Genetic Learning in Evolutionary Games

Abstract

Whereas the previous chapter was dedicated to the analytical examination of the dynamic properties of GAs in SDF systems, the following two chapters will deal with different specific applications. The purpose is to demonstrate how the combination of numerical experiments and the application of mathematical theory may lead to a sound understanding of the process in certain models. In this chapter we deal with GA learning in evolutionary games¹. The theory of evolutionary games was first developed for biological models, but has attracted more and more attention of economists in the last few years. It deals with situations where individuals get some payoff from their interaction with other members of the same population. In general, it is assumed that all individuals have the same set of strategies at their disposal, and that the payoff they receive depends only on the own strategy and the opponent’s strategy. For two-player games the payoffs can be written down in a payoff matrix and a game given by the set of strategies and the payoff matrix is called a normal form game. A game is an evolutionary game if the payoff of an individual is independent from the fact whether he is the first or the second player in the game. Thus, for every evolutionary game the payoff matrix of the second player is the transpose of the payoff matrix of the first player. In some cases it is assumed that each individual meets only one opponent in each period, where the matching is done randomly. Another possible setup is that every individual plays all other individuals in each period. In what follows it is assumed that the second setup holds, which implies that each individual plays against a virtual player who plays a mixed strategy corresponding to the population distribution.