@article{9d51c2aecf21484eb269650fa37b6520,
title = "A nested family of k -total effective rewards for positional games",
abstract = "We consider Gillette{\textquoteright}s two-person zero-sum stochastic games with perfect information. For each k∈ N= \{ 0 , 1 , … \} 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.",
keywords = "Cyclic games, Mean payoff, Stochastic game with perfect information, Total reward, Two-person, Zero-sum",
author = "Endre Boros and Khaled Elbassioni and Vladimir Gurvich and Kazuhisa Makino",
note = "Funding Information: We thank the two anonymous reviewers for the careful reading and many helpful remarks. Part of this research was done at the Mathematisches Forschungsinstitut Oberwolfach during a stay within the Research in Pairs Program from July 26 to August 15, 2015. This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan. The first author also thanks the National Science Foundation (Grant IIS-1161476). Publisher Copyright: {\textcopyright} 2016, Springer-Verlag Berlin Heidelberg.",
year = "2017",
month = mar,
day = "1",
doi = "10.1007/s00182-016-0532-z",
language = "British English",
volume = "46",
pages = "263--293",
journal = "International Journal of Game Theory",
issn = "0020-7276",
publisher = "Springer Verlag",
number = "1",
}