Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T05:21:50.583Z Has data issue: false hasContentIssue false

Welfarism and Axiomatic Bargaining Theory

Published online by Cambridge University Press:  17 August 2016

John E. Roemer*
Affiliation:
University of California, Davis
Get access

Summary

Consider the domain of economic environments E whose typical element is ξ = (U1, U2, Ω, ω*), where ui are Neumann-Morgenstern utility functions, Ω is a set of lotteries on a fixed finite set of alternatives, and ω* ∈ Ω. A mechanism f associates to each ξ a lottery f(ξ) in Ω. Formulate the natural version of Nash’s axioms, from his bargaining solution, for mechanisms on this domain. (e.g., IIA says that if ξ′ = (U1, U2, Δ, ω′), Δ ⊂ Ω, and f ∈ Δ then f(ξ′) = f(ξ).) It is shown that the Nash axioms (Pareto, symmetry, IIA, invariance w.r.t. cardinal transformations of the utility functions) hardly restrict the behavior of the mechanism at all. In particular, for any integer M, choose M environments ξi, i = 1, … , M, and choose a Pareto optimal lottery ωi ∈ Ωi, restricted only so that no axiom is directly contradicted by these choices. Then there is a mechanism f for which f(ξi) = ωi, which satisfies all the axioms, and is continuous on E.

Résumé

Résumé

Considérons le domaine E des environnements économiques. ξ = (U1, U2, Ω, ω*) en est l’élément typique où ui, sont des fonctions d’utilité Neumann-Morgenstern, Ω est un ensemble de loteries portant sur un nombre fixe et fini d’alternatives ω* ∈ Ω. Un mécanisme f associe à chaque ξ une loterie f(ξ) de Ω. Formulons pour les mécanismes dans ce domaine une version naturelle des axiomes de Nash. (Par exemple IIA montre que ξ′ = (U1, U2, Δ, ω*), Δ ⊂ Ω, et f ∈ Δ alors f(ξ′) = f(ξ).) Il est montré que ces axiomes restreignent à peine le comportement du mécanisme. En particulier, pour tout nombre entier M, on peut choisir M environnements ξi, i = 1, & , M, ainsi qu’une loterie Pareto-optimale, ωi ∈ Ωi, avec pour seule restriction que ces choix ne contredisent aucun des axiomes. Alors il existe un mécanisme f pour lequel f(ξi) = ωi, satisfaisant tous les axiomes et qui est continu sur E.

Keywords

Type
Research Article
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Binmore, K., Rubinstein, A. and Wolinsky, A. (1986), The Nash Bargaining Solution in Economic Modelling, Rand Journal of Economics, n° 17, pp. 176–88.Google Scholar
Elster, J. (1989), Incentives and Local Justice, conference paper.Google Scholar
Kalai, E. (1985), Solutions to the Bargaining Problem, in: Hurwicz, L., Schmeidler, D. and Sonnenschein, H. (eds.), Social Goals and Social Organization, Cambridge University Press.Google Scholar
Nash, J. (1950), The bargaining problem, Econometrica, n° 28, pp. 155–62.Google Scholar
Roth, A. (1979), Axiomatic Models of Bargaining, New York, Springer Verlag.Google Scholar
Sen, A. (1979), Utilitarianism and Welfarism, Journal of Philosophy, n° 76, pp. 463–89.Google Scholar
Thomson, W. and Lensberg, T. (1989), Axiomatic Theory of Bargaining with a Variable Number of Agents, New York, Cambridge University Press.Google Scholar
Yaari, M. and Bar-Hillel, M. (1984), On Dividing Justly, Social Choice and Welfare, n° 1, pp. 124.Google Scholar