Behavioral Game Theory

One of the more famous and intriguing results of game theory is that cooperation can be sustained in a repeated prisoners dilemma as long as nobody knows when the last game will be played. To set out the basic issue consider the following game between Bob and Francesca. If they both cooperate they get a nice payoff of 10 each. If they both defect they get 0 each. Clearly mutual cooperation is better than mutual defection. But, look at individual incentives. If Francesca cooperates then Bob does best to defect and get 15 rather than 10. If Francesca defects then Bob does best to defect and get 0 rather than -5. Bob has a dominant strategy to choose defect. So does Francesca. We are likely to end up with mutual defection. But what if Bob and Francesca are going to play the game repeatedly with each other? Intuitively there is now an incentive to cooperate in one play of the game in order to encourage cooperation in subsequent plays of the game. To formalize that logic suppose that