Abstract
We study a bargaining procedure of coalition formation in the class of hedonic games, where players’ preferences depend solely on the coalition they belong to. We provide an example of nonexistence of a pure strategy stationary perfect equilibrium, and a necessary and sufficient condition for existence. We show that when the game is totally stable (the game and all its restrictions have a nonempty core), there always exists a no-delay equilibrium generating core outcomes. Other equilibria exhibiting delay or resulting in unstable outcomes can also exist. If the core of the hedonic game and its restrictions always consist of a single point, we show that the bargaining game admits a unique stationary perfect equilibrium, resulting in the immediate formation of the core coalition structure.
Similar content being viewed by others
References
Alcalde J (1996) Implementation of stable solutions to marriage problems. J Econ Theory 69: 240–254
Alcalde J, Perez-Castrillo D, Romero Medina A (1998) Hiring procedures to implement stable allocations. J Econ Theory 82: 469–480
Alcalde , Romero Medina A (2000) Simple mechanisms to implement the core of college admissions problems. Games Econ Behav 31: 294–302
Alcalde , Romero Medina A (2005) Sequential decisions in the college admissions problem. Econ Lett 86: 153–158
Banerjee S, Konishi H, Sonmez T (2001) Core in a simple coalition formation game. Soc Choice Welfare 18: 135–153
Binmore K, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modeling. RAND J Econ 17: 176–188
Bloch F (1996) Sequential formation of coalitions in games with externalities and fixed payoff division. Games Econ Behav 14: 90–123
Bogomolnaia A, Jackson MO (2002) The stability of hedonic coalition structures. Games Econ Behav 38: 201–230
Chaterjee K, Dutta B, Ray D, Sengupta K (1993) A noncooperative theory of coalitional bargaining. Rev Econ Stud 60: 463–477
Chung K-S (2000) On the existence of stable roommate matchings. Games Econ Behav 33: 206–230
Diamantoudi E, Xue L (2003) Farsighted stability in hedonic games. Soc Choice Welfare 21: 39–61
Drèze JH, Greenberg J (1980) Hedonic coalitions: optimality and stability. Econometrica 48(4): 987–1003
Farrell J, Scotchmer S (1988) Partnerships. Q J Econ 103: 279–297
Gale D, Shapley L (1962) College admissions and the stability of marriage. Am Math Mon 6(9): 9–15
Hart S, Mas Colell A (1996) Bargaining and value. Econometrica 64: 357–380
Kamecke U (1989) Non-cooperative matching games. Int J Game Theory 18: 423–431
Krishna V, Serrano R (1996) Multilateral bargaining. Rev Econ Stud 63: 61–80
Kultti K, Vartiainen H (2009) Multilateral cooperative bargaining in a general utility space. Int J Game Theory, forthcoming
Livshits I (2002) On non-existence of pure strategy markov perfect equilibrium. Econ Lett 76: 393–396
Maskin E (2003) Bargaining, coalitions and externalities. presidential address to the Econometric Society
Moldovanu B, Winter E (1995) Order independent equilibria. Games Econ Behav 9: 21–34
Moulin H, Shenker S (1994) Average cost pricing versus serial cost sharing: an axiomatic comparison. J Econ Theory 64: 178–201
Okada A (1996) A noncooperative coalitional bargaining game with random proposers. Games Econ Behav 16: 97–108
Papai S (2004) Unique stability in simple coalition formation games. Games Econ Behav 48: 337–354
Perez-Castrillo D, Sotomayor M (2002) Simple selling and buying procedure. J Econ Theory 103: 461–474
Ray D (2007) A game theoretic perspective on coalition formation. Oxford University Press, Oxford, UK
Ray D, Vohra R (1999) A theory of endogenous coalition structures. Games Econ Behav 26: 286–336
Roth A, Sotomayor M (1990) Two-sided matching: a study in game theoretic modelling and analysis. Cambridge University Press, Cambridge
Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50: 97–109
Seidmann D, Winter E (1998) A theory of gradual coalition formation. Rev Econ Stud 65: 793–815
Selten R (1981) A noncooperative model of characteristic function bargaining. In: Bohm V, Nachtkamp H (eds) Essays in game theory and mathematical economics. Bibliographisches Institut Mannheim, Mannheim
Shapley L, Scarf H (1974) On cores and indivisibilities. J Math Econ 1: 23–37
Suh SC, Wen Q (2008) Subgame perfect implementation of stable matchings in marriages. Soc Choice Welfare 31: 163–174
Sutton J (1986) Noncooperative bargaining theory: an introduction. Rev Econ Stud 53: 709–724
Vidal-Puga J (2008) Forming coalitions and the shapley NTU value. Eur J Oper Res 190: 659–671
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bloch, F., Diamantoudi, E. Noncooperative formation of coalitions in hedonic games. Int J Game Theory 40, 263–280 (2011). https://doi.org/10.1007/s00182-010-0237-7
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-010-0237-7