ABSTRACT
In this chapter we cover the theory of matrix games. Matrix games are perhaps the simplest type of game, representing independent contests between pairs of individuals where payoffs are linear functions of the (mixed) strategy choices of the players, and so the game can be represented by a payoff matrix. Examples are the Hawk-Dove and Prisoner's Dilemma games from Chapter 4. We show how to find all of the Evolutionarily Stable Strategies (ESSs) of any given matrix in a systematic way. We then look at the possible combinations of ESSs that can occur, through the study of patterns of ESSs. Finally we look at some specific examples of matrix games which are developments of the Hawk-Dove game.
