Some Topics in Continuous Games

Abstract

In Chapter 9 we examined two-person constant sum games with finite numbers of pure strategies. These games can be represented by matrices where the rows designate one player’s pure strategies and the columns the other’s. The number of pure strategies available to each player may be superastronomical (as for example, in chess) so that determining strategies by standard algorithms, such as the simplex method, is out of the question. Limits on the games that can be actually solved in this way need not imply limits on the theoretical conclusions valid for all finite games of a given type. The conclusions do not, however, necessarily hold for games with infinite numbers of strategies.