On the Convergence to the Nash bargaining solution for action-dependent bargaining protocols

Volker Britz (), P. Jean-Jacques Herings and Arkadi Predtetchinski
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Volker Britz: ETH Zürich, Switzerland

No 2013044, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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, though equilibrium acceptance sets do depend on these probabilities. Next 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 and equilibrium payoffs are in general Pareto inefficient. 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 a 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: 2013-09-11
New Economics Papers: this item is included in nep-cdm, nep-gth, nep-hpe and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Related works:
Journal Article: 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 (2014)
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