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Determining the Optimal Strategies for Antagonistic Positional Games in Markov Decision Processes

  • Dmitrii Lozovanu
  • Stefan Pickl
Conference paper
Part of the Operations Research Proceedings book series (ORP)

Abstract

A class of stochastic antagonistic positional games for Markov decision processes with average and expected total discounted costs’ optimization criteria are formulated and studied. Saddle point conditions in the considered class of games that extend saddle point conditions for deterministic parity games are derived. Furthermore, algorithms for determining the optimal stationary strategies of the players are proposed and grounded.

Keywords

Nash Equilibrium Payoff Function Markov Decision Process Stationary Strategy Markov Decision Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. International Journal of Game Theory 8, 109–113 (1979)CrossRefGoogle Scholar
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    Lozovanu, D.: The game-theoretical approach to Markov decision problems and determining Nash equilibria for stochastic positional games. Int. J. Mathematical Modelling and Numerical Optimization 2(2), 162–164 (2011)CrossRefGoogle Scholar
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    Lozovanu, D., Pickl, S.: Discrete control and algorithms for solving antagonistic dynamic games on networks. Optimization 58(6), 665–683 (2009)CrossRefGoogle Scholar
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    Lozovanu, D., Pickl, S., Kropat, E.:Markov decision processes and determining Nash equilibria for stochastic positional games. Proceedings of 18th World Cogress IFAC-2011, 320–327 (2011)Google Scholar
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    Puterman, M.: Markov Decision Processes: Stochastic Dynamic Programming. John Wiley, New Jersey (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChisinauMoldova
  2. 2.Institute for Theoretical Computer Science, Mathematics and Operations ResearchUniversität der Bundeswehr MünchenNeubiberg-MünchenGermany

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