On the Role of External Constraints in a Spatially Extended Evolutionary Prisoner's Dilemma Game

TL;DR

This paper investigates how external constraints influence the emergence of cooperation in a spatial evolutionary prisoner's dilemma game on a lattice, using simulations and mean-field approximations.

Contribution

It introduces two types of external constraints in a spatial evolutionary game and analyzes their effects on cooperation using both theoretical and simulation methods.

Findings

External constraints can promote cooperation under certain conditions.

The probability of strategy replacement affects the stability of cooperative strategies.

Different external constraints lead to distinct stationary strategy distributions.

Abstract

We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T), and their total payoffs come from games with the nearest neighbors. During the random sequential updates the players adopt one of their neighboring strategies if the chosen neighbor has higher payoff. We compare the effect of two types of external constraints added to the Darwinian evolutionary processes. In both cases the strategy of a randomly chosen player is replaced with probability P by another strategy. In the first case, the strategy is replaced by a randomly chosen one among the two others, while in the second case the new strategy is always C. Using generalized mean-field approximations and Monte Carlo simulations the strategy concentrations are evaluated in the stationary state for different strength of external constraints characterized by the probability P.