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.

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".