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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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References

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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.
  2. Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, vol. 19(2), pages 151-179, May.
  3. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  4. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
  5. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
  6. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  7. Massimo Morelli & Maria Montero, 2001. "The Demand Bargaining Set: General Characterization and Application to Majority Games," Economics Working Papers 0011, Institute for Advanced Study, School of Social Science.
  8. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
  9. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  10. Bennett, E. & Van Damme, E., 1990. "Demand Commitment Bargaining: -The Case Of Apex Games," Papers 9062, Tilburg - Center for Economic Research.
  11. 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.
  12. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  13. 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.
  14. 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.
  15. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-80, March.
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Citations

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Cited by:
  1. 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.
  2. Michalis Drouvelis & Maria Montero & Martin Sefton, 2007. "The Paradox of New Members: Strategic Foundations and Experimental Evidence," Discussion Papers 2007-06, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  3. Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
  4. Montero, M.P., 2002. "Two-Stage Bargaining with Reversible Coalitions: The Case of Apex Games," Discussion Paper 2002-26, Tilburg University, Center for Economic Research.
  5. 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.
  6. Joosung Lee, 2013. "Bargaining and Buyout," 2013 Papers ple701, Job Market Papers.
  7. Cecilia Testa, 2003. "Government Corruption and Legislative Procedures: is One Chamber Better Than Two?," STICERD - Development Economics Papers - From 2008 this series has been superseded by Economic Organisation and Public Policy Discussion Papers 41, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. G Frechette & J Kagel & M Morelli, 2004. "Behavioral Identification in Coalition Bargaining: An Experimental Analysis of Demand Bargaining and Alternating Offers," Levine's Bibliography 122247000000000006, UCLA Department of Economics.
  9. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  10. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
  11. Okada, Akira, 2011. "Coalitional bargaining games with random proposers: Theory and application," Games and Economic Behavior, Elsevier, vol. 73(1), pages 227-235, September.
  12. Okada, Akira, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers 2012-06, Graduate School of Economics, Hitotsubashi University.
  13. 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.
  14. Dominik Karos, 2012. "Coalition Formation in Generalized Apex Games," Working Papers 2012.38, Fondazione Eni Enrico Mattei.
  15. Klaus Abbink, 2006. "Majority rip-off in referendum voting," Social Choice and Welfare, Springer, vol. 26(1), pages 1-21, January.

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