Replicator Dynamics

The replicator equation is a game dynamic that has become an essential tool in evolutionary game theory. It helps to show the growth rate of the proportion of agents using a certain strategy, and this growth rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole. The replicator model consists of three primary elements: agent types, which represent a particular strategy and have an associated payoff; a parameter representing how many of each type there is in the population; and rules for agent decision-making, such as copying others or selecting successful strategies. The replicator equation is one way to capture the dynamics of evolutionary games and see which strategies become more prevalent over time. However, it assumes large homogeneous populations with random interactions and does not incorporate mutation.