John Nash, made famous in the book and movie, A Beautiful Mind, extended a concept first developed by Augustin Cournot in his study of oligopoly, to apply to all non-cooperative games. Here non-cooperative means the players make their choices without consultation with the other players. There is no bargaining ahead of time, before the play of the game. Conveniently, the acronym NE can stand for Nash Equilibrium or for Non-Cooperative Equilibrium. It is characterized by mutual best response.
When I teach this to idea to my students, I say that each player makes a guess as to what the other player will do. Economists like fancy words, so instead of guess economists call it an expectation. Based on their expectations, each player then chooses the best possible play. Sometimes this is referred to as a best response, as if the other player has moved first, so the other player's move has become known. That interpretation is sometimes misleading, though the jargon persists. Many games we consider in economics are simultaneous move. Neither player goes first. The expectation then serves the role in decision making about the move that observing what the other player did would have served if the game were sequential rather than simultaneous.
In a Nash equilibrium, expectations are self-fulfilling. What the player expects the other player to do is what the other player chooses to do and vice versa. It is a lovely concept that works well in predicting outcomes in simple non-cooperative games.
Some games, however, are more complex. They have elements of private information. For example, in the popular poker game hold 'em, each player has a couple of down cards, and then there are some common cards dealt up. The down cards are private information, known only to that player. The up cards are public information. As the up cards are revealed sequentially, and there is betting after each round, the game illustrates an interesting sequential character as well.
The Nash Equilibrium concept has been refined in many different ways, because complex games of this sort have many different Nash Equilibria and not all of them are equally plausible. One refinement, the one I will focus on here, is called Subgame Perfection. It conveys the notion of "credible threats" versus incredible threats. An equilibrium based on an incredible threat is not plausible. A sequential game that is played in two stages, where the second stage is a game in itself, which is why it is called a subgame, should be solved by finding the equilibrium of the subgame first. That's what players should predict will happen in the subgame. So that play is credible. Out of equilibrium play is incredible. Then, in possession of equilibrium beliefs about play in the subgame, one determines the equilibrium in the first stage. The result is a subgame perfect equilibrium. It illustrate hyper rationality and strategic insight.
With the game theory lesson over, let me try to apply it to Frank Bruni's column from today, Trump's Leaky Fate. It is an interesting piece about those in the West Wing who are leaking information to the press. They are characterized as good and conscientious people, who have contempt for their President based on their interactions with him (as well as the tweets and what they get from his appearances on TV) and who are looking to serve the greater good by getting the information out in the open. Let's take that as accurate, though I'm not sure how Bruni knows this. But I want to note that what I say next is applicable even if these people are quite bitter and are acting more out of a sense of betrayal than as a public service.
Here's the question that nobody seems to be asking, but they should. Would a person willingly join an administration when believing there would be a reasonable likelihood that the person would become a leaker because the administration had failed badly and the President had lied repeatedly to the American people? Would a passenger have gotten onto the Titanic if there was some knowledge ahead of time that it might hit that iceberg? Would John Dean have become a member of Nixon's White House team if he had a reasonable expectation of the Watergate break in?
In the case of John Dean, where he joined Nixon's team during the 1968 campaign, it is believable that at that time he had no inclination of how things would play out and that for a few years thereafter he remained entirely trusting of Nixon. His views must have transformed in late 1971 or 1972.
With those leakers in Trump's White House, however, is it plausible to believe a rational actor would not harbor any suspicions about Trump at the time he took office? Or is the only way for it to be possible to not harbor suspicions is to willfully suspend belief? We are only four months into Trump's term as President. The leaks seem to have been present from the outset. And there was quite a lot of evidence about Trump before he took office. What gives?
Let me pose a couple of other questions. One is how many people are leaking? People do make mistakes in their personal forecasts. If it is only one or two people doing the bulk of the leaking, maybe they made a forecast error, erroneously trusting Trump when they shouldn't have done that. If it is a couple of dozen people or more than that, however, forecast error is less plausible, particularly if the forecasts were made independently. The other question is this. Were the leakers on the Trump team during the campaign? If members of the campaign team had contempt for the candidate then, why stay on the team?
There are puzzles here that must be solved to make this story consistent with a game theoretic explanation. Blind ambition offers a more plausible story. Rational players, which is what game theory posits, are not blind in this way.
In his column today Tom Friedman, focusing on Republicans in Congress, says they will not challenge the President.
Virtually all the good men and women in this party’s leadership have been purged or silenced; those who are left have either been bought off by lobbies or have cynically decided to take a ride on Trump’s Good Ship Lollipop to exploit it for any number of different agendas.
As lamentable as this may be, it offers no puzzle from a game theory perspective. This is rational play however unsavory. The leakers, however, don't appear to be rational. They pose a puzzle for us. I wonder if we'll be able to understand their motives before too long.