2. Noncooperative Finite Games: Two-Person Zero-Sum

2.1 Introduction This chapter deals with the class of two-person zero-sum games in which the players have a finite number of alternatives to choose from. There exist two different formulations for such games: the normal (matrix) form and the extensive (tree) form. The former constitutes a suitable representation of a zero-sum game when each player's information is static in nature, since it suppresses all the dynamic aspects of the decision problem. The extensive form, on the other hand, displays explicitly the evolution of the game and the existing information exchanges between the players. In the first part of the chapter (Sections 2.2 and 2.3), the normal form is introduced together with several related concepts, and then existence and computation of saddle-point equilibria are discussed for both pure and mixed strategies. In the second part of the chapter (Sections 2.4 and 2.5), extensive form description for zero-sum finite games without chance moves is introduced, and saddle-point equilibria for such games are discussed, also within the class of behavioral strategies. This discussion is first confined to single-act games in which each player is allowed to act only once, and then it is extended to multi-act games.