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T-Space at The University of Toronto Libraries >
Theoretical Economics >
Volume 5, Number 1 (January 2010) >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/18350

Title: Nash implementation with little communication
Authors: Ilya R. Segal; Department of Economics, Stanford University
Keywords: Monotonic social choice rules, Nash implementation, communication complexity,verification, realization, budget sets, price equilibria
D71, D82, D83
Issue Date: 26-Jan-2010
Publisher: Theoretical Economics
Citation: Theoretical Economics; Vol 5, No 1 (2010)
Abstract: [This item is a preserved copy. To view the original, visit http://econtheory.org/] The paper considers the communication complexity (measured in bits or real numbers) of Nash implementation of social choice rules. A key distinction is whether we restrict to the traditional one-stage mechanisms or allow multi-stage mechanisms. For one-stage mechanisms, the paper shows that for a large and important subclass of monotonic choice rules -- called "intersection monotonic" -- the total message space size needed for one-stage Nash implementation is essentially the same as that needed for "verification" (with honest agents who are privately informed about their preferences). According to Segal (2007), the latter is the size of the space of minimally informative budget equilibria verifying the choice rule. However, multi-stage mechanisms allow a drastic reduction in communication complexity. Namely, for an important subclass of intersection-monotonic choice rules (which includes rules based on coalitional blocking such as exact or approximate Pareto efficiency, stability, and envy-free allocations) we propose a two-stage Nash implementation mechanism in which each agent announces no more than two alternatives plus one bit per agent in any play. Such two-stage mechanisms bring about an exponential reduction in the communication complexity of Nash implementation for discrete communication measured in bits, or a reduction from infinite- to low-dimensional continuous communication.
URI: http://hdl.handle.net/1807/18350
Other Identifiers: http://econtheory.org/ojs/index.php/te/article/view/20100051
Rights: Authors who publish in <i>Theoretical Economics</i> will release their articles under the <a href="http://creativecommons.org/licenses/by-nc/2.5/">Creative Commons Attribution-NonCommercial license</a>. This license allows anyone to copy and distribute the article for non-commercial purposes provided that appropriate attribution is given.
Appears in Collections:Volume 5, Number 1 (January 2010)

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