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Non-cooperative bargaining in apex games and the kernel

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  • Montero, Maria

Abstract

This paper studies non-cooperative bargaining with random proposers in apex games. Two di¤erent protocols are considered: the egalitarian propocol, which selects each player to be the proposer with the same probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payo¤s coincide with the kernel for the grand coalition regardless of the protocol. Expected payo¤s conditional on a coalition may depend on the protocol: given a coalition of the apex player with a minor player, an egalitarian protocol yields a nearly equal split whereas a proportional protocol leads to a proportional split.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 41 (2002)
Issue (Month): 2 (November)
Pages: 309-321

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Handle: RePEc:eee:gamebe:v:41:y:2002:i:2:p:309-321

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667 Elsevier.
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  6. Morelli, Massimo & Montero, Maria, 2003. "The demand bargaining set: general characterization and application to majority games," Games and Economic Behavior, Elsevier, vol. 42(1), pages 137-155, January.
  7. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  8. Bennett, E. & Van Damme, E., 1990. "Demand Commitment Bargaining: -The Case Of Apex Games," Papers 9062, Tilburg - Center for Economic Research.
  9. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
  10. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
  11. Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, vol. 19(2), pages 151-179, May.
  12. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
  13. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
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  15. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 463-77, April.
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Citations

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Cited by:
  1. Dominik Karos, 2012. "Coalition Formation in Generalized Apex Games," Working Papers 2012.38, Fondazione Eni Enrico Mattei.
  2. Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
  3. Okada, Akira, 2011. "Coalitional bargaining games with random proposers: Theory and application," Games and Economic Behavior, Elsevier, vol. 73(1), pages 227-235, September.
  4. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  5. Cecilia Testa, 2003. "Government corruption and legislative procedures: is one chamber better than two?," LSE Research Online Documents on Economics 6642, London School of Economics and Political Science, LSE Library.
  6. Montero, Maria, 2003. "Two-Stage Bargaining with Reversible Coalitions: the Case of Apex Games," Royal Economic Society Annual Conference 2003 157, Royal Economic Society.
  7. Michalis Drouvelis & Maria Montero & Martin Sefton, 2007. "The Paradox of New Members: Strategic Foundations and Experimental Evidence," Discussion Papers 2007-13, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  8. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
  9. Guillaume Fréchette & John H. Kagel & Massimo Morelli, 2005. "Behavioral Identification in Coalitional Bargaining: An Experimental Analysis of Demand Bargaining and Alternating Offers," Econometrica, Econometric Society, vol. 73(6), pages 1893-1937, November.
  10. Okada, Akira, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers 2012-06, Graduate School of Economics, Hitotsubashi University.
  11. Michalis Drouvelis & Maria Montero & Martin Sefton, . "Gaining Power through Enlargement: Strategic Foundations and Experimental Evidence," Discussion Papers 09/30, Department of Economics, University of York.
  12. Montero, M.P., 2001. "The Nucleolus as a Consistent Power Index in Noncooerative Majority Games," Discussion Paper 2001-39, Tilburg University, Center for Economic Research.
  13. Joosung Lee, 2013. "Bargaining and Buyout," 2013 Papers ple701, Job Market Papers.
  14. Klaus Abbink, 2006. "Majority rip-off in referendum voting," Social Choice and Welfare, Springer, vol. 26(1), pages 1-21, January.
  15. Maria Montero, 2010. "Bargaining in Legislatures: A New Donation Paradox," Discussion Papers 2010-19, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.

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