Category: Bargaining

Adverse Selection and Cheap Talk in Pokémon: Let’s Go

Suppose you are a pokémon trainer, and a fellow trainer approaches you with the following proposition:

In any real life scenario, this should be a hard pass. But the situation provides a teachable moment on two fronts to justify that claim.

Adverse Selection
Suppose someone tells you they want to engage in a trade. What does that willingness tell you about whether you should do it?

In many contexts, it tells you a lot. Imagine the Exeggutor was the strongest one could possibly imagine. Would the person want to exchange it for another Exeggutor? Absolutely not—no matter the strength of the other Exeggutor the person could receive in return, it would be worse than what he currently has. So a strongest possible Exeggutor would never be offered up in a trade.

Iterating this logic has an interesting implication. Consider the incentives of someone who has the second-strongest possible Exeggutor. Would that person want to exchange it? The only way this could be worth the time is if the other trainer has the strongest possible Exeggutor. But we just discovered that another trainer would not offer such an Exeggutor. So the person with the second-strongest should have no interest in trading either.

What about the third? Well, the only way this would be good is if a strongest or second-strongest Exeggutor were available. But they won’t be. So someone who owns the third-strongest should not engage in a trade either.

That logic unravels all the way down. Even a trainer with a very, very weak Exeggutor should have no interest in a trade. Although it is true that the average Exeggutor is much stronger than the one the trainer currently has, the average Exeggutor being offered for trade is not. In fact, trainers would only want to engage in a trade if the Exeggutor is the worst possible.

This result is well-known in game theory as a product of adverse selection—a situation where one party has private information about the value of a transaction. More specifically, it is an application of the market for lemons, which uses the same mechanism to explain why it is so difficult to buy a quality used car.

Cheap Talk
“But wait!” one might say. “The fellow trainer has assured me that he is very proud of his Exeggutor. It must be not so bad after all.”

Not quite. This is classic cheap talk. The message the other trainer is communicating could just as easily be conveyed by a trainer who actually thinks that his Exeggutor is terrible. Moreover, he does not have a common interest with you in communicating truthful information. Combining these pieces of information together, you should ignore the message altogether.

To make this more concrete, imagine that you were to take whatever the trainer said at his word. Then would a trainer with a truly terrible Exeggutor want to lie? If doing so would convince you to make the trade, then the answer is yes. As a result, you cannot differentiate between an honest assessment and a fib. In turn, the message should not change your beliefs about the Exeggutor’s quality at all.

Nintendo and Strategic Theory
All that said, this is Nintendo we are talking about. They are not interested in teaching you interdependent strategic thinking. The man actually has an exotic Exeggutor from a region you cannot access in the game. The only way to acquire such an Exeggutor is through a trade. You therefore most definitely should make the deal with him.

But this leads to a deeper question: why doesn’t the trainer just lead with that point in the first place? Rather than speaking to your common interest—he has an Exeggutor from his region and wants one from your region, you have an Exeggutor from your region and want one from his—he just speaks strategic nonsense.

Here’s hoping that George Akerlof appears in Pokemon: Sword and Shield offering the same trade. But this time, when you accept, you get a level 1 Exeggutor with all the minimum stats.

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Bargaining Theory in Action: Donald Trump and Executive Orders

Over the past seven days, you have either grown to love or hate executive orders. But regardless of your political perspective, Trump’s actions are showcasing one of the major findings of bargaining theory: namely, that proposal power is one of the greatest sources of bargaining power.

What Is Proposal Power?
Put simply, proposal power is the ability to structure the terms of a possible settlement. It is distinct from receivership, which is the ability to say yes or no to any particular offer.

Perhaps surprisingly, whether you can make an offer has an enormous impact on your welfare. Imagine a seller needs at least $30 to sell and a buyer will buy for no more than $50. Clearly, a transaction should take place, as there is a $20 surplus (the buyer’s maximum minus the seller’s minimum).

If the seller can make a take-it-or-leave-it offer, then he can set the price at $50. The buyer, only having the ability to accept or reject, buys the good—it is just enough to convince him to buy.

Now imagine the buyer makes the take-it-or-leave-it offer. She can set the price at $30. The seller, only having the ability to accept or reject, sells the good—it is just enough to make her willing to part with it.

Who proposes the offer makes a major difference. If we endow the seller with the proposal power, she walks away with the entire $20 surplus. Yet if we endow the buyer with the proposal power, the exact opposite happens: the buyer receives the entire $20 surplus. It’s night and day!

You might think this is because of the take-it-or-leave-it bargaining protocol. It is not. If rejecting simply leads to another round of bargaining where the proposer stays the same, the result is identical: the proposer receives the entire surplus.

The lesson here is simple: without the ability to make offers or counteroffers, the deals reached will look very bad for you.

When it comes to executive orders, the POTUS’s proposal power is YUGE.

Proposal Power in Action
In many contexts, proposal power is easy to acquire. At a flea market or car dealership, for instance, nothing stops a buyer or seller from making the initial offer or responding with a counteroffer of their own. They just do it.

Government is different. Some systems have proposal structures baked into the legal system. And this has major consequences for the types of laws that are ultimately implemented.

In the United States, most of the proposal power rests with Congress. That is because only Congress can write laws; the President can merely sign or veto whatever lands on his desk. Thus, if Congress and the President both agree that a law needs fixing, the solution implemented is going to be much closer to what Congress wants than what the President wants.

There is a key exception to that rule, however, and it is what we have been seeing over the last week. Executive orders essentially flip the script—the President institutes the policy, and it is up to Congress to accept it (by doing nothing) or reject it (by creating a bill that undoes the policy, and then overriding the inevitable presidential veto).

It should be obvious that the President choosing his own policies would result in outcomes closer to his ideological preference. I suspect liberals realized this was an issue weeks ago, but only recently realized how bad it would be for them. Bargaining theory goes deeper here and explains this. It isn’t just that the President fares better when choosing the policy than when he signs a Congressional law. It is saying that a strategic, forward-thinking President can set the policy so far to his liking that Congress is just barely willing to go along with it. And if the gulf between Congressional preferences and Presidential preferences is substantial, so too will be the types of policy outcomes associated with executive orders and standard legislation.

This logic sets expectations for what is to come for both fans and foes of Trump. Foes should continue to fear executive orders and should not be particularly worried about laws passed through Congress. Liberals see Paul Ryan as their last remaining hope. And they might find solace there—but only for standard laws. Undoing executive orders requires having a much larger share of Congress on board, so Paul Ryan does not get you very far.

For Trump supporters, it is the opposite: they will find standard laws relatively unexciting but be thrilled with the executive orders.

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Strategic Bargaining Blunders in The Empire Strikes Back

After rewatching The Empire Strikes Back over the weekend, it became clear that two major blunders ultimately doom the Empire. (Original trilogy spoilers below, obviously.)

Boba Fett’s Terrible Contract
After leaving the asteroid field, the Millennium Falcon’s hyperdrive fails (again). As a Star Destroyer prepares to blow it up, Han Solo turns around the Falcon and attaches it to the Destroyer.

The plan works. Imperial troops have no idea what happened to the Falcon and assume it jumped to hyperspace. Han, meanwhile, plans to sit there until the Destroyer empties its garbage and then drift away while camouflaged in the trash.

Darth Vader, apparently well-versed in comparative advantage, had commissioned bounty hunter Boba Fett (among others) to track down the Falcon.

Contract theory tells us that the reward for finding the Falcon needs to be substantial, going above and beyond basic expenses—otherwise, a bounty hunter would not have incentive to exert maximal effort in a risky and uncertain process. Furthermore, because the Empire cannot observe the effort a bounty hunter exerts, it needs to offer that large amount regardless of the actions leading up to capture.

Resolving this moral hazard problem created a second problem, however, and it was a problem Vader did not fix. If Boba Fett knew exactly what the Falcon was up to, he had incentive to conceal that information. He could wait for the Falcon to do its thing, catch it, and then claim the substantial reward designed to induce high effort despite only exerting very low effort.

And that’s exactly what happened—Boba hid in the garbage along with the Falcon, followed it through hyperspace, and immediately contacted the Empire upon arrival in Cloud City.

Vader could have solved that problem by paying the high amount even if a bounty hunter gave away the information immediately. But he didn’t. (Or a credible commitment problem stopped him, though apparently the bounty hunters are not particularly worried about this.)

So instead of capturing the Falcon on the Empire’s terms and setting up a confrontation with Luke on a Star Destroyer, they end up in Cloud City. This led to the next blunder…

Vader Miscalculates Lando’s Reservation Value
After landing in Cloud City, Vader and Lando Calrissian engage in crisis bargaining, a subject international relations scholars have explored at length. A mutually beneficial agreement certainly existed—rejection would have led to costly conflict, and we have a nice theorem that says a there is range of settlements that are mutually preferable to war under these conditions.

The existence of settlements does not guarantee peace, though. If one side faces uncertainty—perhaps Vader does not know how resolved Lando is—then it may demand more than the opponent is willing to give up. Conflict results.

Something like that appears to have happened in Cloud City. Vader’s initial offer was generous, demanding Han and giving Lando autonomy otherwise. But Vader kept demanding more—including Chewbacca and Leia—causing Lando to eventually begin a fight.

This proved fatal to the Empire. Lando freed Leia. Freeing Leia allowed them to recover Luke. Luke ultimately turned Vader, and Vader killed the Emperor. Meanwhile, Lando led the mission to destroy the second Death Star. All because Vader kept demanding more.

One perspective on this is that Lando’s initial concessions caused Vader to believe that he could profitably extract more. If so, Vader made a clear error: research on this subject shows that you should not increase your demands after an initial acceptance.

In short, this is because your first offer—if it was truly optimal in the first place—maximizes your payoff conditional on acceptance. So if you try to extract more, the potential gains must not be worth the additional risk you face.

The Jedi are supposed to be master negotiators. I can only conclude that Anakin slept through his bargaining classes as a padawan.

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Strategic Thinking on The Newsroom

On Season 1, Episode 9 of The Newsroom, Will McAvoy pitches a new structure for a potential Republican primary debate hosted by cable news channel ACN. Rather than asking questions and letting candidates speak freely, Will wants the ability to interrupt any time a candidate goes off topic or drifts away from the question. Predictably, the Republican National Committee hates the idea and doesn’t give the network a debate.

Maggie’s recap of the day’s events clearly show where the crew went wrong:

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It was exactly as crazy as it sounded. Maggie is applying non-strategic thinking to a situation where there is clear strategic interdependence. Each network can choose what to offer the RNC, and the RNC can pick the terms most favorable to it. This gives each network an incentive to undercut the other until no one is willing to undercut any further. Standard bargaining theory tells us that basically all of the surplus will go to the RNC under these conditions.

But there is another facet of the interaction here that extends past basic bargaining theory. In standard price negotiations, if I don’t ultimately buy the good, I don’t care at all what you paid. That is not the case here. The lower the “price” a network is willing to offer, the more all the non-winners suffer—i.e., if CNN captured the debate by conceding the farm, journalists at CBS News, NBC News, and ACN are all worse off than had CNN captured the debate without compromising its integrity. So what we have here is essentially a collective action problem, which is just a prisoner’s dilemma with more than two players. Everyone is worse off in equilibrium than had all players agreed to cooperate, but individual incentives mandate that all parties defect.

There is some irony here. Earlier, the news team reduced Sloan Sabbath’s airtime to run stories on the Casey Anthony trial. They needed to do this to improve ratings to make them an attractive host for the debate. But Sloan Sabbath has an economics PhD from Duke and is generally frustrated that no one around her understands basic economics and aren’t really willing to spend any time to learn. The one person who could have saved them from the situation was ignored! (Or maybe she never spoke up as a perverse way of getting her revenge…)

TL;DR: McAvoy et al do not know how the prisoner’s dilemma works.

Bargaining and Supreme Court Nominations

With the death of Justice Antonin Scalia over the weekend, the scramble has begun to make sense of the nomination process. Senate Republicans are (predictably) arguing that the seat should remain unfilled until after the 2017 election, presumably so a Republican president could potentially select the nominee. Senate Democrats and President Obama (predictably) feel differently.

Overall, it seems that people doubt that Obama will resolve the problem. But most of the arguments for why this will happen fail to understand basic bargaining theory. That’s what this post is about. In sum, nominees exist that would make both parties better off than if they fail to fill the vacancy. Any legitimate argument for why the seat will remain unfilled until 2017 must address this inefficiency puzzle.

You can watch the video above for a more through explanation, but the basic argument is as follows. The Supreme Court has some sort of status quo ideological positioning. This factors who the current median justice is, the average median of lower court justices (which matters because lower courts break any 4-4 splits from the Supreme Court), and (most importantly) expected future medians. That is, one could think about the relative likelihoods of each presidential candidate winning an election and the type of nominee that president would select and project it into this “status quo” ideology.

Confirmation of a new justice under Obama would change that ideological position. In particular, Obama’s goal is to shift the court to the left. Republicans want to minimize the shift as much as possible.

Nevertheless, failing to fill the position is costly and inefficient for the court. In other words, ideology aside, leaving the seat unfilled hurts everyone. These costs come from overworking the existing justices, wasting everyone’s time debating these issues incessantly, and generally making the federal government look bad. Due to these costs, each side is better off slightly altering the ideological position of the court in a disadvantageous way to avert the costs.

Visually, you can think of it like this:

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(If that isn’t clear, I draw it step-by-step in the video.)

Thus, any nominee to the right of the Republicans’ reservation point and to the left of the Democrats’ reservation value is mutually preferable to leaving the seat unfilled.

This simple theoretical model helps make sense of the debate immediately following Scalia’s death. Senate Majority Leader Mitch McConnell says “The American people should have a voice in the selection of their next Supreme Court justice. Therefore, this vacancy should not be filled until we have a new president.” But what he’s really saying is “Our costs of bargaining breakdown are low, so you’d better nominate someone who is really moderate, otherwise we aren’t going to confirm him.”

And when Senator Elizabeth Warren says…

…what she really means is “Mitch, your costs are high, so you are actually going to confirm whomever we want.”

To be clear, the existence of mutually preferable justices does not guarantee that the parties will resolve their differences. But it does separate good explanations for bargaining breakdown from bad ones. And unfortunately, the media almost exclusively give us bad ones, essentially saying that they will not reach a compromise because compromise is not possible. Yet we know from the above that this intuition is misguided.

So what may cause the bargaining failure? One problem might be that Obama overestimates how costly the Republicans view bargaining breakdown. If Obama believed the Republicans thought it was really costly, he’d be tempted to nominate someone very liberal. But if the Republicans actually had low costs, such a nominee would be unacceptable, and we’d see a rejection. (This is an asymmetric information problem.)

A more subtle issue is that presidents have a better idea of a nominee’s true ideology than senators do. Maya Sen and I explored this issue in a recent paper. Basically, such uncertainty creates a commitment problem, where the Senate sometimes rejects apparently qualified nominees so as to discourage the president from nominating extremists. Unfortunately, this problem gets worse as the Senate and president become more ideologically opposed, and polarization is at an all-time high.

In any case, I think the nomination process highlights the omnipresence of bargaining theory. Knowing the very basics—even just a semester’s worth of topics—helps you identify arguments that do not make coherent sense. And you will be hearing a lot of such arguments in the coming months regarding Scalia’s replacement.

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