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Статья

A nested family of k-total effective rewards for positional games

International Journal of Game Theory. 2017. Vol. 46. No. 1. P. 263-293.
Boros E., Elbassioni K., Gurvich V., Makino K.

We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each k∈N={0,1,…}k∈N={0,1,…} we introduce an effective reward function, called k-total. For k=0k=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.