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# An Intra-Population Imitation Model for Inter-Population 2x2 Symmetric Games

The figure shows the proportion of -strategists in two distinct populations ( and ) with the same number of individuals . At each time step, all individuals are randomly matched in pairs made up of one individual from population and one individual from 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.
At the end of each time step, after all individuals have played the game, one randomly selected player from each population revises her strategy— or —according to the following rule: "I look at another (randomly selected) individual in my population; if and only if she got a payoff higher than mine, I adopt her strategy". Thus, the game is played between individuals of different populations, but imitation takes place within each population.

### DETAILS

Snapshot 1: Hawk–Dove game with 50 individuals in each population ( denotes the Hawk strategy and denotes the Dove strategy)
Snapshot 2: Coordination game with 50 individuals in each population ( denotes "driving on my left" and D denotes "driving on my right")
Snapshot 3: Prisoner's Dilemma game with 500 individuals in each population ( denotes the cooperative strategy and denotes the defective strategy)
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

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