On the stability of a class of noncooperative games |
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Authors: | Charles G Bird |
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Institution: | Mathematics Department General Motors Research Laboratories Warren, Michigan, USA 48090 |
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Abstract: | The Nash equilibrium of a class of games generated from a market is examined. Demands are assumed linear, and production constraints are imposed. The equilibrium is shown to be solvable as a complementarity problem. If the demand matrix is a positive definite symmetric z-matrix, then the Nash equilibrium is stable. If the demand matrix is not symmetric, an additional condition yielding stability is developed. |
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