Decision-theoretic finitely iterated prisoner's dilemmas
Abstract
Decision-theoretic ï¬nitely iterated prisonerâs dilemmas John W. Carroll 1. Introduction There is a well-known puzzle involving ï¬nitely iterated prisonerâs dilemmas (FIPDs). It is the result of the conï¬ict between a pre-theoretic intuition that players faced with a ï¬nite sequence of prisonerâs dilemmas might cooperate at least once and the game-theoretic contention that both players will defect in all the rounds, a contention that is backed by a seemingly valid backward induction argument (BIA). The proper approach to solving this puzzle begins by examining sets of assumptions that characterize FIPDs to identify the ones that really do entail mutual defection throughout (MDT). Once this ï¬rst step is accomplished, the second step is to assess these sets. They can be assessed in various ways. For example, we could see what remains of the puzzle: if the only sets that entail the MDT conclusion are very strong (especially in certain unexpected ways), their strength could undermine the pre-theoretic intuition that a player might cooperate. For another example, we might see whether the sets that do entail MDT have any applicability, determining whether any real-life situations could be modelled by these sets. Though the second stage of this two-step approach is interesting