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Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only recently evolutionarily stable strategies were defined for multi-player games and their properties analyzed (Broom et al., 1997). Here we study the long-run behavior of stochastic dynamics of populations of randomly matched individuals playing symmetric three-player games. We analyze stochastic stability of equilibria in games with multiple evolutionarily stable strategies. We also show that in some games, a population may not evolve in the long run to an evolutionarily stable equilibrium.
We discuss long-run behavior of stochastic dynamics of many interacting agents. In particular, three-player spatial games are studied. The effect of the number of players and the noise level on the stochastic stability of Nash equilibria is investigated.
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between two-player an
Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biol
We study the stochastic dynamics of evolutionary games, and focus on the so-called `stochastic slowdown effect, previously observed in (Altrock et. al, 2010) for simple evolutionary dynamics. Slowdown here refers to the fact that a beneficial mutatio
We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. Long-run behavior of stochastic dynamics of spatial games with multiple Nash equilib