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

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 very 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 are 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.