An Introduction to Evolutionary Games

In an evolutionary game, players are interpreted as populations – of animals or individuals. The probabilities in a mixed strategy of a player in a bimatrix game are interpreted as shares of the population. Individuals within the same part of the population play the same pure strategy. The main ‘solution’ concept is the concept of an evolutionary stable strategy.

Evolutionary game theory originated in the work of the biologists Maynard Smith and Price [77]. Taylor and Jonker [133] and Selten [120], among others, played an important role in applying the developed evolutionary biological concepts to boundedly rational human behavior, and to establish the connection with dynamic systems and with game-theoretic concepts like Nash equilibrium. A relatively recent and comprehensive overview can be found in Weibull [147].

This chapter presents a short introduction to evolutionary game theory. For a somewhat more advanced continuation see Chap. 15.

In Sect. 8.1 we consider symmetric two-player games and evolutionary stable strategies. Evolutionary stability is meant to capture the idea of mutation from the theory of evolution. We also establish that an evolutionary stable strategy is part of a symmetric Nash equilibrium. In Sect. 8.2 the connection with the so-called replicator dynamics is studied. Replicator dynamics intends to capture the evolutionary idea of selection based on fitness. In Sect. 8.3 asymmetric games are considered. Specifically, a connection between replicator dynamics and strict Nash equilibrium is discussed.