Reciprocity and Shared Knowledge Structures in the Prisoner's Dilemma Game

Abstract

A prominent solution to achieving cooperation in prisoner's dilemma situations is repeated interaction between players. Although indefinitely repeated play solves the mutual gains problem, it also creates an unsolved coordination problem because an infinite number of strategies are possible in equilibrium. This article explores whether a “shared grammar of strategies,” formalized by a knowledge-induced equilibrium, resolves the coordination problem by prescribing a unique behavioral rule. Applied to the set of strategies submitted to Axelrod's prisoner's dilemma tournament, tit for tat emerges as that unique coordinating strategy.