Bargaining in a non-stationary environment.
type: Item
instance of: scholarly article
title: Bargaining in a non-stationary environment.
zbMATH Open document ID: 1048.91010
DOI: 10.1016/S0022-0531(02)00034-0
author: Melvyn G. Coles
author: Abhinay Muthoo
published in: Journal of Economic Theory
publication date: 2003-06-09T00:00:00Z
review text: The paper studies Rubinstein's alternating offers bargaining game in the following non-stationary setting. Two players \(A\) and \(B\) alternatively bargain at times \(t=s, s+\Delta, s+2\Delta,\ldots\) (\(s\) and \(\Delta>0\) are fixed), and \(\Omega (t) \subset \mathbb R^2\) is the set of possible utility pairs of their payoffs available at time \(t\). The players negotiate according to the following procedure. At times \(s+2n\Delta\) (\(n=0,1,\ldots\)) player \(A\) makes an offer \((u_A,u_B)\) from the set \(\Omega(s+2n\Delta)\), and player \(B\) decides whether to accept or reject it. If he accepts the offer, then the bargaining game ends and players' payoffs are \((u_A,u_B)\), respectively. Analogous situation occurs to player \(B\) at times \(s+(2n+1)\Delta\) (\(n=0,1,\ldots\)). When both players reject their offers at all times, their payoffs are equal to zero. Three standard assumptions are assumed about the Pareto frontiers of the sets \(\Omega (t)\): concavity, shrinking and vanishing, and smoothly evolving. Using this the authors characterize the set equilibria in the limit as \(\Delta \rightarrow 0\). It is shown that then any Markov and non-Markov subgame perfect equilibrium (SPE) converges to the same unique limiting one. This result is illustrated by an interesting example about players' bargaining over a unit size cake. The second essential result in the paper gives sufficient conditions under which Nash's bargaining solution for the game at initial time \(s\) with the disagreement point \((0,0)\), coincides with the unique limiting SPE payoff pair. In the last part of the paper the authors extend the previous results for time-varying inside options and demonstrate the robustness of this approach.
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A50
Mathematics Subject Classification ID: 91B52
zbMATH DE Number: 1924811
zbMATH Keywords: bargaining solution
zbMATH Keywords: alternating offers
zbMATH Keywords: subgame perfect equilibrium
reviewed by: Tadeusz Radzik
MaRDI profile type: Publication
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full work available at URL: s0022-0531(02)00034-0
OpenAlex ID: W2155931054
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description: scientific article; zbMATH DE number 1924811