Abstract
Approximate solutions to optimization problems are characterized by means of properties like consistency, non-emptiness, behaviour w.r.t. inclusion, invariance w.r.t. translation, multiplication.
The authors wish to thank A. Rustichini, P. Wakker and T. Zolezzi for helpful suggestions on earlier versions of this paper. The financial support of CNR-Italy, the GNAFA group of CNR Italy and Tilburg University is gratefully acknowledged.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arrow K. J. (1951), Social Choice and Individual Values. Wiley, New York.
Chernoff H. (1954), Rational selection of decision functions. Econometrica 22: 422–443.
Dontchev A. and Zolezzi T. (1993), Well-posed Optimization Problems. Lecture Notes in Mathematics, 1543, Springer, Berlin.
Jurg P. and Tijs S. (1993), On the determinateness of semi-infinite bimatrix games. Internat. J. Game Theory 21: 361–369.
Kaneko M. (1980), An extension of the Nash bargaining problem and the Nash social welfare function. Theory and Decision 12, 135–148.
Lucchetti R., Patrone F., Tijs S. (1986), Determinateness of twoperson games. Bollettino U.M.I. 6: 907–924.
Nash, J. F. Jr. (1950), The Bargaining Problem. Econometrica 18: 155–162.
Norde H., Patrone F. and Tijs S. (1999), Characterizing Properties of Approximate Solutions to Optimization Problems, Mimeo. To appear in Mathematical Social Sciences.
Norde H. and Potters J. (1997), On the determinateness of m × ∞-bimatrix games. Mathematics of Operations Research 22: 631–638.
Patrone F. (1987), Well-Posedness as an Ordinal Property. Rivista di Matematica pura ed applicata 1: 95–104.
Patrone F., Pieri G., Tijs S. and Torre A. (1998), On Consistent Solutions for Strategic Games. Internat. J. Game Theory, 27: 191–200.
Peleg B. and Tijs S. (1996), The Consistency Principle for Games in Strategic Form. Internat. J. Game Theory 25: 13–34.
Peters H. (1992), Axiomatic bargaining game theory. Kluwer Academic Publishers, Dordrecht.
Radner R. (1980), Collusive behavior in non-cooperative epsilon equilibria of oligopolies with long but finite lives. Journal of Economic Theory, 22: 121–157.
Shapley L. S. (1953), A Value for n-Person Games. In: Contributions to the Theory of Games II, (eds.: Kuhn H. W. and Tucker A. W.). Annals of Math. Studies, 28, Princeton University Press, Princeton (NJ): 307–317.
Tijs S. (1981), Nash equilibria for noncooperative n-person games in normal form. SIAM Review 23: 225–237.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this chapter
Cite this chapter
Norde, H., Patrone, F., Tijs, S. (2004). Axiomatization for Approximate Solutions in Optimization. In: Giannessi, F., Maugeri, A., Pardalos, P.M. (eds) Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models. Nonconvex Optimization and Its Applications, vol 58. Springer, Boston, MA. https://doi.org/10.1007/0-306-48026-3_13
Download citation
DOI: https://doi.org/10.1007/0-306-48026-3_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-0161-1
Online ISBN: 978-0-306-48026-3
eBook Packages: Springer Book Archive