In this work, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is nontrivial, as some authors found that heterogeneity sustains cooperation, while others obtained different results. Among the possible forms of heterogeneity, we focus on the individual perception of risks and rewards related to a generic event, that can show up in a number of social and biological systems. The modelling approach is based on the framework of Evolutionary Game Theory. To represent this kind of heterogeneity, we implement small and local perturbations on the payoff matrix of simple 2-strategy games, as the Prisoner's Dilemma. So, while usually the payoff is considered as a global and time-invariant structure, i.e. it is the same for all individuals of a population at any time, in our model its value is continuously affected by small variations, both in time and space (i.e. position on a lattice). We found that such perturbations can be beneficial or detrimental to cooperation, depending on their setting. Notably, cooperation is strongly supported when perturbations act on the main diagonal of the payoff matrix, whereas when they act on the off-diagonal the resulting effect is more difficult to quantify. To conclude, the proposed model shows a rich spectrum of possible equilibria, whose interpretation might offer insights and enrich the description of several systems.
Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is in fact strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff…
In this paper, we investigate the effect of "heterogeneity of link weight", heterogeneity of the frequency or amount of interactions among individuals, on the evolution of cooperation. Based on an analysis of the evolutionary prisoner's dilemma game on a weighted one-dimensional lattice network with "intra-individual heterogeneity", we confirm that moderate level of link-weight heterogeneity can facilitate cooperation. Furthermore, we identify two key mechanisms by which link-weight heterogeneity promotes the evolution of cooperation: mechanisms for spread and maintenance of cooperation. We al…
Recent studies on the evolutionary dynamics of the Prisoner's Dilemma game in scale-free networks have demonstrated that the heterogeneity of the network interconnections enhances the evolutionary success of cooperation. In this paper we address the issue of how the characterization of the asymptotic states of the evolutionary dynamics depends on the initial concentration of cooperators. We find that the measure and the connectedness properties of the set of nodes where cooperation reaches fixation is largely independent of initial conditions, in contrast with the behavior of both the set of n…
We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperation and sustaining cooperators. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Watts-Strogatz small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. Moreover, neither the most heterogeneous case nor …
Motivated by the fact that the same social dilemma can be perceived differently by different players, we here study evolutionary multigames in structured populations. While the core game is the weak prisoner's dilemma, a fraction of the population adopts either a positive or a negative value of the sucker's payoff, thus playing either the traditional prisoner's dilemma or the snowdrift game. We show that the higher the fraction of the population adopting a different payoff matrix, the more the evolution of cooperation is promoted. The microscopic mechanism responsible for this outcome is uniqu…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which perception affects reality. By varying the `reality map', which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers, to a purely subjective game in which probabilities equal the amount wagered. The reality map can reflect self-reinforcing str…
The most common assumption in evolutionary game theory is that players should adopt a strategy that warrants the highest payoff. However, recent studies indicate that the spatial selection for cooperation is enhanced if an appropriate fraction of the population chooses the most common rather than the most profitable strategy within the interaction range. Such conformity might be due to herding instincts or crowd behavior in humans and social animals. In a heterogeneous population where individuals differ in their degree, collective influence, or other traits, an unanswered question remains who…
Tuning one's shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite number of possible tap positions, identical agents are unlikely to reach even approximately their favorite water temperature. We show that a population of agents with homogeneous strategies is evolutionary unstable, which gives insights into the emergence of heterogeneity, the latter being tempting but risky.
Strategy Evolution in the Adoption of Conservation Tillage Technology under Time Preference Heterogeneity and Lemon Market: Insights from Evolutionary Dynamics
Northwest A&F University（西北农林科技大学）；Guilin Normal university（桂林师范学院）
How individuals adapt their behavior in cultural evolution remains elusive. Theoretical studies have shown that the update rules chosen to model individual decision making can dramatically modify the evolutionary outcome of the population as a whole. This hints at the complexities of considering the personality of individuals in a population, where each one uses its own rule. Here, we investigate whether and how heterogeneity in the rules of behavior update alters the evolutionary outcome. We assume that individuals update behaviors by aspiration-based self-evaluation and they do so in their o…
Effects of Stochastic Games on Evolutionary Dynamics in Structured Populations
College of Artificial Intelligence, Southwest University（西南大学人工智能学院）；Business College, Southwest University（西南大学商学院）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔市阿道夫·德罗尔克博士社区健康中心）；Department of Physics, Kyung Hee University（庆熙大学物理系）；University College, Korea University（韩国大学大学院）；Institute of Technical Physics and Materials Science, Centre for Energy Research（能源研究中心技术物理与材料科学研究所）
During pandemic events, strategies such as social distancing can be fundamental to curb viral spreading. Such actions can reduce the number of simultaneous infections and mitigate the disease spreading, which is relevant to the risk of a healthcare system collapse. Although these strategies can be suggested, their actual implementation may depend on the population perception of the disease risk. The current COVID-19 crisis, for instance, is showing that some individuals are much more prone than others to remain isolated, avoiding unnecessary contacts. With this motivation, we propose an epidem…
The impact of heterogeneity on the co-evolution of cooperation and epidemic spreading in complex networks
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）；Max Planck Institute of Animal Behavior（马克斯·普朗克动物行为研究所）；University of Konstanz（康斯坦茨大学）
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the coevolutionary dynamics of three cyclically invading strategies for different evolutionary processes on various classes of complex networks, including random graphs, scale-free and small world networks. We find that scale-free and random graphs lead to a strong stabilization of coexistence both for the Moran process and the Local Update process. The stabilization is…
We introduce a framework within evolutionary game theory for studying the distinction between objective and subjective rationality and apply it to the evolution of cooperation on 3-regular random graphs. In our simulations, agents evolve misrepresentations of objective reality that help them cooperate and maintain higher social welfare in the Prisoner's dilemma. These agents act rationally on their subjective representations of the world, but irrationally from the perspective of an external observer. We model misrepresentations as subjective perceptions of payoffs and quasi-magical thinking as…
Involution game with migration and spatial heterogeneity of social resources
Wuhan City Polytechnic（武汉城市职业学院）；School of Economics and Management, University of Chinese Academy of Sciences（中国科学院大学经济与管理学院）；Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences（中国科学院虚拟经济与数据科学研究中心）；Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences（中国科学院大数据管理与知识管理重点实验室）
Evolution of cooperation with temporal information
Center for Systems and Control, Peking University（系统与控制中心，北京大学）；School of Automation, Beijing Institute of Technology（自动化学院，北京理工大学）；Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University（多智能体研究中心，人工智能研究院，北京大学）
The evolution of cooperation in social dilemmas in structured populations has been studied extensively in recent years. Whereas many theoretical studies have found that a heterogeneous network of contacts favors cooperation, the impact of spatial effects in scale-free networks is still not well understood. In addition to being heterogeneous, real contact networks exhibit a high mean local clustering coefficient, which implies the existence of an underlying metric space. Here, we show that evolutionary dynamics in scale-free networks self-organize into spatial patterns in the underlying metric …
We study the effects of individual perceptions of payoffs in two-player games. In particular we consider the setting in which individuals' perceptions of the game are influenced by their previous experiences and outcomes. Accordingly, we introduce a framework based on evolutionary games where individuals have the capacity to perceive their interactions in different ways. Starting from the narrative of social behaviors in a pub as an illustration, we first study the combination of the prisoner's dilemma and harmony game as two alternative perceptions of the same situation. Considering a selecti…
Lurking is a complex user-behavioral phenomenon that occurs in all large-scale online communities and social networks. It generally refers to the behavior characterizing users that benefit from the information produced by others in the community without actively contributing back to the production of social content. The amount and evolution of lurkers may strongly affect an online social environment, therefore understanding the lurking dynamics and identifying strategies to curb this trend are relevant problems. In this regard, we introduce the Lurker Game, i.e., a model for analyzing the tran…
Cooperation among unrelated individuals is frequently observed in social groups when their members combine efforts and resources to obtain a shared benefit that is unachievable by an individual alone. However, understanding why cooperation arises despite the natural tendency of individuals towards selfish behavior is still an open problem and represents one of the most fascinating challenges in evolutionary dynamics. Recently, the structural characterization of the networks in which social interactions take place has shed some light on the mechanisms by which cooperative behavior emerges and e…
Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows to introduce elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of Evolutionary Game Theory, where evolution constitutes an intrinsic mechanism, while innovation requires an opportune represe…
