On the convergence to the Nash bargaining solution for action-dependent bargaining protocols |
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Institution: | 1. Center of Economic Research at ETH Zürich (CER-ETH), Switzerland;2. Department of Economics, Maastricht University, Netherlands;1. Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;1. Google Research, 111 8th Avenue, New York, NY 10011, United States;2. Computer Science Department, Cornell University, Ithaca, NY 14853, United States;1. Department of Economics, University of Exeter, Rennes Drive, Streatham Court, Exeter, EX4 4PU, UK;2. Department of Quantitative Economics, University Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands;1. Singapore Management University, Singapore;2. Indian Statistical Institute, New Delhi, India |
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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. |
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Keywords: | Strategic bargaining Subgame perfect equilibrium Stationary strategies Nash bargaining solution |
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