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

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Abstract

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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Bibliographic Info

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

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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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Keywords: Local Uniqueness of Equilibrium; Regularity; Sequential Bargaining.;

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  1. Liang, Zihao, 1993. "Continuity of equilibria in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 27-34.
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  7. 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.
  8. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-53, September.
  9. 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.
  10. Jackson, Matthew O. & Moselle, Boaz, 2002. "Coalition and Party Formation in a Legislative Voting Game," Journal of Economic Theory, Elsevier, vol. 103(1), pages 49-87, March.
  11. 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.
  12. 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.
  13. Kleinberg, Norman L., 1980. "Continuous economies with a finite set of equilibria," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 35-49, March.
  14. 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.
  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. Shannon, Chris, 1994. "Regular nonsmooth equations," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 147-165, March.
  17. Rader, J Trout, 1973. "Nice Demand Functions," Econometrica, Econometric Society, vol. 41(5), pages 913-35, September.
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Citations

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Cited by:
  1. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
  2. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
  3. Predtetchinski, Arkadi, 2011. "One-dimensional bargaining," Games and Economic Behavior, Elsevier, vol. 72(2), pages 526-543, June.
  4. David Baron & Daniel Diermeier & Pohan Fong, 2012. "A dynamic theory of parliamentary democracy," Economic Theory, Springer, vol. 49(3), pages 703-738, April.
  5. Breitmoser, Yves, 2010. "Proto-coalition bargaining and the core," MPRA Paper 24995, University Library of Munich, Germany.
  6. Herings P. Jean-Jacques & Predtetchinski Arkadi, 2011. "Procedurally Fair Taxation," Research Memorandum 024, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Herings P. Jean-Jacques & Predtetchinski A., 2011. "Procedurally Fair Income Taxation Schemes," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  8. Herings P.J.J. & Meshalkin A. & Predtetchinski A., 2012. "A Folk Theorem for Bargaining Games," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  9. David Baron & Alexander Hirsch, 2012. "Common agency lobbying over coalitions and policy," Economic Theory, Springer, vol. 49(3), pages 639-681, April.
  10. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
  11. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
  12. Herings P. Jean-Jacques & Predtetchinski Arkadi, 2009. "Bargaining with Non-convexities," Research Memorandum 042, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  13. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer, vol. 52(1), pages 103-128, January.
  14. Yves Breitmoser, 2011. "Parliamentary bargaining with priority recognition for committee members," Social Choice and Welfare, Springer, vol. 37(1), pages 149-169, June.

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