Iterated Prisoner's Dilemma among mobile agents performing 2D random walk

Abstract

When Iterated Prisoner's Dilemma takes place on a two-dimensional plane among mobile agents, the course of the game slightly differs from that one in a well-mixed population. In this paper we present a detailed derivation of the expected number of encounters required for Tit-for-tat strategy to get even with Always-Defect strategy in a Brownian-like population. It will be shown that in such an environment Tit-for-Tat can perform better than in a well-mixed population.

Keywords

• game theory
• payoff
• prisoner's dilemma
• random walk
• tit-for-tat