Costless delay in negotiations

P. Jean-Jacques Herings*, Harold Houba

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.
Original languageEnglish
Pages (from-to)69-93
Number of pages25
JournalEconomic Theory
Issue number1
Early online date9 Jun 2021
Publication statusPublished - Jul 2022

JEL classifications

  • c72 - Noncooperative Games
  • c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"
  • c78 - "Bargaining Theory; Matching Theory"


  • Bargaining
  • Subgame perfect equilibrium
  • Stationary strategies
  • Existence
  • Costless delay

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