Spatial evolutionary prisoner's dilemma game with three strategies and external constraints

TL;DR

This study explores how external constraints and multiple strategies influence cooperation in spatial evolutionary prisoner's dilemma games across different dimensions, revealing complex phase transitions and the limited effectiveness of enforced cooperation.

Contribution

It introduces a model with three strategies and external cooperation constraints, analyzing phase transitions and critical behavior in spatial evolutionary games.

Findings

External constraints do not always promote cooperation effectively.

Second order phase transitions occur with strategies' extinction.

Critical exponents belong to the directed percolation universality class.

Abstract

The emergence of mutual cooperation is studied in a spatially extended evolutionary prisoner's dilemma game in which the players are located on the sites of cubic lattices for dimensions d=1, 2, and 3. Each player can choose one of the three strategies: cooperation (C), defection (D) or Tit for Tat (T). During the evolutionary process the randomly chosen players adopt one of their neighboring strategies if the chosen neighbor has higher payoff. Morover, an external constraint imposes that the players always cooperate with probability p. The stationary state phase diagram are computed by both using generalized mean-field approximations and Monte Carlo simulations. Nonequilibrium second order phase transitions assosiated with the extinction of one of the possible strategies are found and the corresponding critical exponents belong to the directed percolation universality class. It is shown that forcing externally the collaboration does not always produce the desired result.