it's one of the most serious problems they'll ever face. For most MBAs, the two years spent getting this degree represents the final time in life when complete attention can be paid to learning and single-mindedly building human and social capital. The constraints of work and family offer vastly less time for such activities in the future. While there may be occasionally breaks for internal training or executive education, such breaks are rare. Moreover, for busy managers, even these times may not constitute a break. Work does not stop simply because you are absent. Crises still need to be dealt with and deadlines met.

Moreover, the gains made during this time can profoundly affect an MBA's career. They can be the difference between the C-suite and merely marking time in middle management. They can be the difference between the success and failure of a startup. They can be the difference between getting a position offering a desired work-life balance and accepting a position that does not. They can be all the difference in life.

Yet, inward thinking would have us see the choices we make quite narrowly. Will an extra weekend in Tahoe be the difference between an A- and a B+? Will it be the difference between making or missing a class? Will it be the difference between actively participating in a case discussion or not? Will they be the difference between seeing or missing some outside speaker in an industry of interest? Viewed in this light, such choices are of decidedly small caliber. An extra day in Tahoe can hardly be the difference in anything of consequence.

Wilhelm Steinetz, the great chess champion, averred that success in chess is a consequence of the accumulation of small advantages. Viewed narrowly, inwardly one might say, the differences Steinetz had in mind seem trivial. To most chess players, the board, and one's chances of winning, are not appreciably different with a slightly better versus a slightly worse pawn formation. Yet a grandmaster does not see things this way at all. Such individuals are consummate outward thinkers, constantly planning for the endgame, for the win, which will only be determined much later. From that perspective, such trivial things are of utmost importance. And indeed they are as, more often than not, they mark the difference between victory and defeat in championship play.

Outward thinking also allows one to take a longer-term view on the time spent while pursuing an MBA. The apparent difference between the talent at the middle and the top tier of many organizations is often remarkably small.  The CFO does not have appreciably more IQ points than someone lower down. She does not work vastly more hours or have vastly better social capital. Rather, her rise commonly represents an accumulation of small advantages--a win early in her career that distinguished her as high potential, a management style that avoided or defused a conflict that might have derailed her progress, an unexpected opportunity because a head at some other firm remembered her as standing out. In the end, it is clear that she is CFO material while the middle manager is not, but it didn't start out that way.

We might be tempted to chalk all this up to luck. She got the breaks while her sister, unhappily struggling as a middle manager somewhere, didn't. Admittedly, luck plays a role, but chance, somehow, seems to mysteriously favor some more than others. Consider the situation of poker or blackjack players. To win, one needs to have a good hand, i.e. one needs to be lucky. Yet some people consistently win at these games and others consistently lose. Luck evens out over many hands, or over many events in the course of a lifetime, yet there are genuine poker all-stars.

Much like evening Jerry, MBA life is filled with temptations, filled with vast stress-easing slices of chocolate cake. We might think, "What's the harm? We all work hard. I deserve this." But unlike the dieter, who can learn from his mistake and say no to the cake the next time around, an MBA gets only one chance to get it right. Mess it up this time and there is no tomorrow to make amends. There are no do-overs. The MBA equivalent of chocolate cake today may not mean a week of salads and workouts, but a lifetime of them.

So the lesson here is our usual one: look forward, reason back. How will our future selves perceive the choices we are making today? Will they be happy?If not, then it's time to make different choices.

So how does any of this relate to the title of this post, Pregnant MBAs. When a woman learns she is pregnant, she will often alter her lifestyle, sometimes radically, After all, she's now responsible for her unborn baby as well as herself, so she eats better, stops smoking and drinking, exercises more, and so on. She wants her baby to have its best chance in the world. In a sense, every MBA is pregnant. You are also responsible for two---your present self and your future self.  Outward thinking is nothing more than this awareness, so obvious to a pregnant woman,,but submerged beneath the surface at all other times. Give your future self his or her best chance in the world.

(Not) Solving Social Dilemmas

The secret ingredient to solving social dilemmas is punishment. Without the ability to punish transgressors, good behavior must rely entirely on individual self-control in abstaining from the temptation to cheat and obtain a reward. Some individuals are up to this challenge. Their consciences are so strongly developed to chasten them for engaging in dishonorable behavior that this is not a problem. But for most, it is. Indeed, a fundamental human weakness is to go for today's reward over tomorrow's, a failing which destroys most attempts at dieting let along social dilemmas.

Sufficient punishment fixes this problem by adding the force of extrinsic incentives to intrinsic. Given sufficient reinforcement, even those more "pragmatic" consciences can be persuaded to do the right thing. Yet, even when such punishments are available, a literal-minded view of game theory suggests that they must always be available. Individuals must never perceive themselves as getting off scot free. The usual version of this argument uses look forward, reason back type reasoning. Suppose the game will end in period N. Then clearly bad behavior in that period is unpunishable and hence everyone will be bad. But this destroys punishment for bad behavior in the penultimate period, and so on. The pure logic of the situation implies that any game known to end at a fixed time, however far into the future, will see cooperation remorselessly break down right from the start.

But, while logically sound, this is a very silly prediction when the number of periods is long. Despite the logic of LFRB, bad behavior in early periods will be punished and good behavior rewarded with reciprocity in early periods of the game, only breaking down when the endgame is sufficiently close. Here again we see the friendly face of irrationality. Suppose there is some chance that others playing the game don't "get it." They, instead, think they are playing the infinitely repeated version of the game whereby cooperation can be sustained by threats of punishment, and play accordingly.

What is a rational soul to do? The answer is, when in Rome, do as Romans do. In other words, pretending that you too don't get the game is a perfectly logical and sensible response, at least until some point deep in the game where knowledge that punishment won't work becomes too hard to ignore. As with some of our other examples, only a seed of doubt about the rationality of others is needed so long as the endgame is sufficiently far off into the future. Such a seed of doubt seems to me eminently more reasonable than the maintained assumption in the standard model, that everyone understands the game perfectly,

But if we're playing a short game consisting of, say, only 8 periods. Now the logic of LFRB has real force, and we would seem to be genuinely doomed. Running such a game in the lab reveals that things are not quite as bad as all that, but they are definitely pretty bad.

Or maybe not. Let's change the game a little. Suppose, at the end of each period, each player has a chance to punish one or more of the others. Punishment involves destroying some of their payoffs. But this punishment is not free, it costs the punishing individual something as well. This would seem of immense help since the whole problem was that we lacked an ability to punish in the last period and, this wrecked the incentives in all the earlier periods. Now, we no longer have this problem. If someone misbehaves in the last period, we punish them via value destruction and all is once again well in the world. But such a plan only works if the punishment is credible, if we can count on the punishment to be delivered should an individual try to test societal resolve. There are two problems with credibility. First, there is a social dilemma in who delivers the punishment. While we all might agree that cheaters should be punished, each of us would rather that someone else delivers the punishment and hence takes the hit to their own payoffs. But even if we sorted this out by agreeing on whose job it was to punish, we might still be in trouble. In the last period of the game, who would actually carry through with the punishment?

This is a version of our earlier problem. In the last period, there is no future reward for today's good behavior nor punishment for bad. Since the whole point of punishing is to obtain future good behavior, what is the point of punishing anyone in the last period of the game? Worse yet, not only is punishment pointless, but it is also costly. So why would anyone believe that misbehavior will be punished in the last period? By the same logic, there is no point in punishing in the penultimate period either and again the endgame casts its long shadow back to the first period. Irrationality seems to work less well as a way out of this particular logical bind. The endgame is simply too near.

Yet, remarkably, such schemes seem to work, at least in western cultures. Economists Ernst Fehr, Simon Gaechter, and a number of other co-authors performed versions of this experiment in labs in the US and Europe. Remarkably, they found the such a scheme proved excellent at producing cooperation. Some individuals tested societal resolve early in the game and invariably received bloody noses for this insolence.

But why does it work? The answer, in this case, seems to be morality. While conscience is weak in resisting temptation, it is rather stronger when we have a chance to unsheathe the sword of justice to be used on others. That is, even though there was a personal cost to punishment, it seemed to be more than offset by a personal benefit in administering justice.

[A curious sidenote to this stories, in Middle Eastern, Greek, and North African cultures, the sword of justice operated in the other direction---those who did not cheat were punished. That is, individuals cooperating in a prisoners dilemma were hit with penalties from those who did. This soon produced conformity in a failure to solve social dilemmas.]

This solution is all well and good when the punishment can be surgically directed at transgressors, but suppose instead that there is collateral damage--to punish the guilty, some innocents must be punished as well. In work in progress by myself and former Berkeley undergrad Seung-Keun Martinez, we investigate this possibility. We first consider the opposite extreme where, to punish one person, you must punish everyone. One might think that such a scheme would be either marginally useful or utterly useless. In fact, it is neither. Compared to the world in which no punishment was allowed, punishment of this sort actually reduces cooperation. This is not simply from the value destroyed by punishment (though there is some of that), but rather from a reaction to the possibility of such punishment. When individuals fear suffering punishment when doing the "right thing," they seem to become despondent and to cooperate less than those under no such threat.

We are now in the process of investigating intermediate levels of "collateral damage" from punishment to determine where the 'tipping point" might lie.

The Costs of Coordination

Large organizations face a fundamental dilemma. They want their employees to coordinate on doing the right thing, on the firm's strategy, but they also want them to coordinate with one another. The two may differ in their importance depending on the organization. For some, coordination with one another may be of little consequence while coordination at large may be crucial--think of creative industries where artists labor alone to achieve some vision consistent with the roadmap of the company. For others, employees working in tandem is the important thing--think of iPhone production lines in Shenzen.

For game theorists and economists, the first trouble that comes to mind is what is known as agency problems, employees might not have the right incentives in mind to perform in conjunction with the firm and so they diverge in their actions and things go wrong. Let us set aside these possibilities and imagine that somehow these issues have been solved. Employees have nothing more than the company's interest at heart. This would suggest that all of our problems are solved and things are well with the world. Or are they? The world is full of miscommunication. While I try my best to articulate various ideas as clearly and carefully as I can, the sad fact is that I am doomed to failure, as is most anyone else caring to do likewise.

For CEOs and other leaders, communicating their vision effectively is central to their quality of leadership.

What can game theory tell us about the problem of imperfect communication of a leader's vision on the firm's prospects, even when incentives are well-aligned? Unlike our sad stories about understanding persuasion, things are a bit more fruitful here.

As usual, we make a simple model to describe the complex world of a leader seeking to impart her vision. To be precise, suppose that the leader's vision can be thought of as a normally distributed random variable with mean equal to 0 known variance, equal to 1 say.  The idea here is that, under average conditions, a leader has a standard, long-run vision, which we will normalize at zero. However, the business climate changes, which requires some alteration of this vision. New rivals emerge, acquisitions are made, employees innovate new business areas. Our normal distribution represents these alterations.

Employees are perfectly aware of the long-run vision. It's part of the firm's core DNA. They also know that it changes with conditions, but don't know precisely how it changes. Indeed, understanding how to translate changes in the business landscape into vision is a large part of the leader's value.

But knowing the right vision is only half the battle. Our leader must also articulate it. So our CEO makes a speech, or composes a set of leadership principles, or does any number of things to express the current vision. All of this is transmitted to employees. Employees, however, only imperfectly understand their leader's wishes. Instead of learning the vision exactly, each gets a signal of the vision, which equals the truth plus a standard normal error term. 

If this sounds like a statistics problem so far, that's because it is. Indeed, we'll tear a page out of our notebook on regressions to assess what the leader would like the employees to do in a moment. Meanwhile, note that employees know that they understand the vision only imperfectly, so they form posteriors about the true vision. These consist of placing some weight on the prior--the long-run visions, with the rest going to the signal. The weight on the signal (optimally) consists of a ratio of the variance in vision divided by the sum of the variance of the vision term and the error term, i.e. a version of the signal to noise ratio. In our example, the weight is 50-50. 

Employees then choose an action to undertake. We will assume there are many employees and that actions are chosen simultaneously. Of course, this is not really the case, but it simulates the idea that it is a big organization and the actions of others are not readily observed. 

How are these actions chosen? Suppose that the payoffs of employees depend on matching the strategy, with a quadratic loss function with 50% weight (importance) , and matching each other, with another quadratic loss function with the complementary weight, also 50%. To be precise, each employee wishes to match the average action of the others. Employees seek to maximize their payoffs.

Now, this would seem the most ordinary of coordination problems--everyone has the same goal and, on average, gets the same signal. Better yet, the signal is unbiased and equal to the truth. But let's see how things play out. 

Before proceeding, let's simplify things still further. Suppose that, from the perspective of the company as a whole, mismatched actions are of no consequence. What matters is simply the coordination of action to strategy. To reconcile this with the individual incentives above, suppose that the payoffs from miscoordination among employees is normalized whereby deviations among employees in terms of coordination add up to zero when summed over the entire firm. (It's not hard to do this, but the exact math is beyond the scope of a blog.)

So what would the firm desire of its employees? The answer is simple and is, in fact, equivalent to a regression. The firm wishes to minimize the sum of squared error between an employee's action and the true visision. The only piece of data an employee has is her signal. Simple statistics will confirm that the "regression coefficient" on this piece of information is equal to 1/2, i.e. the signal-noise statistic from above. That is, under ideal circumstances, each employee will merely do her best to conform her action to the expected value of the vision conditional on her signal.

So far, so good, but what will employees actually do? Also from basic statistics, it is apparent that the best choice for an employee is to selection an action that places half the weight on the expected vision conditional on each employee's signal, s, and the other half on the expectation of the other employees' actions. The expected state, as we saw above, is nothing more than half the signal. The latter is more complicated, but becomes much simpler if we assume the firm is large--indeed so large that we can guess the average action using the law of large numbers, which tells us that sum of others' signals converges to the underlying vision, which, as we saw, was just half of the signal.

Finally, let us suppose, in equilibrium, an individual chooses an action equal to w times her own signal, where w is a mnemonic for weight. Thus, the equilibrium equation becomes:

w s = 0.5 x (s/2) + 0.5 x w (s/2)

where x denotes the "times" symbol. The left-hand side is the equilibrium action while the right-hand side is the weighted average of the expected value of the vision conditional on the signal and the expected average of others' conditional on the signal. Since all employees are alike, we suppose they all play the same strategy. 

Solving this equation yields the equilibrium weight:

w* = s/3

or, equivalently, individuals place a weight equal to one-third on their signal with the remaining 2/3rds weight on the long-term vision (or, more formally, their prior belief) equal to zero. 

The result, then, is shockingly bad. the weak communication skills of the leader combined with the general noise of the business environment meant that, optimally, an employee should only give weight equal to 1/2 on her signal. But the strategic interaction of employees trying to coordinate with one another creates an "echo chamber" wherein employees place even less weight, only one-third, on their signals. As a consequence, the company suffers. 

Intuitively, since employees seek to coordinate with one another, their initial conservatism, placing weight one-half on the long-run vision, creates a focal point for coordinating actions. Thus, a best response when all other employees are placing between one-third and one-half weight on their signals is to place a bit less weight on one's own signal. This creates a kind of "race to the bottom" which only ends when everyone places one-third weight. In short, coordination produces conservatism in the firm. Put differently, by encouraging coordination amongst employees, any organization builds in a type of cultural conservatism that makes the organization resistant to change. This does not mean that coordination, or incentives for coordination are, per se, bad, only that the inertial incentives created thereby and not much appreciated--or even understood. 

Is this something real or merely the fanciful calculations of a game theorist? My own experience suggests that the little model captures something that is true of the world. While working as a research scientist at Yahoo, four CEOs came and went during my time there. Each had a markedly different vision. Yet the needs of coordination at Yahoo were such that, despite changes in CEO, new articulations of vision, and so on, the organization was surprisingly little affected. Employees, based on the need to work in harness with others, willfully discounted the new vision of an incoming CEO. The model seems to capture some, but certainly not all, of these forces. For instance, part of the reason for discounting, absent in the model, was that employees grew skeptical of the likely tenure of any CEO. 

For the record, if we let R denote the weight on matching vision and f the signal-noise statistic from above, the general formula is: 

w* = R f/(1 - (1 - R) f)

whereas the optimal weight is f. It may be easily verified that w* <  f. Also, from this equation, it is clear, and intuitive, that the problem is lessened the smaller the importance of coordinating with other employees (i.e. the larger is R) and the more articulate the leader (i.e. the larger is f).

Some academic housekeeping: The model described above is a version of one due to Morris and Shin, American Economic Review, 2003. They give a rather different interpretation to the model though. Moreover, their version of the model assumes that individuals have no prior beliefs. Under this (peculiar) assumption, the gap between the equilibrium weight on signals and the statistically optimal weight disappears, but this its absence is purely an artifact of their setup. The observations in this blog piece come from theory and experiments I'm currently writing about in a working paper with Don Dale at Muhlenberg College. 

Inspiring Words

Leadership is, to a great extent, the gentle art of persuasion. Leaders inspire others to follow them, to work for them, sometimes even to give up their own lives for them. How do they do it? Partially by example to be sure, but even here persuasion has a role to play. When we say that Jeff Bezos lives the leadership principles articulated and promulgated at Amazon, it makes the valid point that individuals credit others for how they behave, but conveniently ignores the fact that it was Bezos who articulated and promulgated the principles in the first place.

One of the most striking examples of leadership purely by the powers of persuasion was the rise of Barack Obama. Obama, for all his subsequent faults, was matchless in using words to inspire many thousands of young people who had never even voted previously to give him money, work for his organization, and persuade others to vote for him. Even more remarkably, he duplicated the feat again four years later, by most accounts, after spending much of that period by not leading by example. This no doubt overstates the power of his oratory for he had a remarkably savvy organization helping him to vacuum up all that money and effort, but others less gifted have had equally efficient teams, yet achieved nothing like Obama's success.

What can game theory tell us about the power of leaders to persuade? The answer, if we are to be entirely honest, is surprisingly little. A large part of the problem is that communication in the world of game theory is almost entirely informational, but persuasion, while it will certainly draw upon and convey some information, taps into something much deeper and less purely transactional than what one might learn from hearing the local weather forecast. This is not to say that information-centric communication, or persuasion, is uninteresting, rather that it somewhat misses the boat if we truly wish to understand why some individuals are hailed as visionaries while others, offering the same facts and conclusions, are not.

To get the flavor for the bloodless world of communications viewed through the lens of game theory, consider the following problem. A political leader wants to convince a supporter/follower to perform a certain action. The right action depends on something called a state variable, which you might think of as a shorthand description for a set of factors, political, economic, cultural, etc., that influence what a reasonable person would conclude is the correct action. To keep things simple, suppose that one state, which we will call low, represents a low political threat environment. Some action is needed to secure victory, but not too much. The other state, which we will call high threat, requires frenzied activity such as massive calling campaigns to get out the vote, and so on.

The follower wants to do the "right thing" for the leader, but knows little about political threats, and so on.
Knowing nothing about the state, our follower will elect some intermediate range of activity, imperfect for either state but somewhat helpful in both.

Now for the rub or, as we in the profession write, the "central tension of the model." The leader too wants the follower to do the right thing, but prefers that she do more political activity in either state. The degree of difference in views about how much activity to perform in each state represents the conflict between the two. Our leader's job, then, is to inspire his followers to do more than they otherwise would, but this will prove difficult since, in game theory land, the only trump card the leader holds is his knowledge of the state.

So, to inspire his supporters, our leader comes to town and makes a speech attempting to rally them to, in the leader's eyes, the right amount of activity. How does this speech go? What should our leader say? The answer, it turns out, depends on several factors, none of which feel (to me at least) very much like leadership.

Scenario #1: Free Speech
Suppose that our leader is free to say whatever he likes. He can lie about the state, exaggerating the political threat when it is, in fact, low or do the reverse, reassuring followers that there is little to worry about. Or something in between, saying that he's not sure. Or our leader can stonewall, give his standard stump speech, shake hands and kiss babies, Purell his hands and lips afterward, and go home.

So what does he do? To answer this question, we need to make certain assumptions about what, exactly, the followers know. Suppose they know that the leader indeed knows the state and, importantly, they also know that the leader wants them to do more of the activity in each state than they themselves prefer. In the happy scenario, the leader only wants the followers to do a little more in each state, so he informs them about the state truthfully and then harangues them "exceed themselves" or to "go beyond" or something like that. He gets his applause and leaves, satisfied at a good night's work.

Game theory, however, offers the exceptionally dreary conclusion that, no matter how powerful the words of inspiration, no matter that our leader is a Shakespeare or a Churchill, the followers do precisely what they had initially planned to do in each state. They are grateful for the information, but they can hardly be said to be inspired. Ironically, this situation is, in fact, the best our leader can hope for.

Let's rerun the speech but now imagine that the leader's vaunting ambitions create a vast gulf between his preferred activity level in each state and their own. So our leader steps up to the microphone to the hushed crowd and proceeds to speak of crisis--the threat level is high, the stakes are huge, and it's all up to you, the supporters to make the difference. This address, Shakespearean in its majestic, soaring phrases, send chills down the spines of the audience. The crowd roars. They will do it. They will rise to the challenge. They will be the difference-makers. No activity is too much. Our leader, drenched in sweat from the effort, steps down from the lectern and is congratulated for his remarkably moving address. The lights in the auditorium go down, and everyone goes home.

When his supporters get up the next morning, they do...exactly what they would have done if the leader had never shown up in the first place. In game theory land, people are cynics. While the audience may have been moved in the moment, on reflection they realize that the leader makes this same speech everywhere, to all his followers, whether the state is high or low. The talk, for all its pageantry, rings hollow--full of sound and fury, but signifying nothing. Why such an uncharitable view of the leader? The answer is that his own aspirations get in the way. Since he wants a high level of action regardless of the state, the speech lacks all credibility and, since those living in game theory land are not simpletons nor dupes, it is roundly and universally disbelieved.

As a logical analysis, the above is impeccable. As a description of leadership and persuasion, it seems to mis the boat completely. But, sadly, this analysis, or something similar, quite genuinely represents the state of the art, the research frontier, if you will. Is it fixable? Yes, in a way. We can add fools who believe everything the leader says into the mix. We can add some sort of inspiration variable that magically changes tastes so that followers work harder. But none of it really gets to the heart of what makes some leaders persuasive and others not. Indeed, we learn nothing if we simply assume that leader A can change minds and leader B cannot. The whole point of using our tools is to get at the deeper, and ultimately more interesting and important question as to why some leaders are persuasive.

Scenario #2: Factual Speech
Perhaps we've accorded too much freedom to our leader. After all, exagerrations, dissembling, misrepresenting, or any of the myriad of polite words we have for lying can get a politician into terrible trouble. Claiming that the world is hanging by a thread when, in fact, every poll shows that you're 20 points ahead, catches up to most leader's eventually. So let's return to our setting, precisely as before, but with the added restriction that our leader cannot simply make up things that are not true. In academic terms, this moves us out of the world of "cheap talk" and into the world of "persuasion" proper. This nomenclature, by the way, has a lot of problems. First, talk is no less cheap in the sense of being costless to the leader when we add the no lying restriction. Second, why the heck is it "persuasion" when we restrict someone from lying outright. Lies can be an important tool in the arsenal of a persuasive individual. Indeed, criminals engaging in confidence schemes are the ultimate persuaders, but would be entirely crippled were they bound by the no lying restriction. But I digress.

So let's rewind once again and send our leader back to the lectern, but with the following restriction--the heart of his speech can be either the truth or a stonewall, where he says nothing whatever about the state. One might imagine that this changes little. After all, when conflict was low, our leader did not wish to lie even when he could, so the restriction matters not a whit. When conflict was high, our leader wanted to lie about the state, but no one believed him anyway, so the effect is identical to stonewalling. Indeed, our leader in scenario #1 would have been quite happy to make the stonewalling speech instead of what I laid out.

In the case where conflict is low, the above supposition is exactly correct. Our leader steps to the lectern and offers a fact-laden speech truthfully revealing the state. But in the second case, this is wrong. Indeed, remarkably and perhaps absurdly, game theory offers the startling prediction that, no matter how bad the conflict between leader and follower, the leader always makes the truthful speech!

Why in blazes would our leader do that? Let's start with the situation where the threat is high. Here, the leader can do no better than to report the truth. He'd like more effort from his followers to be sure, but there is simply no way to motivate them to work any harder than by revealing the high state. What about the low state? Surely our leader will stonewall here? He might, but it will do no good since, knowing that the leader would have announced high were the state indeed high, our followers treat the stonewall speech as, in effect, a report that the state is low. And they act accordingly. That being the case, the leader might as well report honestly and at least gain the credit, however small, for being straight with followers.

Now, one may suspect that this logic takes too much advantage of the fact that there are exactly two states. What if there were three, or twenty, or a thousand. It turns out that none of it matters because of something called unravelling. Here's the argument: Suppose that there are twenty states in which the leader stonewalls while revealing in the rest. Then, in the highest of these 20 states, he'd be better off revealing than stonewalling since, by stonewalling, followers assume that the average state is lower than the highest state. Repeat this argument ad nauseum to obtain the truth-telling result. In my own work on the topic, I showed how this argument could be extended to virtually any configuration of preferences between leader and follower.

The problem is that the conclusion seems completely absurd. Irrespective of the conflict between leader and follower, the leader will always tell the truth sounds very much unlike the world in which I live. Again, this problem is fixable, but the main fix is even more bizarre than the result. It turns out that the key to credible stonewalling is...drumroll please...stupidity!! Or, more precisely the possibility of stupidity. The idea here is that, if the leader might possibly not know the state then stonewalling becomes believable. But this hardly seems like a satisfying resolution.

So Where Does This Leave Us?
This post, I'm afraid, is a downer. Game theory does lots of things well, but leadership, sadly, is not one of them. This has not stopped game theorists from trying, and perhaps making some headway. There is a clever paper by Dewan and Myatt looking at leadership through communications. In their model, one of the tradeoffs is between stupidity and incomprehensibility. They ask the following question (that only a game theorist would ask) about leaders: Is it better to be smart but incomprehensible or stupid but clear? The answer seems to be that it depends on the importance of doing the right thing versus doing the same thing. But, like all work in the field, the idea that leaders, with their words, could spark passion and devotion, is entirely missing.

Sometimes I despair about my love for game theory in a place devoted to, somehow, creating innovative leaders. I can, however, take some solace that we are no better at articulating how, exactly, that transformation takes place than we are in understanding leadership through game theory.