Selection of dynamical rules in spatial Prisoner's Dilemma games

TL;DR

This paper investigates a co-evolutionary model of spatial Prisoner's Dilemma where players adapt both strategies and imitation rules, leading to a dominant rule that maximizes cooperation influenced by network topology.

Contribution

It introduces a co-evolutionary framework allowing simultaneous adaptation of strategies and imitation rules in spatial Prisoner's Dilemma games, highlighting the emergence of an optimal rule for cooperation.

Findings

The system evolves towards a single dominant imitation rule.

The final rule correlates with the highest cooperation levels.

Topology influences which rule becomes dominant.

Abstract

We study co-evolutionary Prisoner's Dilemma games where each player can imitate both the strategy and imitation rule from a randomly chosen neighbor with a probability dependent on the payoff difference when the player's income is collected from games with the neighbors. The players, located on the sites of a two-dimensional lattice, follow unconditional cooperation or defection and use individual strategy adoption rule described by a parameter. If the system is started from a random initial state then the present co-evolutionary rule drives the system towards a state where only one evolutionary rule remains alive even in the coexistence of cooperative and defective behaviors. The final rule is related to the optimum providing the highest level of cooperation and affected by the topology of the connectivity structure.