# On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

*Volker Britz*,
*P. Jean-Jacques Herings* and
*Arkadi Predtetchinski*

*Games and Economic Behavior*, 2014, vol. 86, issue C, 178-183

**Abstract:**
We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.

**Keywords:** Strategic bargaining; Subgame perfect equilibrium; Stationary strategies; Nash bargaining solution (search for similar items in EconPapers)

**JEL-codes:** C78 (search for similar items in EconPapers)

**Date:** 2014

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**Related works:**

Working Paper: On the convergence to the Nash bargaining solution for action-dependent bargaining protocols (2014)

Working Paper: On the Convergence to the Nash bargaining solution for action-dependent bargaining protocols (2013)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:gamebe:v:86:y:2014:i:c:p:178-183

**DOI:** 10.1016/j.geb.2014.03.016

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