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Infinite Linear Programming in Games with Partial Information

Author

Listed:
  • W. D. Cook

    (York University, Toronto, Ontario)

  • C. A. Field

    (Dalhousie University, Halifax, Nova Scotia)

  • M. J. L. Kirby

    (Dalhousie University, Halifax, Nova Scotia)

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.

Suggested Citation

  • W. D. Cook & C. A. Field & M. J. L. Kirby, 1975. "Infinite Linear Programming in Games with Partial Information," Operations Research, INFORMS, vol. 23(5), pages 996-1010, October.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:5:p:996-1010
    DOI: 10.1287/opre.23.5.996
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    Cited by:

    1. Archis Ghate & Dushyant Sharma & Robert L. Smith, 2010. "A Shadow Simplex Method for Infinite Linear Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 865-877, August.

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