A bargaining model in general equilibrium |
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Authors: | Michele Gori Antonio Villanacci |
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Institution: | (1) Department of Economic Analysis, University of Zaragoza, Zaragoza, Spain;(2) Institute for the Study of Labour-IZA, Bonn, Germany |
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Abstract: | The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework
in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is
the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement
on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining
models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes
a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We
embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and
the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise
if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining
impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement
is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original
viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant
examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist
for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at
the same competitive prices. |
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Keywords: | |
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