Expected Dynamics of an Imitation Model in 2x2 Symmetric Games
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.
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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".
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