Skip to main content

A new old solution for weak tournaments

Abstract

This article uncovers dynamic 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 tournament games. 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.

This is a preview of subscription content, access via your institution.

References

  1. Acemoglu D, Egorov G, Sonin K (2011) Dynamics and stability of constitutions, coalitions, and clubs. Am Econ Rev (Forthcoming)

  2. Anesi V (2006) Committees with farsighted voters: a new interpretation of stable sets. Soc Choice Welf 27: 595–610

    Article  Google Scholar 

  3. Anesi V (2010) Nooncooperative foundations of stable sets in voting games. Games Econ Behav 70: 488–493

    Article  Google Scholar 

  4. Banks JS, Duggan J (2008) A dynamic model of democratic elections in multidimensional policy spaces. Q J Political Sci 3: 269–299

    Article  Google Scholar 

  5. Baron DP, Kalai E (1993) The simplest equilibrium of a majority rule game. J Econ Theory 61: 290–301

    Article  Google Scholar 

  6. Bendor J, Mookherjee D, Ray D (2006) Satisficing and selection in electoral competition. Q J Political Sci 1: 171–200

    Article  Google Scholar 

  7. Brandt F, Fischer F, Harrenstein P (2009) The computational complexity of choice sets. Math Logic Q 55: 460–463

    Article  Google Scholar 

  8. Downs A (1957) An economic theory of democracy. Harper, New York

    Google Scholar 

  9. Duggan J, Le Breton M (1996) Dutta’s minimal covering set and Shapley’s saddles. J Econ Theory 70: 257–265

    Article  Google Scholar 

  10. Duggan J, Le Breton M (2001) Mixed refinements of Shapley’s saddles and weak tournaments. Soc Choice Welf 18: 65–78

    Article  Google Scholar 

  11. Dutta B (1988) Covering sets and a new condorcet choice correspondence. J Econ Theory 44: 63–80

    Article  Google Scholar 

  12. Dutta B, Laslier J-F (1999) Comparison functions and choice correspondences. Soc Choice Welf 16: 513–532

    Article  Google Scholar 

  13. Hudry O (2009) A survey on the complexity of tournament solutions. Math Soc Sci 57: 292–303

    Article  Google Scholar 

  14. Konishi H, Ray D (2003) Coalition formation as a dynamic process. J Econ Theory 110: 1–41

    Article  Google Scholar 

  15. Kramer GH (1977) A dynamical model of political equilibrium. J Econ Theory 19: 565–567

    Article  Google Scholar 

  16. Laffond G, Laslier J-F, Le Breton M (1993) The bipartisan set of a tournament game. Games Econ Behav 5: 182–201

    Article  Google Scholar 

  17. Laslier J-F (1997) Tournament solutions and majority voting. Springer, Berlin

    Book  Google Scholar 

  18. Le Breton M, Weber S (1992) A note on the core and Von Neumann–Morgenstern solutions of simple games. Soc Choice Welf 9: 57–61

    Article  Google Scholar 

  19. McGarvey DC (1953) A theorem on the construction of voting paradoxes. Econometrica 21: 608–610

    Article  Google Scholar 

  20. McKelvey RD, Ordeshook PC, Winer MD (1978) The competitive solution for N-person games without transferable utility, with an application to committee games. Am Political Sci Rev 72: 599–615

    Article  Google Scholar 

  21. Moulin H (1986) Choosing from a tournament. Soc Choice Welf 3: 271–291

    Article  Google Scholar 

  22. Muto S (1984) Stable sets for simple games with ordinal preferences. J Oper Res Soc Jpn 27: 250–258

    Google Scholar 

  23. Ordeshook PC (1986) Game theory and political theory. University press, Cambridge

    Book  Google Scholar 

  24. Peris JE, Subiza B (1999) Condorcet choice correspondences for weak tournaments. Soc Choice Welf 16: 217–231

    Article  Google Scholar 

  25. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton

    Google Scholar 

  26. Wittman D (1977) Candidates with policy preferences: a dynamic model. J Econ Theory 14: 180–189

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Vincent Anesi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Anesi, V. A new old solution for weak tournaments. Soc Choice Welf 39, 919–930 (2012). https://doi.org/10.1007/s00355-011-0561-2

Download citation

Keywords

  • Pure Strategy
  • Condorcet Winner
  • Electoral Competition
  • External Stability
  • Markov Perfect Equilibrium