Abstract
Introduced in earlier papers of these authors, the 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. Now the definitions are extended to cover the case of noncooperative games with restricted individual strategies. The main technical results of the paper concern the existence of the equilibrium in choice. As particular cases, known results on the existence of equilibria in some classical game models 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 chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Based on the paper communicated to the 6th World Conference on 21st Century Mathematics by the first author.
References
Aubin, J.-P.: Mathematical Methods of Game Theory and Economic Theory. North Holland, Amsterdam (1982)
Berge, C., Espaces Topologiques et Fonctions Multivoques. Dunod, Paris (1959)
Browder, E.: The fixed point theory of multi-valued mappings in topological vector spaces. Math. Ann. 177, 283–301 (1968)
Debreu, G.: A social equilibrium existence theorem. Proc. Natl. Acad. Sci. U.S.A. 38, 386–393 (1952)
Fan, K.: Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. U.S.A. 38, 121–126 (1952)
Fan, K.: Sur un théorème minimax. C. R. Acad. Sci. Paris 259, 3925–3928 (1964)
Fan, K.: Some properties of convex sets related to fixed point theorems. Math. Ann. 266, 519–537 (1984)
Nash, J.F.: Equilibrium points in n-person games. Proc. Natl. Acad. Sci. U.S.A. 36, 48–49 (1950)
Nash, J.F.: Noncooperative games. Ann. Math. 54, 286–295 (1951)
Shafer, W., Sonnenschein, H.: Equilibrium in abstract economies without ordered preferences. J. Math. Econ. 2, 345–348 (1975)
Stefanescu, M.V., Stefanescu, A.: On the existence of the equilibrium in choice. Math. Rep. 11(61), N.3, 249–258 (2009)
Stefanescu, A., Ferrara, M., Stefanescu, M.V.: Equilibria of the games in choice form. JOTA 155, 1060–1072 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Basel
About this paper
Cite this paper
Ferrara, M., Stefanescu, A. (2015). Equilibrium in Choice of Generalized Games. In: Cartier, P., Choudary, A., Waldschmidt, M. (eds) Mathematics in the 21st Century. Springer Proceedings in Mathematics & Statistics, vol 98. Springer, Basel. https://doi.org/10.1007/978-3-0348-0859-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0859-0_3
Published:
Publisher Name: Springer, Basel
Print ISBN: 978-3-0348-0858-3
Online ISBN: 978-3-0348-0859-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)