Infinite Linear Programming in Games with Partial Information

W. D. Cook, C. A. Field and M. J. L. Kirby
Additional contact information
W. D. Cook: York University, Toronto, Ontario
C. A. Field: Dalhousie University, Halifax, Nova Scotia
M. J. L. Kirby: Dalhousie University, Halifax, Nova Scotia

Operations Research, 1975, vol. 23, issue 5, 996-1010

Abstract: An area of considerable recent research interest has involved the extension and modification of the basic model for two-person zero-sum game theory. One particular type of extension found in the literature involves the introduction of risk and uncertainty into the model by allowing the m × n payoff matrix A = ( a ij ) to be a discrete random matrix that can assume a finite set of values. This paper considers both one- and two-person games and investigates the situation in which A is a discrete random matrix that can assume a countably infinite set of values { A ( k )} k =1 ∞ . We assume that the players possess certain partial information about P , the distribution of A , in which case the game problems for players 1 and 2 can be reduced to programming equivalents. We prove minimax theorems for both semi-infinite and infinite games, and give some properties of optimal mixed strategies. The paper also develops some extensions of a theorem due to Caratheodory.

Date: 1975
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