How costly punishment, diversity, and density of connectivity influence cooperation in a biological network

Ivan C Ezeigbo

doi:10.1038/s41598-017-17481-0

Abstract

It has been an old unsolved puzzle to evolutionary theorists on which mechanisms would increase large-scale cooperation in human societies. Thus, how such mechanisms operate in a biological network is still not well understood. This study addresses these questions with empirical evidence from agent-based models designed to understand these network interactions. Repeated Prisoner’s Dilemma games were designed to study how costly punishment, diversity, and density of connectivity interact to influence cooperation in a biological network. There were 1000 rounds in each game made up of 18 players engaged in pairwise relationship with their neighbors. This study shows three important interactions. (1) Introducing diversity to costly punishment favors both cooperation and defection, but not vice versa. Introducing costly punishment to diversity disfavors defection but favors cooperation. (2) Costly Punishment, alone, disfavors defection but decreases average payoff. Decreasing the density of connectivity, Dc, when there is no costly punishment applied, increases average payoff. (3) A synergy of diversity and decreasing density of connectivity favors cooperation in a biological network. Furthermore, this study also suggests a likelihood from empirical findings that spatial structures may not be favoring cooperation, as is the widely-accepted notion, but rather disfavoring defection in the global scale.

Highlights

Evolutionary theorists have long pondered the mechanisms that favor emergence of cooperation in a biological network[1,2,3,4]
From equation (2) and equation (3), we have demonstrated that f falls within the range, NN−T1h≤e ufni≤queNr2−ele1.vance of this study, as it concerns addressing the question of evolutionary theorists on cooperation, is that with the power of larger data or sample size, we can observe how evolution occurs not just at the local scale, and at the global scale
It suggests three interactions that occur at the global scale of a biological network, and secondly, it suggests that spatial structures have a similar network interaction as costly punishment

Summary

Introduction

Evolutionary theorists have long pondered the mechanisms that favor emergence of cooperation in a biological network[1,2,3,4]. This study suggests that the following three interesting interactions occur at the global scale in a biological network: (1) Introducing diversity to costly punishment favors both cooperation and defection, but not vice versa. Introducing costly punishment alone in a network would disfavor defection but may not necessarily solely favor cooperation For this reason, it can be misleading to draw conclusions from associations in complex systems observed only at the local scale, as opposed to both the global and local scale. Gracia-Lazaro et al[20] carried out a human experimental study showing that players defected more than they cooperated when playing a Prisoner’s Dilemma game in a heterogeneous and diverse network On replicating their experiment on square lattices, my study suggests that this is true at the local scale. This is consistent with the widely-accepted notion that spatial structures favor cooperation[30,31]; at the global scale, as proposed in this study, we say it rather disfavors defection

Methods

Results

Discussion

Conclusion