Ann Oper Res https://doi.org/10.1007/s10479-018-2898-8 S.I.: STOCHASTIC MODELING AND OPTIMIZATION, IN MEMORY OF ANDRÁS PRÉKOPA Markov decision processes and stochastic games with total effective payoff 1 2 Endre Boros · Khaled Elbassioni · 3 4 Vladimir Gurvich · Kazuhisa Makino © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We consider ﬁnite Markov decision processes with undiscounted total effective payoff. We show that there exist uniformly optimal pure and stationary strategies that can be computed by solving a polynomial number of linear programs. This implies that in a two- player zero-sum stochastic game with perfect information and with total effective payoff there exists a stationary best response to any stationary strategy of the opponent. From this, we derive the existence of a uniformly optimal pure and stationary saddle point. Finally we show that mean payoff can be viewed as a special case of total payoff. Keywords Markov decision processes · Stochastic games · Linear programming · Optimal stationary strategies · Equilibrium computation This research was partially supported by the Scientiﬁc Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan. The ﬁrst author also thanks for partial support the National Science Foundation (Grant and IIS-1161476). The research
Annals of Operations Research – Springer Journals
Published: May 28, 2018
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