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Voting in collective stopping games


  • Herings P.J.J.
  • Predtetchinski A.



At each moment in time, some alternative from a finite set is selected by a dynamic process. Players observe the alternative selected and sequentially cast a yes or a no vote. If the set of players casting a yes–vote is decisive for the alternative in question,the alternative is accepted and the game ends. Otherwise the next period begins.We refer to this class of problems as collective stopping problems. Collective choicegames, quitting games, and coalition formation games are particular examples that fit nicely into this more general framework.When the core of this game is non–empty, a stationary equilibrium in pure strategies is shown to exist. But in general, even mixed stationary equilibria may not exist in collective stopping games. We consider strategies that are pure and action–independent, and allow for a limited degree of history dependence. Under such individual behavior, aggregate behavior can be conveniently summarized by a collective strategy. We consider collective strategies that are simple and induced by two–step game–plans and provide a constructive proof that this collection always contains a subgame perfect equilibrium. The existence of such an equilibrium is shown to imply the existence of a sequential equilibrium in an extended model with incomplete information. Collective equilibria are shown to be robust to perturbations in the dynamic process and in utilities. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to the Baron-Ferejohn model of redistributive politics.

Suggested Citation

  • Herings P.J.J. & Predtetchinski A., 2013. "Voting in collective stopping games," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013014

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    References listed on IDEAS

    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    2. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
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    More about this item


    Existence and Stability Conditions of Equilibrium; Noncooperative Games; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games; Bargaining Theory; Matching Theory;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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