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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.

Suggested Citation

  • Vincent Anesi, 2010. "A New Old Solution for Weak Tournaments," Discussion Papers 2010-08, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  • Handle: RePEc:cdx:dpaper:2010-08
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    References listed on IDEAS

    as
    1. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
    2. 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.
    3. Michel Le Breton & John Duggan, 2001. "Mixed refinements of Shapley's saddles and weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 65-78.
    4. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    5. Josep E. Peris & BegoÓa Subiza, 1999. "Condorcet choice correspondences for weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 217-231.
    6. Banks, Jeffrey S. & Duggan, John, 2008. "A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces," Quarterly Journal of Political Science, now publishers, vol. 3(3), pages 269-299, October.
    7. 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.
    8. John Duggan & Mark Fey, 2006. "Repeated Downsian electoral competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 39-69, December.
    9. Forand, Jean Guillaume, 2014. "Two-party competition with persistent policies," Journal of Economic Theory, Elsevier, vol. 152(C), pages 64-91.
    10. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    11. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    12. 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 1446-1476, June.
    13. 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.
    14. Vincent Anesi, 2006. "Committees with Farsighted Voters: A New Interpretation of Stable Sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 595-610, December.
    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. 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.
    17. Bhaskar Dutta & Jean-Francois Laslier, 1999. "Comparison functions and choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 513-532.
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    19. Wittman, Donald, 1977. "Candidates with policy preferences: A dynamic model," Journal of Economic Theory, Elsevier, vol. 14(1), pages 180-189, February.
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    21. repec:cup:apsrev:v:72:y:1978:i:02:p:599-615_15 is not listed on IDEAS
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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. Vincent Anesi & John Duggan, 2015. "Dynamic Bargaining and External Stability with Veto Players," Discussion Papers 2015-12, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    3. repec:eee:gamebe:v:103:y:2017:i:c:p:30-40 is not listed on IDEAS
    4. Forand, Jean Guillaume, 2014. "Two-party competition with persistent policies," Journal of Economic Theory, Elsevier, vol. 152(C), pages 64-91.
    5. Hannu Vartiainen, 2015. "Dynamic stable set as a tournament solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 309-327, September.

    More about this item

    Keywords

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

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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