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# An Imitation Model for 2x2 Symmetric Games

The figure shows the proportion of -strategists () in a population of individuals who, at each time step, are randomly matched in pairs to play a symmetric 2×2 game. The two possible actions (or pure strategies) in the game are labeled and . Thus, each individual in the population 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 revises her strategy— or —according to the following rule: "I look at another (randomly selected) individual; if and only if she got a payoff higher than mine, I adopt her strategy". The initial proportion of -strategists in the population is the parameter .

### DETAILS

Hawk–Dove game in a population of individuals ( denotes the Hawk strategy and denotes the Dove strategy).
Snapshot 1:
Snapshot 2:
Snapshot 3: Prisoner's Dilemma game in a population of 1000 individuals ( 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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