Prisoner’s Dilemma in Graphs with Heterogeneous Agents

Abstract

Prisoner's dilemma (PD) game has been used as a prototypical model for studying social choice situations with self-interested agents. Although in a single shot PD game, both players playing defect is a Nash equilibrium, in social settings, cooperation among self-interested agents is usually observed. This phenomenon of emergence of cooperation can be captured by repeated PD games in graphs consisting of agents of same type. In this paper, motivated by modeling of conflict scenarios in societies with multiple ethno-religious groups, we study repeated PD games in graph with multiple types of agents. In our model with two types of agents, agents play PD game with neighbors of the other type and their strategy update neighborhood can consist of either (a) neighbors of their own type or (b) neighbors of both type. We show by simulation that in both cases the fraction of players playing defect in the final solution is much more than the conventional case where no distinction exists between game playing and strategy update neighbors (i.e., the agents are of the same type). We also present a theoretical analysis of the strategy evolution dynamics, and design algorithms to compute all fixed points of the evolution dynamics.