Abstract
A general nontransferable utility (NTU) game is interpreted as a collection of pure bargaining games that can be played by individual coalitions. The threatpoints or claims points respectively, in these pure bargaining games reflect the players’ opportunities outside a given coalition. We develop a solution concept for general NTU games that is consistent in the sense that the players’ outside opportunities are determined by the solution to a suitably defined reduced game. For any general NTU game the solution predicts which coalitions are formed and how the payoffs are distributed among the players.
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
Albers, W. (1974) Zwei Lösungskonzepte für kooperative Mehrpersonenspiele, die auf Anspruchsniveaus der Spieler basieren. Operations Research Verfahren 21: 1–13
Albers, W. (1979) Core- and Kernel-variants based on imputations and demand profiles. In: Moeschlin, O., Pallaschke, D. (eds.) Game Theory and Related Topics. North-Holland Publishing Company, Amsterdam
Asscher, N. (1976) An ordinal bargaining set for games without side payments. Mathematics of Operations Research 1(4): 381–389
Asscher, N. (1977) A cardinal bargaining set for games without side payments. International Journal of Game Theory 6(2): 87–114
Aumann, R.J. (1985) On the non-transferable utility value: A comment on the Roth—Shafer examples. Econometrica 53(3): 667–677
Aumann, R.J. (1986) Rejoinder. Econometrica 54(4): 985–989
Aumann, R.J., Drèze, J.H. (1974) Cooperative games with coalition structures. International Journal of Game Theory 3(4): 217–237
Aumann, R.J., Maschler, M. (1964) The bargaining set for cooperative games. In: Dresher, M., Shapley, L.S., Tucker, A.W. (eds.) Advances in Game Theory (Annals of Mathematics Studies 52). Princeton University Press, Princeton
Bennett, E. (1991) Three approaches to bargaining in NTU games. In: Selten, R. (ed.) Game Equilibrium Models III. Springer, Berlin, Heidelberg, New York
Bennett, E. (1997) Multilateral bargaining problems. Games and Economic Behavior 19(2): 151–179
Bennett, E., Zame, W.R. (1988) Bargaining in cooperative games. International Journal of Game Theory 17(4): 279–300
Chun, Y., Thomson, W. (1992) Bargaining problems with claims. Mathematical Social Sciences 24: 19–33
Chwe, M. S.-Y. (1994) Farsighted coalitional stability. Journal of Economic Theory 63(2): 299–325
Crawford, V.P., Rochford, S.C. (1986) Bargaining and competition in matching markets. International Economic Review 27(2): 329–348
Gale, D., Shapley, L.S. (1962) College admissions and the stability of marriage. American Mathematical Monthly 69(1): 9–15
Guesnerie, R., Oddou, C. (1979) On economic games which are not necessarily superadditve. Economics Letters 3: 301–306
Harsanyi, J.C. (1959) A bargaining model for the cooperative n-person game. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games IV (Annals of Mathematics Studies 40). Princeton University Press, Princeton, New Jersey
Harsanyi, J.C. (1963) A simplified bargaining model for the n-person cooperative game. International Economic Review 4(2): 194–220
Hart, S., Kurz, M. (1983) Endogenous formation of coalitions. Econometrica 51(4): 1047–1064
Kalai, E., Pazner, E.A., Schmeidler, D. (1976) Collective choice correspondences as admissible outcomes of social bargaining processes. Econometrica 44(2): 233–240
Kalai, E., Smorodinsky, M. (1975) Other solutions to Nash’s bargaining problem. Econometrica 43(3): 513–518
Maschler, M. (1978) Playing an n-person game — An experiment. In: Sauermann, H. (ed.) Beiträge zur experimentellen Wirtschaftsforschung, Vol. VIII: Coalition Forming Behavior. J. C. B. Mohr, Tübingen
Nash, J. (1950) The bargaining problem. Econometrica 18(2): 155–162
Owen, G. (1972) Values of games without side payments. International Journal of Game Theory 1: 95–109
Ray, D., Vohra, R. (1997) Equilibrium binding agreements. Journal of Economic Theory 73: 30–78
Roth, A.E. (1980) Values for games without sidepayments. Some difficulties with current concepts. Econometrica 48(2): 457–465
Roth, A.E. (1986) On the non-transferable utility value: A reply to Aumann. Econometrica 54(4): 981–984
Roth, A.E., Vande Vate, J.H. (1990) Random paths to stability in two-sided matching. Econometrica 58(6): 1475–1480
Scarf, H.E. (1967) The core of an N-person game. Econometrica 35(1): 50–69
Shafer, W.J. (1980) On the existence and interpretation of value allocation. Econometrica 48(2): 467–476
Shapley, L.S. (1953) A value for n-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games II (Annals of Mathematics Studies 28). Princeton University Press, Princeton
Shapley, L.S. (1969) Utility comparison and the theory of games. In: Éditions du Centre National de la Recherche Scientifique. La Décision: Agrégation et Dynamique des Ordres de Préférence. Paris
Shenoy, P.P. (1979) On coalition formation: A game-theoretical approach. International Journal of Game Theory 8(3): 133–164
Shenoy, P.P. (1980) A dynamic solution concept for abstract Games. Journal of Optimization Theory and Applications 32(2): 151–169
Zhou, L. (1994) A new bargaining set of an N-person game and endogenous coalition formation. Games and Economic Behavior 6(3): 512–526
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gerber, A. (2003). Coalition Formation in General NTU Games. In: Dutta, B., Jackson, M.O. (eds) Networks and Groups. Studies in Economic Design. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24790-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-24790-6_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07719-7
Online ISBN: 978-3-540-24790-6
eBook Packages: Springer Book Archive