# Evolutionary prisoner's dilemma games coevolving on adaptive networks

## TL;DR

This paper models the coevolution of strategies and network structure in Prisoner's Dilemma games, demonstrating the effectiveness of approximate master equations in predicting system behavior and exploring different partner-switching dynamics.

## Contribution

It introduces an approximate master equation framework for analyzing coevolving adaptive networks in Prisoner's Dilemma games, improving upon existing pair approximation methods.

## Key findings

- Approximate master equations accurately predict simulation results.
- System evolution and stationary states depend on partner-switching rules.
- Different model variants show qualitative differences in utilities and dynamics.

## Abstract

We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) across all of its neighbors, changing that strategy and possibly changing partners in response to local changes in the network of player pairing and in the strategies used by connected partners. We compare and contrast numerical simulations with existing pair approximation differential equations for describing this system, as well as more accurate equations developed here using the framework of approximate master equations. We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximate master equations for describing the system observations made from simulations. We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.