CHANCE-CONSTRAINED GAMES WITH PARTIALLY CONTROLLABLE STRATEGIES.
Systems research memo.,
NORTHWESTERN UNIV EVANSTON ILL TECHNOLOGICAL INST
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The paper is directed at the investigation of relationships of chance-constrained programming to problems in game theory. The model introduced and analyzed herein is a two-person game model with zero-sum payoff matrix in which the strategies selected by the players do not in themselves determine the payoffs, but in which random perturbations with known distributions modify the strategy of each player before actual implementation of the strategies. A major hypothesis is that, while the strategy perturbations may be random vectors with known distributions, the selection of strategies or more accurately strategy policies is to be made before any observations of the random variables are made so that the strategies chosen are to be zero-order decision functions of the random perturbations, in the customary terminology of chance-constrained programming. The strategy selected by each player is to be chosen to extremize that payoff which the player can be assured with at least some a priori specified probability. The point of departure in formulation and analysis of the model is a chance-constrained version of the two dual linear-programming problems which characterize an ordinary zero-sum two-person game. A key result shows that the deterministic equivalents for these problems yield an equivalent deterministic two-person game which is not zero-sum, and that a pair of optimal strategies for the original game are given by an equilibrium point for the latter. Author
- Operations Research