Efficiency of scalar-parameterized mechanisms
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Johari+JNT-Efficiency.pdf
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Author(s)
Johari, Ramesh
Tsitsiklis, John N.
Date Issued
July 2008
Journal
Operations Research
Publisher
Institute for Operations Research and the Management Sciences
Citation
Johari, Ramesh, and John N. Tsitsiklis. “Efficiency of Scalar-Parameterized Mechanisms.” Operations Research 57.4 (2009): 823-839.
Version
Author's final manuscript
Abstract
We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple
competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to
mechanisms that satisfy certain scalability constraints motivated by large scale communication networks;
in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy
spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differen-
tiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the
maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes
the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price
differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we con-
struct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient.
These mechanisms are shown to be fully efficient even in general convex environments, under reasonable
assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility
available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually
improve the efficiency guarantee.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
http://dx.doi.org/10.1287/opre.1080.0638
