Nash implementation with little communication

• 成果类型: Article
• 署名作者: Segal, Ilya R.
• 署名单位: Stanford University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1555-7561
• DOI: 10.3982/TE576
• 发表日期: 2010-01-01
• 页码: 51-71
• 关键词: Monotonic social choice rules; Nash implementation; communication complexity; verification; realization; budget sets; price equilibria; message space dimension

摘要

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 multistage 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, multistage 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-stageNash implementation mechanism in which at most 5 alternatives plus 4N log(2) N bits are announced 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.