The Informational Efficiency of Finite Price Mechanisms
2002-02
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The Informational Efficiency of Finite Price Mechanisms
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2002-02
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Center for Economic Research, Department of Economics, University of Minnesota
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Working Paper
Abstract
This paper obtains finite counterparts of previous results that showed the informational efficiency of the
Walrasian mechanism among all mechanisms yielding Pareto-optimal individually rational trades in an exchange
economy while using a continuum of possible messages. Such mechanisms lack realism, since it is not possible to
transmit or announce all points of a continuum, and it generally takes infinite time to find an equilibrium message,
among all the messages in a continuum. Accordingly, the paper studies approximations of the continuum
Walrasian mechanism, in which the number of messages is finite. It applies general results from a companion
paper, which considered finite approximations of continuum mechanisms in general organizations, with exchange
economies as a particular example. For classic exchange economies, we compare the continuum Walrasian
mechanism with alternative continuum mechanisms that also find a Pareto-optimal and individually rational
allocation. There are many of them, and some of them, like the continuum Direct Revelation mechanism, do
not use prices at all. A finite approximation to a continuum mechanism will have an error. Its overall error
for a given class of economies is the worst distance (over all members of the class) between the continuum
mechanism's final allocation and the approximation's final allocation. We measure a finite mechanism's cost by
the number of its (equilibrium) messages. We consider exchange economies in which traders' utility functions
are quasi-linear and strictly concave. We find that the overall error of a sufficiently fine finite approximation
of the Walrasian mechanism is arbitrarily close to the overall error of a not more costly approximation of an
alternative continuum mechanism that has the same number of message variables. The former overall error is
smaller than the latter if the alternative continuum mechanism has a larger number of message variables. A
continuum Direct Revelation mechanism is an example of an alternative mechanism with a larger number of
message variables than the Walrasian mechanism.
Thus the informational superiority of the Walrasian mechanism emerges again when we approximate it and
take the finite number of messages as our cost measure.
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Previously Published Citation
Hurwicz, L. and Marschak, T., (2002), "The Informational Efficiency of Finite Price Mechanisms", Discussion Paper No. 314, Center for Economic Research, Department of Economics, University of Minnesota.
Suggested citation
Hurwicz, Leonid; Marschak, Thomas. (2002). The Informational Efficiency of Finite Price Mechanisms. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/55881.
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