Stochastic Evolutionary Game Dynamics

Game theory is often described as the study of interactive decision-making by rational agents. However, there are numerous applications of game theory where the agents are not fully rational, yet many of the conclusions remain valid. A case in point is biological competition between species, a topic pioneered by Maynard Smith and Price (1973). In this setting the ‘agents’ are representatives of different species that interact and receive payoffs based on their strategic behaviour, whose strategies are hard-wired rather than consciously chosen. The situation is a game because a given strategy’s success depends upon the strategies of others. The dynamics are not driven by rational decision-making but by mutation and selection: successful strategies increase in frequency compared to relatively unsuccessful ones. An equilibrium is simply a rest point of the selection dynamics. Under a variety of plausible assumptions about the dynamics, it turns out that these rest points are closely related (though not necessarily identical) to the usual notion of Nash equilibrium in normal form games (Weibull, 1995; Nachbar, 1990; Ritzberger and Weibull, 1995; Sandholm, 2010, particularly Ch. 5).