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Nash implementation with little communication


  • Segal, Ilya R.

    () (Department of Economics, Stanford University)


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.

Suggested Citation

  • Segal, Ilya R., 2010. "Nash implementation with little communication," Theoretical Economics, Econometric Society, vol. 5(1), January.
  • Handle: RePEc:the:publsh:576

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    References listed on IDEAS

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    Cited by:

    1. Babaioff, Moshe & Blumrosen, Liad & Schapira, Michael, 2013. "The communication burden of payment determination," Games and Economic Behavior, Elsevier, vol. 77(1), pages 153-167.
    2. Yakov Babichenko & Leonard J. Schulman, 2015. "Pareto Efficient Nash Implementation Via Approval Voting," Papers 1502.05238,, revised Mar 2017.

    More about this item


    Monotonic social choice rules; Nash implementation; communication complexity; verification; realization; budget sets; price equilibria;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness


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