Abstract
Some cooperative game solutions can be represented with the help of functions measuring a distance between an arbitrary characteristic function (a characteristic function of a cooperative game) and an additive function defined on the players’ power set. In contrast to such ‘utilitarian’ solutions there are ‘egalitarian’ ones minimizing the maximal difference between the values of these functions, and their lexicographic extensions.
In this paper we use such an approach to cooperative games with or without transferable utilities (TU and NTU) and with non-empty cores. A new egalitarian solution called a lexicographical maxmin core solution (LMCS) is defined. It assigns to each cooperative game the payoff vector defined by the lexicographic maximization of minimal components of the vectors from the core. Axiomatization of the LMCS, both for TU and NTU games, is given. It turns out that for convex TU games, the LMCS coincides with the Dutta egalitarian solution.
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
Dutta, B. (1990): “The Egalitarian Solution and the Reduced Game Properties in Convex Games,” International Journal of Game Theory, 19, 153–169.
Imai, H. (1983): “Individual Monotonicity and Lexicographical Maxmin Solutions,” Economerica, 51, 389–402.
Keiding, H. (1986): “An Axiomatization of the Core of a Cooperative Game,” Economic Letters, 20, 111–115.
Myerson, R. (1977): “Two-player Bargaining Problems and Comparable Utility,” Econometrica, 45, 1631–1637.
Roberts, K. W. S. (1980): “Possibility Theorems with Interpersonally Comparable Welfare Levels,” Review of Economic Studies, 47, 409–420.
Sen, A. K. (1971): “Choice Functions and Revealed Preference,” Review of Economic Studies, 38, 307–317.
Yanovskaya, E. (1985): “Axiomatic Derivation of Maxmin and Lexicographically Maxmin Solutions to Bargaining Problems,” Avtomatika i Telemechanika, 9, 128–136. (in Russian.)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yanovskaya, E. (1997). Lexicographical Maxmin Core Solutions for Cooperative Games. In: Tangian, A., Gruber, J. (eds) Constructing Scalar-Valued Objective Functions. Lecture Notes in Economics and Mathematical Systems, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48773-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-48773-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63061-6
Online ISBN: 978-3-642-48773-6
eBook Packages: Springer Book Archive