Sparse cliques trump scale-free networks in coordination and competition.

David A Gianetto,Babak Heydari

doi:10.1038/srep21870

Abstract

Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner’s Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner’s Dilemma game.

Highlights

The puzzling existence of cooperation in the face of the seemingly selfish process of natural selection has occupied researchers across many disciplines for over 30 years[1,2]
Game play occurs between agents who play twoplayer repeated games with each of their nearest neighbors and receive payoffs according to the moves of each player, commensurate with the payoff structure of the game, equation (4)
Agents, with memory of their opponent’s last move within a repeated game, determine their move according to their stochastic reactive strategy, which is based on the three-component, Markovian, mixed-strategy framework from[43,44], where y is the probability to trust on the first move, p is the probability to reciprocate a cooperative move and q is the probability to forgive defection

Summary

Introduction

The puzzling existence of cooperation in the face of the seemingly selfish process of natural selection has occupied researchers across many disciplines for over 30 years[1,2]. One way to tackle this problem that has proven useful is to consider evolving players of social dilemma games within a network, where the games provide a framework for understanding the simplest local interactions and the network frames community-level and global interaction[12]. This general approach has shown that relatively sparse connectivity[15] or less frequent interaction[16] helps encourage cooperation. If a range, or spectrum of motifs is considered a network hierarchy may be determined, when the network is directed[42]

Methods

Results

Conclusion