Predicting transitions in cooperation levels from network connectivity

TL;DR

This paper introduces a simple predictive rule based on network degree sequences to forecast cooperation phase transitions in social dilemma games on arbitrary networks, validated through simulations.

Contribution

The study presents a novel, easy-to-apply method for predicting cooperation shifts using network degree sequences, advancing understanding of social dynamics on complex networks.

Findings

Accurate predictions of cooperation transitions in networked games.

Good agreement between predictions and simulation results.

Method applicable to various network types, including scale-free networks.

Abstract

Networks determine our social circles and the way we cooperate with others. We know that topological features like hubs and degree assortativity affect cooperation, and we know that cooperation is favoured if the benefit of the altruistic act divided by the cost exceeds the average number of neighbours. However, a simple rule that would predict cooperation transitions on an arbitrary network has not yet been presented. Here we show that the unique sequence of degrees in a network can be used to predict at which game parameters major shifts in the level of cooperation can be expected, including phase transitions from absorbing to mixed strategy phases. We use the evolutionary prisoner's dilemma game on random and scale-free networks to demonstrate the prediction, as well as its limitations and possible pitfalls. We observe good agreements between the predictions and the results obtained with concurrent and Monte Carlo methods for the update of the strategies, thus providing a simple and fast way to estimate the outcome of evolutionary social dilemmas on arbitrary networks without the need of actually playing the game.