Expected Dynamics of an Imitation Model in 2x2 Symmetric Games
The figure shows the actual (in blue) and expected (in black) proportion of -strategists in a population of individuals who, at each iteration (of time length ), 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.[more]
At the end of each iteration, 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".[less]
The first three Snapshots show the Hawk-Dove game in a population of individuals ( denotes the Hawk strategy and denotes the Dove strategy).
The last three Snapshots show the Prisoner's Dilemma game in a population of individuals ( denotes the cooperative strategy and denotes the defective strategy).
 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. Download preprint.