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Highlight • The result exists an obvious piecewise phenomenon for individual's aspiration level on promoting cooperation Abstract In real life, everyone is full of yearning and pursuit for future life. The difference between reality and ideals encourage people to constantly adjust the current state, so that they can better adapt to changes in the surrounding environment. Thus, we propose a spatial prisoner's dilemma game model where individuals have expectation towards the payoff obtained from nearest neighbors, and individuals can adaptively adjust their update willingness based on the satisfaction of income. Through numerical calculation, we find that different b values will have an appropriate aspiration level to promote cooperation. In addition, the results have an obvious phase transition phenomenon for individual's aspiration level on promoting cooperation. Moreover, only moderate aspiration level can promote the evolution of cooperative behavior, due to it can lead to the heterogeneous distribution of update willingness, which will be beneficial to the evolution of cooperation. [ABSTRACT FROM AUTHOR]

We investigate the ability-based fitness calculation in an asymmetric setup to the evolution of cooperation on square lattice. In particular, if players can maintain its strategy for a round, then its abilities will increase 1, otherwise, its ability will turn to 0. We also assume that if players' abilities exceed a certain threshold M , then its environment is integrated into its fitness calculation via a simple parameter α. Through extensive numerical simulation, we find that large threshold M decreases cooperation, and large α, players' fitness is mainly decided by its dynamical environment, promotes cooperation. We also provide theoretical analysis and get the same results with simulation. Finally, we test its robustness on homogeneous random network and small-world network. Our work provides a deeper insight to network reciprocity. [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]

Cooperation in human interactions often involves voluntary participation rather than obligatory requirements. This paper investigates the impact of voluntary exit strategies on cooperation within scale-free networks, employing spatial prisoner's dilemma games as the framework. We analyze three distinct exit strategies: leader priority exit, fringe priority exit, and random exit, across varying dilemma strengths. Our findings reveal that in scenarios of weak dilemma strength, leader priority exit significantly diminishes cooperation, particularly when only a small subset of players is granted exit rights. In contrast, under strong dilemma strength conditions, both leader priority and random exits serve to unexpectedly bolster cooperation. This enhancement is primarily facilitated by high-degree nodes opting out, thereby enabling low-degree nodes to establish stable cooperation. Furthermore, our study underscores the pivotal role of network structure. In assortative networks, random exit emerges as the most effective strategy in promoting cooperation. On the other hand, disassortative networks exhibit a substantial increase in cooperation levels when employing leader priority exit. These results highlight the intricate interplay between exit strategies, dilemma strength, and network topology, offering critical insights for promoting cooperation in varied social contexts. • Study on leaders' priority exit's impact on cooperation dynamics. • Cooperation affected by leader priority exit varies with dilemma strength and network type. • Leader priority exit boosts cooperation in disassortative networks. • Random exit boosts cooperation in assortative networks. [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]

• a mechanism is proposed aiming to investigate the co-evolution of personal reputation and strategy under a general framework of interactive diversity. • Numerous simulations are conducted with sufficient analyses of the obtained results being followed. • The consideration of interaction diversity is able to ensure the maintenance of cooperation even if the temptation of adopting antisocial behavior (here, defection is considered) is relatively large. • Various discussions are performed in order to explain the reason of this effect from various perspectives, for instance, by counting the number of various chains and the evolution of clusters. In practice, there exists numerous examples indicating the phenomenon that individuals are inclined to employ different strategies when interacting with the others. This is incurred by the fact that individuals are able to adjust their strategies adaptively under different interacting environments. Scholars have devoted their efforts to this topic; nevertheless, the impact of diverse interactions on cooperation still needs to be further explored. In this manuscript, we propose a mechanism aiming to investigate the co-evolution of personal reputation and strategy under a general framework of interactive diversity (being referred to as edge-strategy for simplicity). Numerous simulations are conducted with sufficient analyses of the obtained results being provided. As illustrated by the evolutionary dynamics, we find that there exists an optimal reputation value which can promote the frequency of cooperation by a large extent. Furthermore, we can clearly conclude that the consideration of interaction diversity is able to ensure the maintenance of cooperation even if the temptation to adopt antisocial behavior is relatively large. Aiming to understand the phenomenon better, we also quantitatively analyze the results by investigating the statistics of interaction chain, cluster size and other microscopic information. Overall, we hope the findings here can provide some interesting insights in solving social dilemmas. [ABSTRACT FROM AUTHOR]