A nested family of $$\varvec{}$$-total effective rewards for positional games |
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Authors: | Endre Boros Khaled Elbassioni Vladimir Gurvich Kazuhisa Makino |
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Institution: | 1.MSIS Department and RUTCOR,Rutgers University,Piscataway,USA;2.Masdar Institute of Science and Technology,Abu Dhabi,UAE;3.National Research University, Higher School of Economics,Moscow,Russia;4.Research Institute for Mathematical Sciences (RIMS) Kyoto University,Kyoto,Japan |
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Abstract: | We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each \(k \in \mathbb {N}=\{0,1,\ldots \}\) we introduce an effective reward function, called k-total. For \(k = 0\) 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 \((k+1)\)-total reward games. |
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