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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 2010-08.

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Date of creation: May 2010
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Handle: RePEc:not:notcdx:2010-08

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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. 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.
  2. Forand, Jean Guillaume, 2014. "Two-party competition with persistent policies," Journal of Economic Theory, Elsevier, vol. 152(C), pages 64-91.
  3. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
  4. John Duggan & Mark Fey, 2006. "Repeated Downsian electoral competition," International Journal of Game Theory, Springer, vol. 35(1), pages 39-69, December.
  5. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
  6. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
  7. Josep E. Peris & BegoÓa Subiza, 1999. "Condorcet choice correspondences for weak tournaments," Social Choice and Welfare, Springer, vol. 16(2), pages 217-231.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer, vol. 16(4), pages 513-532.
  13. Duggan, John & Le Breton, Michel, 1996. "Dutta's Minimal Covering Set and Shapley's Saddles," Journal of Economic Theory, Elsevier, vol. 70(1), pages 257-265, July.
  14. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
  15. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
  16. 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.
  17. Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2012. "Dynamics and Stability of Constitutions, Coalitions, and Clubs," American Economic Review, American Economic Association, vol. 102(4), pages 1446-76, June.
  18. 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.
  19. Wittman, Donald, 1977. "Candidates with policy preferences: A dynamic model," Journal of Economic Theory, Elsevier, vol. 14(1), pages 180-189, February.
  20. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
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Cited by:
  1. Vincent Anesi & Daniel J. Seidmann, 2011. "Bargaining over an Endogenous Agenda," Discussion Papers 2011-10, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  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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