Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
On the Push&Pull Protocol for Rumour Spreading Read chapter Read first chapter

2017 | OriginalPaper | Chapter

The Asymptotic Value in Finite Stochastic Games

Author : Miquel Oliu-Barton

Published in: Extended Abstracts Summer 2015

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In 1976, Bewley and Kohlberg proved that the discounted values v λ of finite zero-sum stochastic games have a limit, as λ tends to 0, using the Tarski–Seidenberg elimination theorem from real algebraic geometry. This was a fundamental step in the development of the theory of stochastic games. The current paper provides a new and direct proof for this result, relying on the explicit description of asymptotically optimal strategies. Both approaches can be used to obtain the existence of the uniform value using the construction from Mertens and Neyman (1981).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Population Protocols for Majority in Arbitrary Networks
next chapter Almost All 5-Regular Graphs Have a 3-Flow
Footnotes
1
Theorem 1 is stated in this form in [4].
 
2
\(\Phi \) is the Shapley operator, defined in (1).
 
Literature
1.
T. Bewley and E. Kohlberg, “The asymptotic theory of stochastic games”, Mathematics of Operation Research 1 (1976), 197–208.
2.
J. Bolte, S. Gaubert, and G. Vigeral, “Definable zero-sum stochastic games”, Math. Oper. Res. 40 (1) (2015), 171–191.
3.
J.F. Mertens and A. Neyman, “Stochastic games”, International Journal of Game Theory 10 (1981), 53–66.
4.
J.F. Mertens, A. Neyman, and D. Rosenberg, “Absorbing games with compact action spaces”, Mathematics of Operation Research 34 (2009), 257–262.
5.
L.S. Shapley, “Stochastic games”, Proc. Nat. Acad. Sci. 39 (1953), 1095–1100.
6.
E. Solan and N. Vieille, “Computing uniformly optimal strategies in two-player stochastic games”, Econ. Theory 42 (2010), 237–253.
7.
G. Vigeral, “A zero-sum stochastic game with compact action sets and no asymptotic value”, Dynamic Games and Applications 3 (2) (2013), 172–186.
8.
B. Ziliotto, “Zero-sum repeated games: counterexamples to the existence of the asymptotic value and the conjecture \(\mathop{\mathrm{maxmin}}\nolimits =\mathop{ \mathrm{lim}}\nolimits v_{n}\)”, Ann. Probab. 44 (2) (2016), 1107–1133.
Metadata
Title
The Asymptotic Value in Finite Stochastic Games
Author
Miquel Oliu-Barton
Copyright Year
2017
Book
Extended Abstracts Summer 2015

Print ISBN: 978-3-319-51752-0

Electronic ISBN: 978-3-319-51753-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-51753-7_14

Premium Partner

    Image Credits