Simple collective equilibria in stopping games

P. Jean-Jacques Herings*, Arkadi Predtetchinski

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class of problems as stopping games. Collective choice games, quitting games, and coalition formation games are particular examples. When the core of a stopping game is non-empty, a subgame perfect equilibrium in pure stationary strategies is shown to exist. But in general, even subgame perfect equilibria in mixed stationary strategies may not exist. We show that aggregate voting behavior can be summarized by a collective strategy. We insist on pure strategies, allow for simple forms of punishment, and provide a constructive proof to show that so-called two-step simple collective equilibria always exist. This implies the existence of a pure strategy subgame perfect equilibrium. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to a model of redistributive politics.
Original languageEnglish
Article number102467
Number of pages15
JournalJournal of Mathematical Economics
Publication statusPublished - Aug 2021


  • Coalition formation
  • collective choice
  • stationary equilibrium
  • subgame perfect equilibrium
  • Collective choice
  • Voting
  • Subgame perfect equilibrium
  • Stationary equilibrium

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