An Altruism Parameter for Prisoner's Dilemma

Abstract

This paper is an attempt to relate the player's behavior in a PD game to a loosely defined psychological attitude of altruism. The game matrix is transformed into a zero-sum game matrix that for each player reflects the strategic elements of the original game as modified by the degree of altruism he may feel toward his opponent. The transformation consists of adding to a player's payoffs those of his opponent multiplied by a factor designated as the player's "altruism parameter." Three sets of assumptions are considered in order to make predictions about the play of the game to differing degrees of detail. The results of the analysis include qualitative and quantitative measures of conflict inherent in a PD game, estimates of the distribution of the altruism parameter among players, and qualitative predictions concerning the dynamics of play when interactive changes of altruism occur. These results are shown to be broadly consistent with the experimental findings of Rapoport and Chammah.