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.