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A New Old Solution for Weak Tournaments

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  • Vincent Anesi

    (University of Nottingham)

Abstract

This note uncovers new properties of the von Neumann-Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of the tournament game introduced by Laffond, Laslier and Le Breton (1993) [The bipartisan set of a tournament game. Games and Economic Behavior 5, 182-201]. The exploration of a specific class of Markov perfect equilibria in these "dynamic tournament games" yields a new solution concept for weak tournaments - the A-stable set. The alternatives in an A-stable set constitute persistent, long-run policy outcomes in the corresponding dynamic tournament games. We find that, in any weak tournament, the class of A-stable sets coincides with that of von Neumann-Morgenstern stable sets.

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Paper provided by The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham in its series Discussion Papers with number 2010-04.

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Date of creation: Mar 2010
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Handle: RePEc:cdx:dpaper:2010-04

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Keywords: Electoral competition; stable set; stationary Markov equilibrium; weak tournament; solution theory;

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References

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  1. Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2008. "Dynamics and Stability of Constitutions, Coalitions, and Clubs," NBER Working Papers 14239, National Bureau of Economic Research, Inc.
  2. Jean Guillaume Forand, 2010. "Two-Party Competition with Persistent Policies," Working Papers 1011, University of Waterloo, Department of Economics, revised Nov 2010.
  3. Wittman, Donald, 1977. "Candidates with policy preferences: A dynamic model," Journal of Economic Theory, Elsevier, vol. 14(1), pages 180-189, February.
  4. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
  5. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer, vol. 16(4), pages 513-532.
  6. Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1997. "Condorcet choice correspondences for weak tournaments," Working Papers. Serie AD 1997-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Banks, Jeffrey S. & Duggan, John, 2008. "A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces," International Quarterly Journal of Political Science, now publishers, vol. 3(3), pages 269-299, October.
  8. 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.
  9. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
  10. Le Breton, M. & Weber, S., 1991. "A Note on the Core and von Neumann-Morgenstern Solutions of Simple Games," Papers 91-12, York (Canada) - Department of Economics.
  11. Vincent Anesi, 2007. "Noncooperative Foundations of Stable Sets in Voting Games," Discussion Papers 2007-09, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  12. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
  13. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  14. Michel Le Breton & John Duggan, 2001. "Mixed refinements of Shapley's saddles and weak tournaments," Social Choice and Welfare, Springer, vol. 18(1), pages 65-78.
  15. Duggan, J. & Le Breton, M., 1995. "Dutta's Minimal Covering Set and Shapeley's Saddles," G.R.E.Q.A.M. 95a02, Universite Aix-Marseille III.
  16. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
  17. Vincent Anesi, 2006. "Committees with Farsighted Voters: A New Interpretation of Stable Sets," Social Choice and Welfare, Springer, vol. 27(3), pages 595-610, December.
  18. Bendor, Jonathan & Mookherjee, Dilip & Ray, Debraj, 2006. "Satisficing and Selection in Electoral Competition," International Quarterly Journal of Political Science, now publishers, vol. 1(2), pages 171-200, March.
  19. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
  20. John Duggan & Mark Fey, 2006. "Repeated Downsian electoral competition," International Journal of Game Theory, Springer, vol. 35(1), pages 39-69, December.
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Cited by:
  1. Anesi, Vincent & Seidmann, Daniel J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.
  2. Jean Guillaume Forand, 2010. "Two-Party Competition with Persistent Policies," Working Papers 1011, University of Waterloo, Department of Economics, revised Nov 2010.

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