Abstract
I present a non-cooperative bargaining game, in which responders may exit at any time and have endogenous outside options. When the order of proposers corresponds to the power that players have in the underlying coalitional function, the unique Markov perfect equilibrium outcome of the game is the prenucleolus. The result holds for 3-player superadditive games. An example shows that it cannot be extented to the same class of games forn players. The mechanism is inspired by the consistency property of the prenucleolus.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Davis M, Maschler M (1965) The kernel of a cooperative game. Naval Research Logistics Quarterly 12:223–259
Hart S, Mas-Colell A (1992) A model ofn-person non-cooperative bargaining. Mimeo, Harvard University
Krishna V, Serrano R (1990) Multilateral bargaining. Working paper 93-23. Department of Economics, Brown University
Maschler M (1992) The bargaining set, kernel and nucleolus: A survey. In: Aumann RJ, Hart S (Eds) Handbook of Game Theory (Vol. I), Elsevier Science Publishers BV
Maskin E, Tirole J (1989) Markov perfect equilibrium. Mimeo, Harvard University
Moulin H (1988) Axioms of cooperative decision making. Cambridge University Press Cambridge
Nash JF (1951) Non-cooperative games. Annals of Mathematics 48:286–295
Nash JF (1953) Two person cooperative games. Econometrica 21:128–140
Peleg B (1986) On the reduced game property and its converse. International Journal of Game Theory 15:187–200
Peters H, Tijs S, Zarzuelo J (1991) Consistency and implementation of the Kalai-Smorodinsky bargaining solution. Mimeo
Schmeidler D (1969) The nucleolus of a characteristic function game. SIAM Journal of Applied Mathematics 17:1163–1170
Serrano R (1991) Non-cooperative implementation of the core. Working paper 92-25, Department of Economics, Brown University
Sobolev AI (1975) The characterization of optimality principles in cooperative games by functional equations (in Russian). In: Vorby'ef NN (Ed) Mathematical Methods in the Social Sciences 6, Academy of Sciences of the Lithuanian SSR, Vilnius 94–151
Thomson W (1990) The consistency principle. In: Ichiishi T, Neyman A, Tauman Y (eds) Game Theory and Applications 187–215. Academic Press, San Diego, CA
Author information
Authors and Affiliations
Additional information
I am grateful to Vijay Krishna, Andreu Mas-Colell, Eric Maskin, Amy Salsbury, and an anonymous referee for helpful comments and suggestions.
Rights and permissions
About this article
Cite this article
Serrano, R. Non-cooperative implementation of the nucleolus: The 3-player case. Int J Game Theory 22, 345–357 (1993). https://doi.org/10.1007/BF01240131
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01240131