Skip to main content
SpringerLink
Log in

Cognitively Stable Generalized Nash Equilibrium in Static Games with Unawareness

  • Conference paper
  • First Online:
Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9376))

Abstract

In game theory, recently models and solution concepts of games with unawareness have been developed. This paper focuses on static games with unawareness and points out a conceptual problem of an existing equilibrium concept called generalized Nash equilibrium. Some generalized Nash equilibria can be cognitively unstable in the sense that, once such an equilibrium is played, some agent may feel that the outcome is unexpected one at some level of someone’s perception hierarchy. This may lead to change in the agent’s perception and thus her behavior. Based on the observation, we characterize a class of generalized Nash equilibrium that satisfies cognitive stability so that it can avoid such a problem. Then we discuss relationships between cognitively sable generalized Nash equilibrium and Nash equilibrium of the objective game, that is, how unawareness can or cannot change the equilibrium convention.

Y. Sasaki—The author thanks two anonymous referees for helpful comments on this paper. This research is supported by KAKENHI Grant-in-Aid for Young Scientists (B) 15K16292.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dekel, E., Lipman, B.L., Rustichini, A.: Standard state-space models preclude unawareness. Econometrica 66(1), 159–173 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Feinberg, Y.: Games with unawareness. Stanford University, Graduate School of Business discussion papers (2012)

    Google Scholar 

  3. Halpern, J.Y., Rêgo, L.C.: Extensive games with possibly unaware players. Mathematical Social Sciences 70, 42–58 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Harsanyi, J.C.: Games with incomplete information played by Bayesian players. Management Science 14, 159–182, 320–334, 486–502 (1967)

    Google Scholar 

  5. Heifetz, A., Meier, M., Schipper, B.C.: Dynamic unawareness and rationalizable behavior. Games and Economic Behavior 81, 50–68 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Karni, E., Vierø, M.L.: “Reverse Bayesianism”: A choice-based theory of growing awareness. The American Economic Review 103(7), 2790–2810 (2013)

    Article  Google Scholar 

  7. Perea, A.: Epistemic Game Theory: Reasoning and Choice. Cambridge University Press (2012)

    Google Scholar 

  8. Sasaki, Y.: Subjective rationalizability in hypergames. Advances in Decision Sciences (2014). doi:10.1155/2014/263615

  9. Sasaki, Y.: Bayesian representation of static games with unawareness. unpublished manuscript (2015)

    Google Scholar 

  10. Schipper, B.C.: Awareness-dependent subjective expected utility. International Journal of Game Theory 42(3), 725–753 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Schipper, B.C.: Unawareness–a gentle introduction to both the literature and the special issue. Mathematical Social Sciences 70, 1–9 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, 1-1, Asahidai, Nomi, Ishikawa, Japan

    Yasuo Sasaki

Authors
  1. Yasuo Sasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yasuo Sasaki .

Editor information

Editors and Affiliations

  1. Science and Technology, Japan Advanced Institute of, Nomi, Japan

    Van-Nam Huynh

  2. Science, Dept of Systems Innovation, Osaka University,Graduate School of, Osaka, Japan

    Masahiro Inuiguchi

  3. Université de Technologie de Compiègne, Compiègne, France

    Thierry Demoeux

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Sasaki, Y. (2015). Cognitively Stable Generalized Nash Equilibrium in Static Games with Unawareness. In: Huynh, VN., Inuiguchi, M., Demoeux, T. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2015. Lecture Notes in Computer Science(), vol 9376. Springer, Cham. https://doi.org/10.1007/978-3-319-25135-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25135-6_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25134-9

  • Online ISBN: 978-3-319-25135-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation