# Expected Dynamics of an Intra-Population Imitation Model for Inter-Population 2x2 Symmetric Games

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Consider two distinct populations with the same number of individuals . At each iteration (of time length ), all individuals are randomly matched in pairs made up of one individual from each population to play a symmetric 2×2 game. The two possible actions (or pure strategies) in the game are labeled and . Thus, each individual (regardless of the population to which it belongs) is either an -strategist or a -strategist. The payoffs of the game are , , , and (parameters), where, for instance, denotes the payoff obtained by an -strategist when he plays with a -strategist.

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Contributed by: Luis R. Izquierdo and Segismundo S. Izquierdo (May 2010)

Open content licensed under CC BY-NC-SA

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Reference

[1] S. S. Izquierdo and L. R. Izquierdo, "Stochastic Approximation to Understand Simple Simulation Models," *Journal of Statistical Physics*, Dec 2012. dx.doi.org/10.1007/s10955-012-0654-z