BAYESIAN BOUNDEDLY RATIONAL AGENTS PLAY THE FINITELY REPEATED PRISONERS-DILEMMA

In this paper a model of boundedly rational decision making in the Fin itely Repeated Prisoner's Dilemma is proposed in which: (1) each playe r is Bayesian-rational; (2) this is common knowledge; (3) players are constrained by limited state spaces (their Bayesian minds) in 'process ing' (1) and (2). Under these circumstances, we show that cooperative behavior may arise as an individually optimal response, except for the latter part of the game. Indeed, such behavior will necessarily obtai n in long enough games if belief systems satisfy a natural condition: essentially, that all events consistent with the players' analysis of the game be attributed by them positive (although arbitrarily small) s ubjective probability.