A finite step algorithm via a bimatrix game to a single controller non-zero sum stochastic game

A finite step algorithm via a bimatrix game to a single controller non-zero sum stochastic game

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Article ID: iaor19942322
Country: Netherlands
Volume: 59
Issue: 2
Start Page Number: 249
End Page Number: 259
Publication Date: Apr 1993
Journal: Mathematical Programming (Series A)
Authors: ,
Abstract:

Given a non-zero sum discounted stochastic game with finitely many states and actions one can form a bimatrix game whose pure strategies are the pure stationary strategies of the players and whose penalty payoffs consist of the total discounted costs over all states at any pure stationary pair. It is shown that any Nash equilibrium point of this bimatrix game can be used to find a Nash equilibrium point of the stochastic game whenever the law of motion is controlled by one player. The theorem is extended to undiscounted stochastic games with irreducible transitions when the law of motion is controlled by one player. Examples are worked out to illustrate the algorithm proposed.

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