Finite Two-Person Games

In this chapter we consider two-player games where each player chooses from finitely many pure strategies or randomizes among these strategies. In contrast to Chap. 2 it is no longer required that the sum of the players’ payoffs is zero (or, equivalently, constant). This allows for a much larger class of games, including many games relevant for economic or other applications. Famous examples are the ‘Prisoners’ Dilemma’ and the ‘Battle of the Sexes’ discussed in Sect. 1.3.2.

In Sect. 3.1 we introduce the model and the concept of ‘Nash equilibrium’. Section 3.2 shows how to compute Nash equilibria in pure strategies for arbitrary games, all Nash equilibria in games where both players have exactly two pure strategies, and how to use the concept of strict domination to facilitate computation of Nash equilibria and to compute equilibria also of larger games. The structure of this chapter thus parallels the structure of Chap. 2. For a deeper and more comprehensive analysis of finite two-person games see Chap. 13.