SOME TOPICS IN TWO-PERSON GAMES

Abstract : Several loosely-related essays on the theory of finite, two-person games are presented. The topics covered are: (1) the block decomposition of symmetric games; (2) saddle points in matrices having submatrices with saddle points; (3) generalized saddle points and 'order matrices'; (4) the existence of values in games with almost perfect information; and (5) the nonconvergence of 'fictitious play' in non-zero-sum games. Throughout, there is an emphasis on features of the theory that depend only on the ordering of the payoffs, as opposed to their numerical values.