Optimal threat strategies of bimatrix games |
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Authors: | Guillermo Owen |
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Institution: | 1. Department of Mathematical Sciences, Rice-University, Houston, Texas
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Abstract: | A bi-matrix threat game is defined as a triple (A,B,S) whereA andB arem×n payoff matrices, andS is a closed convex subset of the plane, with (a ij,B ij) εS for eachi,j. Given (threat) mixed strategiesx andy,Nash's model suggests that the eventual outcome will be that point (u, v) εS which maximizes the product (u ?xAy t) (v ?xBy t) subject tou ≥xAy t,v ≥xBy t. Optimality of the threat strategies is then defined in the obvious way. A constructive proof of existence of optimal threat strategies is given; in particular, it is shown that they are optimal strategies for the matrix gameA-kB, wherek is to be determined. In this paper,k is approximated by aNewton-Raphson technique. Two examples are solved in detail. |
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