Abstract
I argue in this paper that there are two considerations which govern the dynamics of a two-person bargaining game, viz. relative proportionate utility loss from conceding to one's opponent's proposal and relative non-proportionate utility loss from not conceding to one's opponent's proposal, if she were not to concede as well. The first consideration can adequately be captured by the information contained in vNM utilities. The second requires measures of utility which allow for an interpersonal comparison of utility differences. These considerations respectively provide for a justification of the Nash solution and the Kalai egalitarian solution. However, none of these solutions taken by themselves can provide for a full story of bargaining, since, if within a context of bargaining one such consideration is overriding, the solution which does not match this consideration will yield unreasonable results. I systematically present arguments to the effect that each justification from self-interest for respectively the Nash and the Kalai egalitarian solution is vulnerable to this kind of objection. I suggest that the search for an integrative model may be a promising line of research.
Similar content being viewed by others
References
Barry, B.: 1979, ‘Don't Shoot the Trumpeter - He's Doing His Best’, Theory and Decision 11, 153–180.
Bartos, I. J.: 1967, Simple Models of Group Behavior (Columbia University Press, London).
Hamburger, H.: 1979, Games as Models of Social Phenomena (Freeman, San Francisco).
Harsanyi, J.: 1977, Rational Behavior and Bargaining Equilibrium in Games and Social Situations (Cambridge University Press, Cambridge).
Kalai, E. and Smorodinsky, M.: 1975, ‘Other Solutions to Nash's Bargaining Problem’, Econometrica 43, 513–518.
Kalai, E.: 1977, ‘Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons’, Econometrica 45, 1623–1630.
Kalai, E.: 1983, ‘Solutions to the Bargaining Problem’, in Hurwicz, Schmeidler and Sonnenschein, Social Goals and Social Organisation (forthcoming) (references to: Discussion paper No. 556, Department of Managerial Economics and Decision Sciences. Northwestern University, March 1983).
Kalai, E. and Samet, D.: 1985, ‘Monotonic Solutions to General Cooperative Games’, Econometrica 53, 307–327.
Luce and Raiffa: 1957, Games and Decisions (John Wiley and Sons, New York).
Nash, J.: 1950, ‘The Bargaining Problem’, Econometrica 18, 155–162.
Rawls, J.: 1971, A Theory of Justice (Harvard University Press, Cambridge, MA).
Roemer, J. E.: 1984, The Mismarriage of Bargaining Theory and Distributive Justice, Working Paper Series, No. 253, Dept. of Economics, University of California, Davis (Ethics 79, (1986)).
Sen, A.: 1970, Collective Choice and Welfare (Holden-Day, San Francisco).
Author information
Authors and Affiliations
Additional information
I am grateful to Jon Elster, A. Hylland, F. Spinnewijn, J. Verhoeven and the members of the research group for theoretical sociology in the K.U.L. for their comments on an earlier version of this paper. I also thank the Ministry for Foreign Affairs (Norway) for its financial support and the members of the department of sociology in the University of Oslo for their hospitality and interest in my work.
Rights and permissions
About this article
Cite this article
Bovens, L. On arguments from self-interest for the Nash solution and the Kalai egalitarian solution to the bargaining problem. Theor Decis 23, 231–260 (1987). https://doi.org/10.1007/BF00129149
Issue Date:
DOI: https://doi.org/10.1007/BF00129149