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Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games

For a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.

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File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_37.pdf
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Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP37.

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Length: 25 pages
Date of creation: Apr 2004
Date of revision:
Handle: RePEc:roc:wallis:wp37
Contact details of provider: Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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  1. Jackson, Matthew O. & Moselle, Boaz, 1998. "Coalition and Party Formation in a Legislative Voting Game," Working Papers 1036, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Eraslan, Hulya, 2002. "Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model," Journal of Economic Theory, Elsevier, vol. 103(1), pages 11-30, March.
  3. Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, EconWPA, revised 03 Jun 1999.
  4. DEBREU, Gérard, . "Economies with a finite set of equilibria," CORE Discussion Papers RP 67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  6. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, vol. 61(2), pages 290-301, December.
  7. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
  8. 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.
  9. Shannon, Chris, 1994. "Regular nonsmooth equations," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 147-165, March.
  10. Liang, Zihao, 1993. "Continuity of equilibria in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 27-34.
  11. Kleinberg, Norman L., 1980. "Continuous economies with a finite set of equilibria," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 35-49, March.
  12. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
  13. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-99, March.
  14. Rader, J Trout, 1973. "Nice Demand Functions," Econometrica, Econometric Society, vol. 41(5), pages 913-35, September.
  15. Banks, Jeffrey S. & Duggan, John, 1999. "A Bargaining Model of Collective Choice," Working Papers 1053, California Institute of Technology, Division of the Humanities and Social Sciences.
  16. Rui Pascoa, Mario & Ribeiro da Costa Werlang, Sergio, 1999. "Determinacy of equilibria in nonsmooth economies," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 289-302, November.
  17. Tasos Kalandrakis, 2004. "Genericity of Minority Governments : The Role of Policy and Office," Wallis Working Papers WP39, University of Rochester - Wallis Institute of Political Economy.
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