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Register a new userDiverse strategic identities induce dynamical states in evolutionary games
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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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Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $dge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $sigma^2I$. The games we consider have payoff matrices of the form ${bf 1} + wG$ where ${bf 1}$ is matrix of all 1s and $w$ is small and positive. Since our population size $N=infty$, we call our selection small rather than weak which usually means $w =O(1/N)$. The key to studying these games is the fact that when the dynamics are suitably rescaled in space and time they convergence to solutions of a reaction diffusion equation (RDE). Inspired by work of Ohtsuki and Nowak and Tarnita et al we show that the reaction term is the replicator equation for a modified game matrix and the modifications of the game matrix depend on the interaction kernel only through the values of two or three simple probabilities for an associated coalescing random walk. Two strategy games lead to an RDE with a cubic nonlinearity, so we can describe the phase diagram completely. Three strategy games lead to a pair of coupled RDE, but using an idea from our earlier work, we are able to show that if there is a repelling function for the replicator equation for the modified game, then there is coexistence in the spatial game when selection is small. This enables us to prove coexistence in the spatial model in a wide variety of examples where the replicator equation of the modified game has an attracting equilibrium with all components positive. Using this result we are able to analyze the behavior of four evolutionary games that have recently been used in cancer modeling.
Residential mobility is deeply entangled with all aspects of hunter-gatherer life ways, and is therefore an issue of central importance in hunter-gatherer studies. Hunter-gatherers vary widely in annual rates of residential mobility, and understanding the sources of this variation has long been of interest to anthropologists and archaeologists. Since mobility is, to a large extent, driven by the need for a continuous supply of food, a natural framework for addressing this question is provided by the metabolic theory of ecology. This provides a powerful framework for formulating formal testable hypotheses concerning evolutionary and ecological constraints on the scale and variation of hunter-gatherer residential mobility. We evaluate these predictions using extant data and show strong support for the hypotheses. We show that the overall scale of hunter-gatherer residential mobility is predicted by average human body size, and the limited capacity of mobile hunter-gatherers to store energy internally. We then show that the majority of variation in residential mobility observed across cultures is predicted by energy availability in local ecosystems. Our results demonstrate that large-scale evolutionary and ecological processes, common to all plants and animals, constrain hunter-gatherers in predictable ways as they move through territories to effectively exploit resources over the course of a year. Moreover, our results extend the scope of the metabolic theory of ecology by showing how it successfully predicts variation in the behavioral ecology of populations within a species.
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 March of this year, COVID-19 was declared a pandemic and it continues to threaten public health. This global health crisis imposes limitations on daily movements, which have deteriorated every sector in our society. Understanding public reactions to the virus and the non-pharmaceutical interventions should be of great help to fight COVID-19 in a strategic way. We aim to provide tangible evidence of the human mobility trends by comparing the day-by-day variations across the U.S. Large-scale public mobility at an aggregated level is observed by leveraging mobile device location data and the measures related to social distancing. Our study captures spatial and temporal heterogeneity as well as the sociodemographic variations regarding the pandemic propagation and the non-pharmaceutical interventions. All mobility metrics adapted capture decreased public movements after the national emergency declaration. The population staying home has increased in all states and becomes more stable after the stay-at-home order with a smaller range of fluctuation. There exists overall mobility heterogeneity between the income or population density groups. The public had been taking active responses, voluntarily staying home more, to the in-state confirmed cases while the stay-at-home orders stabilize the variations. The study suggests that the public mobility trends conform with the government message urging to stay home. We anticipate our data-driven analysis offers integrated perspectives and serves as evidence to raise public awareness and, consequently, reinforce the importance of social distancing while assisting policymakers.
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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