Trading Payoffs to Enlarged Neighborhoods? A New Evidence from Evolutionary Game Theory

TL;DR

This paper investigates how paying for neighborhood upgrades influences cooperation in spatial evolutionary Prisoner's Dilemma, revealing that optimal costs and neighborhood sizes can promote cooperation and cluster formation.

Contribution

It introduces a framework where players can pay to upgrade neighborhoods, highlighting the role of upgrade costs in cooperation dynamics and cluster formation.

Findings

Reasonable upgrade costs support cooperation in high dilemma environments.

Larger neighborhoods promote cooperation if accessible to all players.

High upgrade costs can lead to encirclement of defectors, hindering cooperation.

Abstract

Population diversity is an important aspect of Prisoner's Dilemma Game (PDG) research. However, the studies on dynamic diversity and its associated cost still need further investigation. Based on a framework comprising 2-dimensional spatial evolutionary PDG, this work examines the change in a player's neighborhood by enabling each player to pay for an upgrade of their neighborhood to switch from the von Neumann to Moore neighborhood. The upgrade cost (i.e., the cost of the advanced neighborhood) plays a vital role in cooperation promotion and serves as an entry-level to screen players. The results show that a reasonable price (entry-level) supports the cooperators' survival in an environment with high dilemma strength since it allows the formation of "normal-edge-advantage-core" clusters. On the low entry-level side, the privilege of having a larger neighborhood supports cooperation if it is accessible to all the players. On the high entry-level side, encirclements of advantage defectors appear out of the cooperative clusters. To break the encirclement and enable the expansion of the advantage clusters, the entry-level should be increased to interrupt the advantage defectors. The encirclement can be observed only in the deterministic models. Stochastic simulations are provided as robustness benchmarks.