Conformity-Driven Agents Support Ordered Phases in the Spatial Public Goods Game

We investigate the spatial Public Goods Game in the presence of fitness-driven and conformitydriven agents. This framework usually considers only the former type of agents, i.e., agents that tend to imitate the strategy of their fittest neighbors. However, whenever we study social systems, the evolution of a population might be affected also by social behaviors as conformism, stubbornness, altruism, and selfishness. Although the term evolution can assume different meanings depending on the considered domain, here it corresponds to the set of processes that lead a system towards an equilibrium or a steady-state. We map fitness to the agents’ payoff so that richer agents are those most imitated by fitness-driven agents, while conformity-driven agents tend to imitate the strategy assumed by the majority of their neighbors. Numerical simulations aim to identify the nature of the transition, on varying the amount of the relative density of conformity-driven agents in the population, and to study the nature of related equilibria. Remarkably, we find that conformism generally fosters ordered cooperative phases and may also lead to bistable behaviors. ∗ [email protected] 1 ar X iv :1 60 2. 01 80 8v 2 [ ph ys ic s. so cph ] 2 9 A ug 2 01 7 In the last two decades, Evolutionary Game Theory [1–6] (EGT) has strongly developed into a mature field that, nowadays, represents a vivid and independent research area with a list of applications spanning from biology to social systems [1, 3, 7–11]. In particular, EGT constitutes a powerful tool for modelling a myriad of natural phenomena characterized by evolutionary dynamics [12] and complex interaction patterns [13]. The emergence of cooperation [14] is one of the central topics in EGT. The Prisoner’s Dilemma [3] (PD) and its n-person PD, also called Public Goods Game, represent the typical game-theoretical framework in which individual and group interests collide. In fact, in the PD game two players can decide to mutually cooperate for achieving a common goal and, at the same time, are both tempted to exploit their opponent in order to obtain an higher payoff at the expense of the other player. Among other mechanisms [15], network reciprocity has been proposed as a fundamental tool to promote cooperation in structured populations of unlabeled and anonymous individuals. Recently, a series of works [8, 18, 19] unveiled that, even when agents’ interactions are based upon Nash Equilibria [20] in which defection (not cooperation) theoretically dominates cooperative strategies, agent, and even human, populations are able to attain a cooperative equilibrium [18, 19, 21–26]. In this context, it is interesting to identify behaviors and properties that may lead a population towards cooperation, although defection is risk-less and constitutes, egoistically, the most convenient strategy. For instance, random or purposeful motion [16–19, 25] and competitiveness [24] are able to increase the level of cooperation in the spatial Prisoner’s Dilemma. Remarkably, EGT allows also to study the role of peer influences in social dilemmas, as reported in [27, 28]. In [27] the authors investigate the role of conformism [29] in social dilemmas, by simulating a twospecies population whose agents, embedded in a scale-free network [30], play pairwise the PD game with their neighbors; the two species forming the population were payoff-driven agents and conformist agents. Their result shows that conformism can enhance social reciprocity highlighting its beneficial role in the resolution of social dilemmas. In [28], the authors report that scale-free networks reduce the amplification of cooperation when an opportune amount of conformists is introduced in the imitation rules. It is worth observing that conformism is one of the most investigated behaviors in the field of sociophysics [31, 32], i.e, the field attempting to analyze socio-economic systems under the lens of statistical physics [31, 33]. Moreover, conformism has been shown to deeply influence opinion dynamics [33–35], and more in general phenomena of social spreading, as well as evolutionary dynamics [27, 36].