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Nonlinear programming and stationary equilibria in stochastic games

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Abstract

Stationary equilibria in discounted and limiting average finite state/action space stochastic games are shown to be equivalent to global optima of certain nonlinear programs. For zero sum limiting average games, this formulation reduces to a linear objective, nonlinear constraints program, which finds the “best” stationary strategies, even whenε-optimal stationary strategies do not exist, for arbitrarily smallε.

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The work of the first author was supported in part by the Air Force Office of Scientific Research, and by the National Science Foundation under Grant No ECS-8704954.

The work of the third author was supported by The Netherlands Organization for Scientific Research NWO, project 10-64-10.

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Filar, J.A., Schultz, T.A., Thuijsman, F. et al. Nonlinear programming and stationary equilibria in stochastic games. Mathematical Programming 50, 227–237 (1991). https://doi.org/10.1007/BF01594936

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  • DOI: https://doi.org/10.1007/BF01594936

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