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

Endre Boros, Khaled Elbassioni (), Vladimir Gurvich and Kazuhisa Makino
Additional contact information
Endre Boros: Rutgers University
Khaled Elbassioni: Masdar Institute of Science and Technology
Vladimir Gurvich: Rutgers University
Kazuhisa Makino: Research Institute for Mathematical Sciences (RIMS) Kyoto University

International Journal of Game Theory, 2017, vol. 46, issue 1, No 13, 263-293

Abstract: 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.

Keywords: Stochastic game with perfect information; Cyclic games; Two-person; Zero-sum; Mean payoff; Total reward (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00182-016-0532-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0532-z

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-016-0532-z

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().