Abstract
This paper provides a framework for implementing and comparing several solution concepts for transferable utility cooperative games. We construct bidding mechanisms where players bid for the role of the proposer. The mechanisms differ in the power awarded to the proposer. The Shapley, consensus and equal surplus values are implemented in subgame perfect equilibrium outcomes as power shifts away from the proposer to the rest of the players. Moreover, an alternative informational structure where these solution concepts can be implemented without imposing any conditions of the transferable utility game is discussed as well.
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Baliga, S., Brusco, S.: Collusion, renegotiation and implementation. Soc Choice Welf 17, 69–83 (2000)
van den Brink, R., Funaki, Y.: Axiomatizations of a class of equal surplus sharing solutions for TU-games. Tinbergen Institute Discussion Paper, TI 2004-136/1, Tinbergen Institute, The Netherlands (2004). Theory and Decision (forthcoming)
van den Brink, R., Funaki, Y., Ju, Y.: Axiomatizations of the convex combinations of a class of equal surplus solutions and the Shapley value. Manuscript, Free University Amsterdam, The Netherlands (2005)
Dagan, N., Serrano, R., Volij, O.: A non-cooperative view of consistent bankruptcy rules. Games Econ Behav 18, 55–72 (1997)
Dasgupta, A., Chiu, Y.S.: On implementation via demand commitment games. Int J Game Theory 27, 161–189 (1998)
Driessen, T.S.H., Funaki, Y.: Coincidence of and collinearity between game theoretic solutions. OR Spektrum 13, 15–30 (1991)
García-Jurado, I., González-Díaz, J., Villar, A.: A non-cooperative approach to bankruptcy problems. Spanish Econ Rev 8, 189–197 (2006)
Gul, F.: Bargaining foundations of Shapley value. Econometrica 57, 81–95 (1989)
Gul, F.: Efficiency and immediate agreement: a reply to Hart and Levy. Econometrica 67, 913–918 (1999)
Hart, S., Mas-Colell, A.: Bargaining and value. Econometrica 64, 357–380 (1996)
Hart, O., Moore, J.: Property rights and the theory of the firm. J Polit Econ 98, 1119–1158 (1990)
Ju, Y.: The consensus value for games in partition function form. Int Game Theory Rev 9, 437–452 (2007)
Ju, Y., Borm, P.: Externalities and compensation: primeval games and solutions. J Math Econ 44, 367–382 (2008)
Ju, Y., Borm, P., Ruys, P.: The consensus value: a new solution concept for cooperative games. Soc. Choice Welf 28, 685–703 (2007)
Krishna, V., Serrano, R.: Perfect equilibria of a model of n-person non-cooperative bargaining. Int J Game Theory 27, 259–272 (1995)
Macho-Stadler, I., Pérez-Castrillo, D., Wettstein, D.: Efficient bidding with externalities. Games Econ Behav 57, 304–320 (2006)
Maniquet, F.: Implementation under perfect information in economic environments. Soc Choice Welf 21, 323–346 (2003)
Maskin, E.: Bargaining, coalitions and externalities. Presidential Address of the Econometric Society (2003)
Maskin, E., Moore, J.: Implementation and renegotiation. Rev Econ Stud 66, 39–56 (1999)
Moldovanu, B., Winter, E.: Core implementation and increasing returns to scale for cooperation. J Math Econ 23, 533–548 (1994)
Moore, J., Repullo, R.: Subgame perfect implementation. Econometrica 58, 1083–1099 (1988)
Moulin, H.: Fair Division and Collective Welfare. MIT Press, Cambridge, MA (2003)
Myerson, R.B.: Conference structures and fair allocation rules. Int J Game Theory 9, 169–182 (1980)
Nash, J.F.: Two person cooperative games. Econometrica 21, 128–140 (1953)
Owen, G.: Values of games with a priori unions. In: Henn, R., Moeschlin, O.(eds) Essays in Mathematical Economics and Game Theory, pp. 76–88. Springer, Berlin (1977)
Pérez-Castrillo, D., Wettstein, D.: Bidding for the surplus: a non-cooperative approach to the Shapley value. J Econ Theory 100, 274–294 (2001)
Pérez-Castrillo, D., Wettstein, D.: Choosing wisely: a multi-bidding approach. Am Econ Rev 92, 1577–1587 (2002)
Pham Do, K.H., Norde, H.: The Shapley value for partition function form games. Int Game Theory Rev 9, 353–360 (2007)
Rubinstein, A.: Perfect equilibrium in a bargaining model. Econmetrica 50, 97–109 (1982)
Schmeidler, D.: The Nucleolus of a characteristic function game. SIAM J Appl Math 17, 1163–1170 (1969)
Serrano, R.: Strategic bargaining, surplus sharing problems and the Nucleolus. J Math Econ 24, 319–329 (1995)
Serrano, R.: Fifty years of the Nash program, 1953–2003. Investig Econ 29, 219–258 (2005)
Shapley, L.S.: A value for n-person games. In: Kuhn, H.W., Tucker, A.W.(eds) Contributions to the Theory of Games II, pp. 307–317. Princeton University Press, Princeton, NJ (1953)
Thomson, W.: Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey. Math Soc Sci 45, 249–297 (2003)
Vidal-Puga, J.: Bargaining with commitments. Int J Game Theory 33, 129–144 (2004)
Vidal-Puga, J.: A bargaining approach to the Owen value and the Nash solution with coalition structure. Econ Theory 25, 679–701 (2005)
Vidal-Puga, J., Bergantiños, G.: An implementation of the Owen value. Games Econ Behav 44, 412–427 (2003)
Winter, E.: The demand commitment bargaining game and snowballing cooperation. Econ Theory 4, 255–273 (1994)
Young, H.P., Okada, N., Hashimoto, T.: Cost allocation in water resources development. Water Resour Res 18, 463–475 (1982)
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The authors thank Yukihiko Funaki, Andreu Mas-Colell, David Pérez-Castrillo and Jana Vyrastekova for helpful discussions. We also appreciate the comments from the seminar and conference participants at Keele University, Tilburg University, University of Haifa, University of Warwick, CORE at Louvain-la-Neuve, Catholic University Leuven, Pablo de Olavide University in Seville, University of Vigo, the 2006 Annual Conference of the Israeli Mathematical Union in Neve Ilan, Israel, and the 61st European Meeting of the Econometric Society in Vienna, Austria in 2006. In particular, we are grateful to the associate editor and an anonymous referee. Their valuable comments and constructive suggestions contributed to a significant improvement of the paper. Wettstein acknowledges the financial support of the Pinchas Sapir Center for Development in Tel Aviv University.
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Ju, Y., Wettstein, D. Implementing cooperative solution concepts: a generalized bidding approach. Econ Theory 39, 307–330 (2009). https://doi.org/10.1007/s00199-008-0335-y
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DOI: https://doi.org/10.1007/s00199-008-0335-y