Reputational Bargaining with Ultimatum Opportunities

TL;DR

This paper analyzes how ultimatum opportunities influence reputation dynamics and bargaining outcomes in two-sided negotiations, revealing conditions for equilibrium uniqueness, efficiency, and potential for endless negotiation.

Contribution

It introduces a model of two-sided reputational bargaining with ultimatum opportunities, highlighting their effects on equilibrium behavior and dispute resolution.

Findings

Ultimatum opportunities can both accelerate and decelerate reputation building.

Unique equilibrium exists when only one player can issue an ultimatum.

Fast ultimatum opportunities may lead to multiple equilibria with endless negotiations.

Abstract

We study two-sided reputational bargaining with opportunities to issue an ultimatum -- threats to force dispute resolution. Each player is either a justified type, who never concedes and issues an ultimatum whenever an opportunity arrives, or an unjustified type, who can concede, wait, or bluff with an ultimatum. In equilibrium, the presence of ultimatum opportunities can harm or benefit a player by decelerating or accelerating reputation building. When only one player can issue an ultimatum, equilibrium play is unique. The hazard rate of dispute resolution is discontinuous and piecewise monotonic in time. As the probabilities of being justified vanish, agreement is immediate and efficient, and if the set of justifiable demands is rich, payoffs modify Abreu and Gul (2000), with the discount rate replaced by the ultimatum opportunity arrival rate if the former is smaller. When both players' ultimatum opportunities arrive sufficiently fast, there may exist multiple equilibria in which their reputations do not build up and negotiation lasts forever.