 The Replicator Dynamics. Suppose each player selects someone else from the population at random (with all individuals equally likely to be selected), and compares their payoff in the last round of play with the payoff earned by the person selected. If the person selected received a higher payoff, then the player adopts the strategy used by the person selected with a probability proportional to the payoff difference. Schlag (1998) showed that this learning rule yields the replicator dynamics.