Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proven valuable for studying pattern formation, equilibrium selection, and self-organisation in evolutionary games. Here we review recent advances in the study of evolutionary dynamics of group interactions on structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.
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…
Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms, and the competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more regardl…
We discuss a model for evolutionary game dynamics in a growing, network-structured population. In our model, new players can either make connections to random preexisting players or preferentially attach to those that have been successful in the past. The latter depends on the dynamics of strategies in the game, which we implement following the so-called Fermi rule such that the limits of weak and strong strategy selection can be explored. Our framework allows to address general evolutionary games. With only two parameters describing the preferential attachment and the intensity of selection, …
The emergence and maintenance of cooperative behavior is a fascinating topic in evolutionary biology and social science. The public goods game (PGG) is a paradigm for exploring cooperative behavior. In PGG, the total resulting payoff is divided equally among all participants. This feature still leads to the dominance of defection without substantially magnifying the public good by a multiplying factor. Much effort has been made to explain the evolution of cooperative strategies, including a recent model in which only a portion of the total benefit is shared by all the players through introduci…
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…
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）
Extortion strategies can dominate any opponent in an iterated prisoner's dilemma game. But if players are able to adopt the strategies performing better, extortion becomes widespread and evolutionary unstable. It may sometimes act as a catalyst for the evolution of cooperation, and it can also emerge in interactions between two populations, yet it is not the evolutionary stable outcome. Here we revisit these results in the realm of spatial games. We find that pairwise imitation and birth-death dynamics return known evolutionary outcomes. Myopic best response strategy updating, on the other han…
With the volume of manuscripts submitted for publication growing every year, the deficiencies of peer review (e.g. long review times) are becoming more apparent. Editorial strategies, sets of guidelines designed to speed up the process and reduce editors workloads, are treated as trade secrets by publishing houses and are not shared publicly. To improve the effectiveness of their strategies, editors in small publishing groups are faced with undertaking an iterative trial-and-error approach. We show that Cartesian Genetic Programming, a nature-inspired evolutionary algorithm, can dramatically i…
Evolution of cooperation in the prisoner's dilemma and the public goods game is studied, where initially players belong to two independent structured populations. Simultaneously with the strategy evolution, players whose current utility exceeds a threshold are rewarded by an external link to a player belonging to the other population. Yet as soon as the utility drops below the threshold, the external link is terminated. The rewarding of current evolutionary fitness thus introduces a time-varying interdependence between the two populations. We show that, regardless of the details of the evoluti…
We study the evolution of cooperation in the spatial prisoner's dilemma game, where besides unconditional cooperation and defection, tit-for-tat, win-stay-lose-shift and extortion are the five competing strategies. While pairwise imitation fails to sustain unconditional cooperation and extortion regardless of game parametrization, myopic updating gives rise to the coexistence of all five strategies if the temptation to defect is sufficiently large or if the degree distribution of the interaction network is heterogeneous. This counterintuitive evolutionary outcome emerges as a result of an unex…
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…
The emergence and prevalence of cooperative behavior within a group of selfish individuals remains a puzzle for \text{evolutionary game theory} precisely because it conflicts directly with the central idea of natural selection. Accordingly, in recent years, the search for an understanding of how cooperation can be stimulated, even when it conflicts with individual interest, has intensified. We investigate the emergence of cooperation in an age-structured evolutionary spatial game. In it, players age with time and the payoff that they receive after each round \text{depends on} their age. \text{…
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 …
Societies consisting of cooperative individuals seem to require for their continuing success that defectors be policed. The precise connection between punishers and benefits, population structure, and division of labour, however, remains ill-understood. Many models assume costly "peer punishment" to enforce cooperation, but results in the economics literature suggest that this assumption may not be generally valid. In many human and animal societies, there is a division of labour between a purely supportive majority and a dedicated minority of police-like enforcers. Here we present several ext…
The commonly used accumulated payoff scheme is not invariant with respect to shifts of payoff values when applied locally in degree-inhomogeneous population structures. We propose a suitably modified payoff scheme and we show both formally and by numerical simulation, that it leaves the replicator dynamics invariant with respect to affine transformations of the game payoff matrix. We then show empirically that, using the modified payoff scheme, an interesting amount of cooperation can be reached in three paradigmatic non-cooperative two-person games in populations that are structured according…
The study of the evolution of cooperative behaviours --which provide benefits to others-- and altruism --which provides benefits to others at a cost to oneself-- has been on the core of the evolutionary game theoretical framework since its foundation. The fast development of the theory during the last years has improved our knowledge of the issue, but carried attached a diversification of concepts which affected communication between scientists. Furthermore, the main root of conflict in the struggle for life identified by Darwin, the limited amount of resources present in any ecosystem, which …
The minimum-effort coordination game, having potentially important implications in both evolutionary biology and sociology, draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the predictions of classic game theory. In the framework of classic game theory, any common effort level is a strict and trembling hand perfect Nash equilibrium, so that no desideratum is provided for selecting among them. Behavior experiments, however, show that the effort levels employed by subjects are inversely related to the effort costs. Here, we combine …
Social comparison shapes the evolution of cooperation in structured populations
The 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）；Department of Complexity Science, Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所复杂性科学系）；Institute of Physics, Humboldt University of Berlin（柏林洪堡大学物理研究所）；Institute of Technical Physics and Materials Science, Centre for Energy Research（匈牙利能源研究中心技术物理与材料科学研究所）
Joint Institute for Nuclear Research（联合核研究所）；ETH Zürich, Swiss Federal Institute of Technology（苏黎世联邦理工学院）
The review presents the basics of quantum decision theory, with the emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. The difference of an operationally testable rational choice between alternatives from a choice decorated by irrational feelings is elucidated. Quantum-classical correspondence is emphasized. A model of quantum intelligence network is described. Dynamic inconsistencies are shown to be resolved in the frame of the quantum decision theory.
