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Register a new userCritical mass effect in evolutionary games triggered by zealots
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Tiny perturbations may trigger large responses in systems near criticality, shifting them across equilibria. Committed minorities are suggested to be responsible for the emergence of collective behaviors in many physical, social, and biological systems. Using evolutionary game theory, we address the question whether a finite fraction of zealots can drive the system to large-scale coordination. We find that a tipping point exists in coordination games, whereas the same phenomenon depends on the selection pressure, update rule, and network structure in other types of games. Our study paves the way to understand social systems driven by the individuals benefit in presence of zealots, such as human vaccination behavior or cooperative transports in animal groups.
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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 regardless of the particularities of the game. Here we review recent advances on the rock-paper-scissors and related evolutionary games, focusing in particular on pattern formation, the impact of mobility, and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional rock-paper-scissors models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related for example to dynamical effects of coevolutionary rules and invasion reversals due to multi-point interactions, are outlined as well.
In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the correlations that influence the decisions of the players. The current theory for correlated games, however, enforces the players to obey the instructions from a third party or correlation device to reach equilibrium, but this cannot be achieved for all initial correlations. We extend here the existing framework of correlated games and find that there are other interesting and previously unknown Nash equilibria that make use of correlations to obtain the best payoff. This is achieved by allowing the players the freedom to follow or not to follow the suggestions of the correlation device. By assigning independent probabilities to follow every possible suggestion, the players engage in a response game that turns out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and mixed-strategy solutions. We determine the Nash equilibria for all possible correlated Snowdrift games, which we find to be describable by Ising Models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.
Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoners dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoners dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions.
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 space. The resulting metric clusters of cooperators are able to survive in social dilemmas as their spatial organization shields them from surrounding defectors, similar to spatial selection in Euclidean space. We show that under certain conditions these metric clusters are more efficient than the most connected nodes at sustaining cooperation and that heterogeneity does not always favor--but can even hinder--cooperation in social dilemmas. Our findings provide a new perspective to understand the emergence of cooperation in evolutionary games in realistic structured populations.
Evolutionary games provide the theoretical backbone for many aspects of our social life: from cooperation to crime, from climate inaction to imperfect vaccination and epidemic spreading, from antibiotics overuse to biodiversity preservation. An important, and so far overlooked, aspect of reality is the diverse strategic identities of individuals. While applying the same strategy to all interaction partners may be an acceptable assumption for simpler forms of life, this fails to account} for the behavior of more complex living beings. For instance, we humans act differently around different people. Here we show that allowing individuals to adopt different strategies with different partners yields a very rich evolutionary dynamics, including time-dependent coexistence of cooperation and defection, system-wide shifts in the dominant strategy, and maturation in individual choices. Our results are robust to variations in network type and size, and strategy updating rules. Accounting for diverse strategic identities thus has far-reaching implications in the mathematical modeling of social games.
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