Manual Nash Equilibria and Power Plays in Happy Wars

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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.

Game Theory | SpringerLink

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. 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. 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.

4.1 Social interactions: Game theory

It was exactly as crazy as it sounded. Maggie is applying non-strategic thinking to a situation where there is clear strategic interdependence. 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.

That is not the case here. 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. They needed to do this to improve ratings to make them an attractive host for the debate. 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….

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 election, presumably so a Republican president could potentially select the nominee.

Ronald Peeters

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. 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 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 splits from the Supreme Court , and most importantly expected future medians.

Confirmation of a new justice under Obama would change that ideological position. 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. 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. Therefore, this vacancy should not be filled until we have a new president.

Abandoning their Senate duties would also prove that all the Republican talk about loving the Constitution is just that — empty talk. 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. This is an asymmetric information problem.


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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.


  • Seasons of Pain.
  • A Game of Peace;
  • Berlin Blues; and other stories.
  • 4.2 Equilibrium in the invisible hand game.
  • Existence of Nash equilibria.

If not, the basic idea is that two ice cream vendors are on a beach that stretches the interval. Customers are uniformly distributed along that interval. The vendors simultaneously select a position. Customers go to the closest vendor and split themselves evenly if the vendors choose an identical position. Each vendors want to maximize its number of customers. You can reframe the question as two candidates placing themselves along an ideological spectrum, with citizens voting for whichever one is closest. The Nash equilibrium is for both vendors to select the median location.

Full details here:. But what happens when there are more than two players? Someone posed me that question earlier today. It turns out, the solution for this game is complicated when there are an odd number of players. But fairly simple pure strategy Nash equilibria exist for an even number of players:.

18. Imperfect information: information sets and sub-game perfection

This is the median voter theorem. No one occupies the median! The median is back!