Correlation and Cooperation
In our spring school devoted to Arrow’s economics, Menahem Yaari gave a talk entitled “correlation and cooperation.” It was about games as a model of people’s behavior, and Yaari made the following points:
It is an empirical fact that people (players in a game) act in a correlated way,
It is unscientific not to take this into account (although this is not taken into account in game theory and economics).
The prisoner’s dilemma
A basic example in game theory (which also played a central part in Yaari’s lecture) is the Prisoner’s dilemma. Let’s talk about this example a little, before getting to Yaari’s claims. Here is Wikipedia’s description of the dilemma:
“Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (“defects”) for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act? “
And here is a more “personal” description from Stanford’s online Encyclopedia of Philosophy.
“Tanya and Cinque have been arrested for robbing the Hibernia Savings Bank and placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each. ‘You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I’ll see to it that you both get early parole. If you both remain silent, I’ll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning.’ “
The matrix of payoffs is described by the following nice picture.
Millions of words have been spoken and written on the prisoner’s dilemma. One thing that I was always curious about is this: Why, when we hear about it, do we tend to sympathize with the prisoners? Don’t we want them to serve a long time in prison for the crimes they committed?
One explanation is that when we are faced with the story we automatically identified with the prisoners, the heroes of the story. Another explanation is that we automatically tend to favour cooperation, and regard cooperation as morally superior. Or is it that we tend to favour efficiency and we dislike the non efficient equilibrium point. Still I regard our sympathy with the prisoners as a little puzzle.
The sympathy for the prisoners in the prisoner’s dilemma is almost as strange as the sympathy created for Tommy deVitto, the character played by Joe Pesci in “Goodfellas,” and for the famous Clyde Barrow and Bonnie Parker.
Do we like the character played by Joe Pesci (left) from Goodfellas because he is a good son, and even uses his mother’s kitchen knife for his work?
And arn’t they lovable? (Clyde and Bonnie)
Let’s move now to the claim made by Menachem Yaari. He argues that, empirically, it is the case that players’ behavior in games like the prisoner’s dilemma is positively correlated. This claim assumes that we can a priori associate the strategies of one player with those of another player. But this is often the case. In various cases the strategies of all players can be described as: “compromise”, “going to war.” In such cases the claim about players’ actions being positively correlated is meaningful.
In his talk Yaari discusses this claim, various difficulties and various connections with all sorts of cool stuff (“free will”, Newcomb paradox, etc.). He then tries to analyze theoretic game solutions (basically Nash equilibrium), based on the positive correlation hypothesis.
Yaari’s claims and line of research are interesting, although it is not clear where they can go.