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Nash Bargaining Solution with Coalitions and The Joint Bargaining Paradox

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Author Info
Suchan Chae
Paul Heidhues

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Abstract

We propose a solution for bargaining problems where coalitions are bargainers. The solution generalizes the Nash solution and allows one to interpret a coalition as an institutional player whose preferences are obtained by aggregating the preferences of the individual members. One implication of our solution is that forming a coalition is unprofitable in pure-bargaining situations (the joint-bargaining paradox). We show, however, that forming a coalition can be profitable in a non-pure bargaining situation.

ZUSAMMENFASSUNG - (Die Nash Verhandlungslösung mit Koalitionen und Harsanyi's Verhandlungsparadox)
In der vorliegenden Arbeit schlagen wir ein Lösungskonzept für Verhandlungsspiele vor, bei denen die verhandelnden Parteien aus Koalitionen von Individuen bestehen können. Unser Lösungskonzept basiert auf einer Verallgemeinerung der Nash-Verhandlungslösung. Nach unserem Lösungskonzept kann eine Koalition als ein institutioneller Spieler aufgefasst werden, dessen Präferenzordnung auf einer Aggregierung der Präferenzen seiner Mitglieder basiert. Eine Implikation unserer Verhandlungslösung ist, dass Koalitionen in "reinen Verhandlungsspielen" nicht im Interesse der Individuen sind. In "nicht reinen Verhandlungsspielen" hingegen können Koalitionen durchaus vorteilhaft seien.

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Publisher Info
Paper provided by Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG) in its series CIG Working Papers with number FS IV 01-15.

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Length: 37 pages
Date of creation: Aug 2001
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Publication status: Published in Mathematical Social Sciences (under the title "A Group Bargaining Solution"), 48(1), 2004, pp. 37-53.
Handle: RePEc:wzb:wzebiv:fsiv01-15

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Related research
Keywords: Nash Bargaining Solution; Coalition; Joint-Bargaining Paradox;

Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

References listed on IDEAS
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  1. Segendorff, Bjorn, 1998. "Delegation and Threat in Bargaining," Games and Economic Behavior, Elsevier, vol. 23(2), pages 266-283, May. [Downloadable!] (restricted)
  2. Jun, Byoung Heon, 1989. "Non-cooperative Bargaining and Union Formation," Review of Economic Studies, Blackwell Publishing, vol. 56(1), pages 59-76, January. [Downloadable!] (restricted)
  3. Haller, Hans & Holden, Steinar, 1997. "Ratification Requirement and Bargaining Power," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 825-51, November.
  4. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April. [Downloadable!] (restricted)
  5. Manzini, Paola & Mariotti, Marco, 2005. "Alliances and negotiations," Journal of Economic Theory, Elsevier, vol. 121(1), pages 128-141, March. [Downloadable!] (restricted)
    Other versions:
  6. Horn, Henrik & Wolinsky, Asher, 1988. "Worker Substitutability and Patterns of Unionisation," Economic Journal, Royal Economic Society, vol. 98(391), pages 484-97, June. [Downloadable!] (restricted)
  7. Motty Perry & Larry Samuelson, 1994. "Open- versus Closed-Door Negotiations," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 348-359, Summer. [Downloadable!] (restricted)
  8. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June. [Downloadable!] (restricted)
  9. Salant, Stephen W & Switzer, Sheldon & Reynolds, Robert J, 1983. "Losses from Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, MIT Press, vol. 98(2), pages 185-99, May. [Downloadable!] (restricted)
  10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  11. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August. [Downloadable!] (restricted)
  12. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August. [Downloadable!] (restricted)
  13. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-26, March. [Downloadable!] (restricted)
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  14. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
  15. Cai, Hongbin, 2000. "Bargaining on Behalf of a Constituency," Journal of Economic Theory, Elsevier, vol. 92(2), pages 234-273, June. [Downloadable!] (restricted)
  16. Raymond Deneckere & Carl Davidson, 1985. "Incentives to Form Coalitions with Bertrand Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 473-486, Winter. [Downloadable!] (restricted)
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