Subgame perfect equilibria in majoritarian bargaining

P. Jean-Jacques Herings*, Andrey Meshalkin, Arkadi Predtetchinski

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory experiments show various deviations from this equilibrium, where different offers are typically made and delay may occur before acceptance. We address the issue to what extent these findings are compatible with subgame perfect equilibrium and characterize the set of subgame perfect equilibrium payoffs for any value of the discount factor. We show that for any proposal in the interior of the space of possible agreements there exists a discount factor such that the proposal is made and accepted. We characterize the values of the discount factor for which equilibria with one-period delay exist. We show that any amount of equilibrium delay is possible and we construct subgame perfect equilibria such that arbitrary long delay occurs with probability one. 
Original languageEnglish
Pages (from-to)101-112
JournalJournal of Mathematical Economics
Publication statusPublished - May 2018
Externally publishedYes


  • Dynamic games
  • Bargaining
  • Majoritarian voting
  • Subgame perfect equilibrium
  • Delay of acceptance
  • GAME


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