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,