Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/150132 
Authors: 
Year of Publication: 
2010
Citation: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 5 [Issue:] 1 [Publisher:] The Econometric Society [Place:] New Haven, CT [Year:] 2010 [Pages:] 51-71
Publisher: 
The Econometric Society, New Haven, CT
Abstract: 
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.
Subjects: 
Monotonic social choice rules
Nash implementation
communication complexity
verification
realization
budget sets
price equilibria
JEL: 
D71
D82
D83
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc Logo
Document Type: 
Article

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.