Chapter 7
Search and Bargaining Models
of Exchange
7.1
Introduction
In this chapter we consider models of the exchange process where, as in the
previous chapter, once agents meet they exchange and part company (they
do not form enduring relationships); but we now generalize things so that
the rate at which they exchange is determined by bilateral bargaining. We
take for granted that the reader understands the relation between strategic
bargaining models and the Nash solution, as detailed in the Appendix, and
already used in other chapters. We less interested here in this issue than in
showing how the models can be used to address substantive questions.
In Section 2, we begin with a model due to Rubinstein and Wolinsky
(1985), in which there are large numbers of homogeneous buyers and homo
geneous sellers who meet at random and trade according to terms given by
bargaining theory. They constructed this model in order to contrast the pre
dictions of competitive (Walrasian) equilibrium theory with the predictions
of a model with explicit frictions and price setting. They argue that standard
competitive equilibrium theory is useful to the extent that it provides a good
approximation to more “reasonable micromechanisms” describing the trad
1
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ing process. That is, if the real world is characterized by real frictions, then
competitive theory is a useful description to the real world if it generates
similar outcomes when the frictions are not too big.
As frictions vanish the unique equilibrium of the RubinsteinWolinsky
model converges to something that does not generally coincide with a Wal
rasian equilibrium of a simple static model with demand and supply de…ned
using the steady state numbers of buyers and sellers in the market. Hence,
Rubinstein and Wolinsky conclude that models with small frictions are
not
Walrasian. However, this is not the last word on the matter. In Section 3,
we consider a version of a model due to Gale (1987) that, in a sense, implies
the opposite conclusion.
First, we generalize the RubinsteinWolinsky model to allow heterogene
ity. Equilibrium in his model generally involves a price distribution, with, for
example, high valuation buyers paying higher prices. As the frictions vanish,
the price distribution collapses to a point, consistent with competitive the
ory.
1
This could not be observed in the RubinsteinWolinsky model, since
with homogeneous buyers and sellers the equilibrium never yields a nonde
generate price distribution.
However, the limiting price is again di¤erent
from the prediction of a simple static Walrasian model where demand and
supply are de…ned using set of agents in the market in steady state, just as
Rubinstein and Wolinsky found in their special case.
What is one to make of this? Our view is that it is not very informative to
compare the predictions of a static Walrasian model with those of a dynamic
model, even as the frictions vanish in the latter.
In particular, the set of
buyers and sellers in the dynamic model is not the same as the set one
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 Spring '02
 Krueger
 Equilibrium, Game Theory, Bargaining, Economic equilibrium, Nash bargaining game

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