Cooperation in spatial Prisoner's Dilemma with two types of players for increasing number of neighbors

TL;DR

This paper investigates how the presence of two player types and varying neighbor counts influence cooperation levels in a spatial Prisoner's Dilemma, revealing that inhomogeneous activity can promote cooperation.

Contribution

It introduces a model with two player types affecting strategy adoption probabilities and analyzes how increasing neighbors impacts cooperation, highlighting the role of influential players.

Findings

Inhomogeneous activity increases cooperation density depending on player influence.

Increasing neighbors can both promote and hinder cooperation based on parameters.

Phase diagrams show noise effects on cooperation dynamics.

Abstract

We study a spatial two-strategy (cooperation and defection) Prisoner's Dilemma game with two types ($A$ and $B$) of players located on the sites of a square lattice. The evolution of strategy distribution is governed by iterated strategy adoption from a randomly selected neighbor with a probability depending on the payoff difference and also on the type of the neighbor. The strategy adoption probability is reduced by a pre-factor ($w < 1$) from the players of type $B$. We consider the competition between two opposite effects when increasing the number of neighbors ($k=4$, 8, and 24). Within a range of the portion of influential players (type $A$) the inhomogeneous activity in strategy transfer yields a relevant increase (dependent on $w$) in the density of cooperators. The noise-dependence of this phenomenon is also discussed by evaluating phase diagrams.