The effects of varying game payoffs and lattice dimensionality on Prisoner’s Dilemma games

Abstract

We systematically explore the outcomes in simulations of populations playing the Prisoner’s Dilemma. The agents are placed on a two dimensional toroidal lattice and each agent plays in a fixed neighbourhood participating in a two-player one shot Prisoner’s Dilemma with each neighbour. We show that by moving from a square lattice to a rectangular lattice with a reduced column height (or row width), different outcomes arise. We categorise the outcomes and explain the phenomena observed. We consider the possible payoffs obtainable by an agent given the different potential neighbourhoods. We calculate these possible payoffs for both cooperators and defectors. We then identify the complete set of possible non-equal payoffs relationships available and use this set to identify a set of simulations to undertake.