Common Belief of Rationality in the Finitely Repeated Prisoners' Dilemma

Abstract

In the finitely repeated Prisoners' Dilemma, an intuitive argument suggests that if rationality is common belief, both players will “defect” in every period of the game. But in a strategic (normal) form analysis, a “defect-always” outcome requires an additional condition. This paper uses a precise formalism to state and prove the following result: if rationality is common belief, and if the players' beliefs are mutually absolutely continuous, then the players defect in every period. When beliefs are mutually absolutely continuous, it is common belief that each player assigns positive probability to the true state of the world.Journal of Economic LiteratureClassification Numbers: C72, D82.