Stochasticity and evolutionary stability

Abstract

In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash equilibria correspond to stable fixed points that are always evolutionarily stable. However, in finite populations stochastic effects can drive the system away from strict Nash equilibria, which gives rise to a new concept for evolutionary stability. The conventional and the new stability concepts may apparently contradict each other leading to conflicting predictions in large yet finite populations. We show that the two concepts can be derived from the frequency dependent Moran process in different limits. Our results help to determine the appropriate stability concept in large finite populations. The general validity of our findings is demonstrated showing that the same results are valid employing vastly different co-evolutionary processes.

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Cited by in corpus (29)

• Evolutionary games on graphs
• Universality of weak selection
• Fixation times in evolutionary games under weak selection
• Noise-guided evolution within cyclical interactions
• Deterministic evolutionary game dynamics in finite populations
• Fixation probabilities in evolutionary dynamics under weak selection
• Intrinsic noise in game dynamical learning
• Evolutionary games on cycles with strong selection
• Learning dynamics explains human behavior in Prisoner's Dilemma on networks
• Stochastic dynamics of the prisoner's dilemma with cooperation facilitators
• Stochastic slowdown in evolutionary processes
• Optional games on cycles and complete graphs
• Finite-population evolution with rare mutations in asymmetric games
• Metastability and anomalous fixation in evolutionary games on scale-free networks
• Fixation in Evolutionary Games under Non-Vanishing Selection
• Fixation probabilities in populations under demographic fluctuations
• The limits of weak selection and large population size in evolutionary game theory
• Large Fluctuations and Fixation in Evolutionary Games
• Navigating the Landscape of Multiplayer Games
• Fixation in large populations: a continuous view of a discrete problem
• Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games
• Evolutionary games with facilitators: When does selection favor cooperation?
• The prisoners dilemma on a stochastic non-growth network evolution model
• On the stochastic evolution of finite populations
• Frequency-dependent returns in nonlinear public goods games
• Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
• Stationary Stability for Evolutionary Dynamics in Finite Populations
• Large Fluctuations in Anti-Coordination Games on Scale-Free Graphs
• Entropy Rates of the Multidimensional Moran Processes and Generalizations