We study the evolution of cooperation in structured populations within popular models of social dilemmas, whereby simple coevolutionary rules are introduced that may enhance players abilities to enforce their strategy on the opponent. Coevolution thus here refers to an evolutionary process affecting the teaching activity of players that accompanies the evolution of their strategies. Particularly, we increase the teaching activity of a player after it has successfully reproduced, yet we do so depending on the disseminated strategy. We separately consider coevolution affecting either only the cooperators or only the defectors, and show that both options promote cooperation irrespective of the applied game. Opposite to intuitive reasoning, however, we reveal that the coevolutionary promotion of players spreading defection is, in the long run, more beneficial for cooperation than the likewise promotion of cooperators. We explain the contradictory impact of the two considered coevolutionary rules by examining the differences between resulting heterogeneities that segregate participating players, and furthermore, demonstrate that the influential individuals completely determine the final outcome of the games. Our findings are immune to changes defining the type of considered social dilemmas and highlight that the heterogeneity of players, resulting in a positive feedback mechanism, is a fundamental property promoting cooperation in groups of selfish individuals.
This paper studies scenarios of cyclic dominance in a coevolutionary spatial model in which game strategies and links between agents adaptively evolve over time. The Optional Prisoner's Dilemma (OPD) game is employed. The OPD is an extended version of the traditional Prisoner's Dilemma where players have a third option to abstain from playing the game. We adopt an agent-based simulation approach and use Monte Carlo methods to perform the OPD with coevolutionary rules. The necessary conditions to break the scenarios of cyclic dominance are also investigated. This work highlights that cyclic dom…
Wealthy individuals may be less tempted to defect than those with comparatively low payoffs. To take this into consideration, we introduce coevolutionary success-driven multigames in structured populations. While the core game is always the weak prisoner's dilemma, players whose payoffs from the previous round exceed a threshold adopt only a minimally low temptation to defect in the next round. Along with the strategies, the perceived strength of the social dilemma thus coevolves with the success of each individual player. We show that the lower the threshold for using the small temptation to …
We study the evolution of cooperation in the prisoner's dilemma game, whereby a coevolutionary rule is introduced that molds the random topology of the interaction network in two ways. First, existing links are deleted whenever a player adopts a new strategy or its degree exceeds a threshold value, and second, new links are added randomly after a given number of game iterations. These coevolutionary processes correspond to the generic formation of new and deletion of existing links that, especially in human societies, appear frequently as a consequence of ongoing socialization, change of lifes…
Heterogeneity has been studied as one of the most common explanations of the puzzle of cooperation in social dilemmas. A large number of papers have been published discussing the effects of increasing heterogeneity in structured populations of agents, where it has been established that heterogeneity may favour cooperative behaviour if it supports agents to locally coordinate their strategies. In this paper, assuming an existing model of a heterogeneous weighted network, we aim to further this analysis by exploring the relationship (if any) between heterogeneity and cooperation. We adopt a weig…
Exploiting others is beneficial individually but it could also be detrimental globally. The reverse is also true: a higher cooperation level may change the environment in a way that is beneficial for all competitors. To explore the possible consequence of this feedback we consider a coevolutionary model where the local cooperation level determines the payoff values of the applied prisoner's dilemma game. We observe that the coevolutionary rule provides a significantly higher cooperation level comparing to the traditional setup independently of the topology of the applied interaction graph. Int…
Recently, Antonioni and Cardillo proposed a coevolutionary model based on the intertwining of oscillator synchronization and evolutionary game theory [Phys. Rev. Lett. \textbf{118}, 238301 (2017)], in which each Kuramoto oscillator can decide whether to interact-or not-with its neighbors, and all oscillators can receive some benefits from the local synchronization but those who choose to interact must pay a cost. Oscillators are allowed to update their strategies according to payoff difference, wherein the strategy of an oscillator who has obtained higher payoff is more likely to be followed. …
Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new connections and thus permanently extend their neighborhoods, provided they have been successful in passing their strategy to the opponents. We show that this simple coevolutionary rule shifts the survival barrier of cooperators towards high temptations to defect and results in highly heterogeneous interaction networks with an exponential fit best characterizing their…
Mutual relationships, such as cooperation and exploitation, are the basis of human and other biological societies. The foundations of these relationships are rooted in the decision making of individuals, and whether they choose to be selfish or altruistic. How individuals choose their behaviors can be analyzed using a strategy optimization process in the framework of game theory. Previous studies have shown that reference to individuals' previous actions plays an important role in their choice of strategies and establishment of social relationships. A fundamental question remains as to whether…
Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperat…
Dynamics of evolutionary games strongly depend on underlying networks. We study the coevolutionary prisoner's dilemma in which players change their local networks as well as strategies (i.e., cooperate or defect). This topic has been increasingly explored by many researchers. On the basis of active linking dynamics [J. M. Pacheco et al., J. Theor. Biol. 243, 437 (2006), J. M. Pacheco et al., Phys. Rev. Lett. 97, 258103 (2006)], we show that cooperation is enhanced fairly robustly. In particular, cooperation evolves when the payoff of the player is normalized by the number of neighbors; this is…
Aging is always present, tailoring our interactions with others and postulating a finite lifespan during which we are able to exercise them. We consider the prisoner's dilemma game on a square lattice, and examine how quenched age distributions and different aging protocols influence the evolution of cooperation when taking the life experience and knowledge accumulation into account as time passes. In agreement with previous studies, we find that a quenched assignment of age to players, introducing heterogeneity to the game, substantially promotes cooperative behavior. Introduction of aging an…
We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation ir…
The evolution of cooperation among unrelated individuals in human and animal societies remains a challenging issue across disciplines. It is an important subject also in the evolutionary game theory to understand how cooperation arises. The subject has been extensively studied especially in Prisoners' dilemma game(PD) but the emergence of cooperation is also an important subject in public goods game(PGG). In this article, we consider coevolutionary PGG on complex networks where both the topology of the networks and strategies that players adopt under the influence of game dynamics varies. Thou…
Learning from a partner who collects higher payoff is a frequently used working hypothesis in evolutionary game theory. One of the alternative dynamical rules is when the focal player prefers to follow the strategy choice of the majority in the local neighborhood, which is often called as conformity-driven strategy update. In this work we assume that both strategy learning methods are present and compete for space within the framework of a coevolutionary model. Our results reveal that the presence of payoff-driven strategy learning method becomes exclusive for high succer's payoff and/or high …
Eco-evolutionary game dynamics which characterizes the mutual interactions and the coupled evolutions of strategies and environments has been of growing interests in very recent years. Since such feedback loops widely exist in a range of coevolutionary systems, such as microbial systems, social-ecological system and psychological-economic system, recent modeling frameworks that unveil the oscillating dynamics of social dilemmas have great potential for practical applications. In this perspective article, we overview the latest progress of evolutionary game theory in this direction. We describe…
The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population, sometimes promoting, sometimes inhibiting cooperation. Here we show that random dilution and mobility may suppress the inhibiting factors of the spatial structure in the Snowdrift game, while enhancing the already larger cooperation found in the Prisoner's dilemma and Stag Hunt games.
Promoting cooperation is an intellectual challenge in the social sciences, for which the iterated Prisoners' Dilemma (IPD) is a fundamental framework. The traditional view that there exists no simple ultimatum strategy whereby one player can unilaterally control the share of the surplus has been challenged by a new class of "zero-determinant" (ZD) strategies raised by Press and Dyson. In particular, the extortionate strategies can subdue the opponent and obtain higher scores. However, no empirical evidence has yet been found to support this theoretical finding. In a long-run laboratory experim…
Is it rational for selfish individuals to cooperate? The conventional answer based on analysis of games such as the Prisoners Dilemma (PD) is that it is not, even though mutual cooperation results in a better outcome for all. This incompatibility between individual rationality and collective benefit lies at the heart of questions about the evolution of cooperation, as illustrated by PD and similar games. Here, we argue that this apparent incompatibility is due to an inconsistency in the standard Nash framework for analyzing non-cooperative games and propose a new paradigm, that of the co-actio…
The emergence of cooperation among self-interested agents has been a key concern of the multi-agent systems community for decades. With the increased importance of network-mediated interaction, researchers have shifted the attention on the impact of social networks and their dynamics in promoting or hindering cooperation, drawing various context-dependent conclusions. For example, some lines of research, theoretical and experimental, suggest the existence of a threshold effect in the ratio of timescales of network evolution, after which cooperation will emerge, whereas other lines dispute this…
We study the coevolutionary dynamics of the diversity of phenotype expression and the evolution of cooperation in the Prisoner's Dilemma game. Rather than pre-assigning zero-or-one interaction rate, we diversify the rate of interaction by associating it with the phenotypes shared in common. Individuals each carry a set of potentially expressible phenotypes and expresses a certain number of phenotypes at a cost proportional to the number. The number of expressed phenotypes and thus the rate of interaction is an evolvable trait. Our results show that nonnegligible cost of expressing phenotypes r…
The design of mechanisms that encourage pro-social behaviours in populations of self-regarding agents is recognised as a major theoretical challenge within several areas of social, life and engineering sciences. When interference from external parties is considered, several heuristics have been identified as capable of engineering a desired collective behaviour at a minimal cost. However, these studies neglect the diverse nature of contexts and social structures that characterise real-world populations. Here we analyse the impact of diversity by means of scale-free interaction networks with hi…
We explore the evolution of cooperation in the framework of the evolutionary game theory using the prisoner's dilemma as metaphor of the problem. We present a minimal model taking into account the growing process of the systems and individuals with imitation capacity. We consider the topological structure and the evolution of strategies decoupled instead of a coevolutionary dynamic. We show conditions to build up a cooperative system with real topological structures for any natural selection intensity. When the system starts to grow, cooperation is unstable but becomes stable as soon as the sy…
University of Tübingen（图宾根大学）；University of Twente（特文特大学）；University of Amsterdam（阿姆斯特丹大学）
In this work, we ask for and answer what makes classical temporal-difference reinforcement learning with epsilon-greedy strategies cooperative. Cooperating in social dilemma situations is vital for animals, humans, and machines. While evolutionary theory revealed a range of mechanisms promoting cooperation, the conditions under which agents learn to cooperate are contested. Here, we demonstrate which and how individual elements of the multi-agent learning setting lead to cooperation. We use the iterated Prisoner's dilemma with one-period memory as a testbed. Each of the two learning agents lea…
We study the effects of conformity, the tendency of humans to imitate locally common behaviors, in the evolution of cooperation when individuals occupy the vertices of a graph and engage in the one-shot Prisoner's Dilemma or the Snowdrift game with their neighbors. Two different graphs are studied: rings (one-dimensional lattices with cyclic boundary conditions) and scale-free networks of the Barabasi-Albert type. The proposed evolutionary-graph model is studied both by means of Monte Carlo simulations and an extended pair-approximation technique. We find improved levels of cooperation when ev…
We consider the coupled dynamics of the adaption of network structure and the evolution of strategies played by individuals occupying the network vertices. We propose a computational model in which each agent plays a $n$-round Prisoner's Dilemma game with its immediate neighbors, after that, based upon self-interest, partial individuals may punish their defective neighbors by dismissing the social tie to the one who defects the most times, meanwhile seek for a new partner at random from the neighbors of the punished agent. It is found that the promotion of cooperation is attributed to the enta…
