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Dynamic stable set as a tournament solution

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  • Hannu Vartiainen

Abstract

We define a notion of dynamic (vNM) stable set for a tournament relation. Dynamic stable set satisfies (i) an external direct stability property, and (ii) an internal indirect stability property. Importantly, stability criteria are conditioned on the histories of past play, i.e. the dominance system has memory. Due to the asymmetry of the defining stability criteria, a dynamic stable set is stable both in the direct and in the indirect sense. We characterize a dynamic stable set directly in terms of the underlying tournament relation. A connection to the covering set of Dutta (J Econ Theory 44:63–80, 1988 ) is established. Using this observation, a dynamic stable set exists. We also show that a maximal implementable outcome set is a version of the ultimate uncovered set. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:2:p:309-327
    DOI: 10.1007/s00355-015-0897-0
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    1. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    2. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    3. John Duggan, 2012. "Noisy Stochastic Games," Econometrica, Econometric Society, vol. 80(5), pages 2017-2045, September.
    4. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    5. B. D. Bernheim & S. N. Slavov, 2009. "A Solution Concept for Majority Rule in Dynamic Settings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 33-62.
    6. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    7. , & , J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.
    8. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    9. Vincent Anesi, 2012. "A new old solution for weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 919-930, October.
    10. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
    11. Douglas K. R. Robinson & Arie Rip, 2012. "Socio-economic Dynamics of Innovation and Uptake," Post-Print hal-00794453, HAL.
    12. Diamantoudi, Effrosyni & Xue, Licun, 2007. "Coalitions, agreements and efficiency," Journal of Economic Theory, Elsevier, vol. 136(1), pages 105-125, September.
    13. 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.
    14. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    15. Daron Acemoglu & Mikhail Golosov & Aleh Tsyvinski & Pierre Yared, 2012. "A Dynamic Theory of Resource Wars," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(1), pages 283-331.
    16. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    17. Elizabeth Penn, 2008. "A distributive N-amendment game with endogenous agenda formation," Public Choice, Springer, vol. 136(1), pages 201-213, July.
    18. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    19. Kultti, Klaus & Vartiainen, Hannu, 2007. "Von Neumann-Morgenstern stable sets, discounting, and Nash bargaining," Journal of Economic Theory, Elsevier, vol. 137(1), pages 721-728, November.
    20. Mariotti, Marco, 1997. "A Model of Agreements in Strategic Form Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 196-217, May.
    21. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
    22. Diermeier, Daniel & Fong, Pohan, 2012. "Characterization of the von Neumann–Morgenstern stable set in a non-cooperative model of dynamic policy-making with a persistent agenda setter," Games and Economic Behavior, Elsevier, vol. 76(1), pages 349-353.
    23. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    24. Alain Kabundi, 2012. "Working Paper 152 - Dynamics of Inflation in Uganda," Working Paper Series 401, African Development Bank.
    25. John Duggan, 2013. "Uncovered sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 489-535, September.
    26. 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.
    27. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
    28. Ye, Fanglin & Lu, Liang & Du, Xiaoxue, 2012. "A Theory of Dynamic Biofuel Tax Credit," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 123750, Agricultural and Applied Economics Association.
    29. ,, 2014. "Endogenous agenda formation processes with the one-deviation property," Theoretical Economics, Econometric Society, vol. 9(1), January.
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    Cited by:

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    2. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.

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    More about this item

    Keywords

    C71; C72;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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