Inductive Reasoning in Repeated Games

Abstract

It is generally agreed that rational players in a one-off Prisoner’s Dilemma will defect. It is true that both players would do better if they both cooperated; but each is still acting rationally when he or she defects. Most decision theorists have no trouble in accepting this conclusion; and I shall not be challenging it. But what if two rational individuals play a finite sequence of n Prisoner’s Dilemmas? There is a well-known argument of backward induction or backward recursion which leads to the conclusion that rational players will defect in every round — no matter how large n may be. This argument was presented by Duncan Luce and Howard Raiffa (1957, pp.97–102) over thirty years ago. Ever since then, the formal validity of this conclusion has been widely accepted. John Harsanyi and Reinhard Selten (1988, p.345), for example, say that they regard ‘backward-induction rationality’ as ‘an essential aspect of game-theoretic rationality when dealing with sequential games’.