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A nested family of $$\varvec{k}$$ k -total effective rewards for positional games


  • Endre Boros

    (Rutgers University)

  • Khaled Elbassioni

    () (Masdar Institute of Science and Technology)

  • Vladimir Gurvich

    (Rutgers University
    National Research University, Higher School of Economics)

  • Kazuhisa Makino

    (Research Institute for Mathematical Sciences (RIMS) Kyoto University)


Abstract We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each $$k \in \mathbb {N}=\{0,1,\ldots \}$$ k ∈ N = { 0 , 1 , … } we introduce an effective reward function, called k-total. For $$k = 0$$ k = 0 and 1 this function is known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case. For all k, we prove the existence of a saddle point which can be realized by uniformly optimal pure stationary strategies. We also demonstrate that k-total reward games can be embedded into $$(k+1)$$ ( k + 1 ) -total reward games.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0532-z
    DOI: 10.1007/s00182-016-0532-z

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    References listed on IDEAS

    1. Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino, 2013. "On Canonical Forms for Zero-Sum Stochastic Mean Payoff Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 128-161, June.
    2. N. N. Pisaruk, 1999. "Mean Cost Cyclical Games," Mathematics of Operations Research, INFORMS, vol. 24(4), pages 817-828, November.
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