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Total Reward Stochastic Games and Sensitive Average Reward Strategies

Author

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  • F. Thuijsman

    (aastricht University)

  • O. J. Vrieze

    (Maastricht University)

Abstract

In this paper, total reward stochastic games are surveyed. Total reward games are motivated as a refinement of average reward games. The total reward is defined as the limiting average of the partial sums of the stream of payoffs. It is shown that total reward games with finite state space are strategically equivalent to a class of average reward games with an infinite countable state space. The role of stationary strategies in total reward games is investigated in detail. Further, it is outlined that, for total reward games with average reward value 0 and where additionally both players possess average reward optimal stationary strategies, it holds that the total reward value exists.

Suggested Citation

  • F. Thuijsman & O. J. Vrieze, 1998. "Total Reward Stochastic Games and Sensitive Average Reward Strategies," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 175-196, July.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:1:d:10.1023_a:1022697100194
    DOI: 10.1023/A:1022697100194
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    References listed on IDEAS

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    1. Truman Bewley & Elon Kohlberg, 1978. "On Stochastic Games with Stationary Optimal Strategies," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 104-125, May.
    2. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
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    Cited by:

    1. Endre Boros & Paolo Giulio Franciosa & Vladimir Gurvich & Michael Vyalyi, 2024. "Deterministic n-person shortest path and terminal games on symmetric digraphs have Nash equilibria in pure stationary strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 449-473, June.
    2. Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino, 2017. "A nested family of $$\varvec{k}$$ k -total effective rewards for positional games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 263-293, March.

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