An epistemic approach to stochastic games
Andrés Perea () and
Additional contact information
Andrés Perea: Maastricht University
International Journal of Game Theory, 2019, vol. 48, issue 1, No 8, 203 pages
Abstract In this paper we focus on stochastic games with finitely many states and actions. For this setting we study the epistemic concept of common belief in future rationality, which is based on the condition that players always believe that their opponents will choose rationally in the future. We distinguish two different versions of the concept—one for the discounted case with a fixed discount factor $$\delta ,$$ δ , and one for the case of uniform optimality, where optimality is required for all discount factors close enough to 1” . We show that both versions of common belief in future rationality are always possible in every stochastic game, and always allow for stationary optimal strategies. That is, for both versions we can always find belief hierarchies that express common belief in future rationality, and that have stationary optimal strategies. We also provide an epistemic characterization of subgame perfect equilibrium for two-player stochastic games, showing that it is equivalent to mutual belief in future rationality together with some “correct beliefs assumption”.
Keywords: Epistemic game theory; Stochastic games; Common belief in future rationality (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s00182-018-0644-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:48:y:2019:i:1:d:10.1007_s00182-018-0644-8
Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2
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 ().