Skip to main content
SpringerLink
Log in

Equilibria of the Games in Choice Form

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Equilibrium in choice is a solution-concept for noncooperative games defined in a general framework—the game in choice form. There are two leading ideas of the new definition. One is that the players’ preferences need not be explicitly represented, but earlier accepted solution concepts should be formally derived as particular cases. Secondly, the choice of a player need not be a best reply to the strategy combination of the others, if the choices of the other players are motivated for themselves and a best reply does not exist.

It is shown that in the present framework are included classical models of game theory, and the new concept extends various known noncooperative solutions. The main technical results of the paper concern the existence of the equilibrium in choice. As particular cases, known results on the existence of classical solutions are found. Thus, our approach can be also seen as a general method for proving the existence of different solutions for noncooperative games.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Nash, J.F.: Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 36, 48–49 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  2. Nash, J.F.: Noncooperative games. Ann. Math. 54, 286–295 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  3. Shafer, W., Sonnenschein, H.: Equilibrium in abstract economies without ordered preferences. J. Math. Econ. 2, 345–348 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  4. Stefanescu, A., Ferrara, M.: Implementation of voting operators. J. Math. Econ. 42, 315–324 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Debreu, G.: A social equilibrium existence theorem. Proc. Natl. Acad. Sci. USA 38, 386–393 (1952)

    Article  MathSciNet  Google Scholar 

  6. Fan, K.: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. USA 38, 121–126 (1952)

    Article  MATH  Google Scholar 

  7. Fan, K.: Some properties of convex sets related to fixed point theorems. Math. Ann. 266, 519–537 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  8. Parthasarathy, K.R.: Probability Measures on Metric Spaces. AMS, Providence (2005)

    MATH  Google Scholar 

  9. Nikaido, H., Isoda, K.: Note on noncooperative convex games. Pac. J. Math. 5, 807–815 (1955)

    MathSciNet  Google Scholar 

  10. Browder, F.E.: The fixed point theory of multi-valued mappings in topological vector spaces. Math. Ann. 177, 283–301 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tan, K.-K., Yu, J., Yuan, X.-Z.: Existence theorems of Nash equilibria for non-cooperative N-person games. Int. J. Game Theory 24, 217–222 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Köthe, G.: Topological Vector Spaces I. Springer, Berlin (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Bucharest, Bucharest, Romania

    Anton Stefanescu

  2. Department SSGES, University “Mediterranea” of Reggio Calabria, Reggio Calabria, Italy

    Massimiliano Ferrara

  3. Academy of Economic Studies, Bucharest, Romania

    Maria Viorica Stefanescu

Authors
  1. Anton Stefanescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Massimiliano Ferrara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria Viorica Stefanescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anton Stefanescu.

Additional information

Communicated by Irinel Chiril Dragan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stefanescu, A., Ferrara, M. & Stefanescu, M.V. Equilibria of the Games in Choice Form. J Optim Theory Appl 155, 1060–1072 (2012). https://doi.org/10.1007/s10957-012-0093-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-012-0093-7

Keywords

Search

Navigation