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• This paper introduces expectation-based reinforcement learning methods in the public goods game. • The results under total population density show that individuals behavior exhibits conditional cooperation and its variant moody conditional cooperation. • In the network with empty nodes, conditional cooperation shows opposite trends. In social dilemmas, individual behavior generally follows the characteristics of conditional cooperation and emotional conditional cooperation. However, it is hard to adequately explain the behavior patterns of conditional cooperation with the evolutionary game theory. This paper introduces expectation-based reinforcement learning methods in the public goods game to investigate and account for the behavior patterns. Instead of letting individuals occupy the entire network as previous studies have done, we focus on studying individual behavior patterns on a network with empty nodes. The results under total population density show the effectivity of our model as they are consistent with those of the previous studies, that is, individuals' behavior exhibits conditional cooperation and its variant moody conditional cooperation. However, in the network with empty nodes, conditional cooperation shows opposite trends. We finally demonstrate that an appropriate population density can facilitate the maintenance and development of cooperation. [ABSTRACT FROM AUTHOR]

Our social interactions vary over time and they depend on various factors that determine our preferences and goals, both in personal and professional terms. Researches have shown that this plays an important role in promoting cooperation and prosocial behavior in general. Indeed, it is natural to assume that ties among cooperators would become stronger over time, while ties with defectors (non-cooperators) would eventually be severed. Here we introduce reinforcement learning as a determinant of adaptive interaction intensity in social dilemmas and study how this translates into the structure of the social network and its propensity to sustain cooperation. We merge the iterated prisoner's dilemma game with the Bush-Mostelle reinforcement learning model and show that there exists a moderate switching dynamics of the interaction intensity that is optimal for the evolution of cooperation. Besides, the results of Monte Carlo simulations are further supported by the calculations of dynamical pair approximation. These observations show that reinforcement learning is sufficient for the emergence of optimal social interaction patterns that facilitate cooperation. This in turn supports the social capital hypothesis with a minimal set of assumptions that guide the self-organization of our social fabric. [ABSTRACT FROM AUTHOR]

• We introduce third parties and disputants on interdependent network. • Disputants play prisoner's dilemma game and bring third parties extra payoffs. • Third parties intervene disputants play snowdrift dilemma game or not. • Conflicts in disputants are relieved though non-interventions exist in third party layer. Interventions from third parties, such as governmental agencies or organizations, play an important role in mitigating conflicts in modern human societies. The goal thereby is to pacify disputants, although this is subject to failure on account of self-interest from all involved. To study how relationships between disputants and third parties evolve, we propose an interdependent network model, where one layer is occupied by disputants and the other layer is occupied by third parties. Disputants play a prisoner's dilemma game, where defection is the dominant strategy, whereas third parties play a snowdrift game, where cooperation and defection coexist more commonly. Moreover, third parties have the ability to mediate a conflict on the other layer by enforcing a snowdrift game onto disputants, for which they can receive a fee. We show that third party interventions improve the evolution of cooperation between disputants, and also, that the improvement of cooperation in turn promotes interventions. Nonetheless, non-intervention does not go extinct, which enables defectors to survive, thus creating a feedback loop between the two networks layers. The evolutionary dynamics is characterized by fascinating spatial pattern formation, which we explore by means of Monte Carlo simulations and via replicator equations. [ABSTRACT FROM AUTHOR]