Modeling Social Interactions Using Approaches in Evolutionary Game Theory

Abstract

Evolutionary Game Theory is often used to model and describe social interactions. One of the most famous games, Prisoner’s Dilemma (PD), has served as the basis for a variety of social dilemmas where people can choose to cooperate or defect. The social dilemma I investigate here is friendliness; why do people decide to ignore one another when being friendly has no apparent cost? What might people on a college campus gain or lose from day-to-day social interactions with their peers? I use PD as a basis for defining a variety of cooperator and defector personalities, who are differentiated by the payoffs they receive against other players in the game. After developing a payoff matrix with 10 distinct strategies and a variety of parameters, I utilize the frameworks of Evolutionarily Stable Strategies (ESS) and Replicator Dynamics to analyze the dynamics of a population evolving within this model. Friendly Cooperators are most robustly ESS, while other cooperators are ESS if and only if Friendly Cooperators also are ESS. Loner Defectors, who gain an increased payoff from mutual defection, are notably the only defector strategy that can be ESS. Mean Defectors, who gain a relatively greater payoff from defecting against cooperators, though never ESS, can both invade all other cooperator strategies and exist at equilibria with them in a variety of combinations. Amongst other results, these theoretical analyses were complemented by a simulation that modeled a population of these 10 strategies existing on a dynamic network. The frequency results showed a consistent dominance of Friendly Cooperators, implying that defectors might only be successful in populations where individual relationships are inconsequential to their satisfaction.