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Efficient Repeated Implementation

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  • Lee, J.
  • Sabourian, H.

Abstract

This paper examines repeated implementation of a social choice function (SCF) with infinitely-lived agents whose preferences are determined randomly in each period. An SCF is repeated-implementable in (Bayesian) Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that (i) its equilibrium set is non-empty and (ii) every equilibrium outcome corresponds to the desired social choice at every possible history of past play and realizations of uncer- tainty. We first show, with minor qualifications, that in the complete information environment an SCF is repeated-implementable if and only if it is effcient. We then extend this result to the incomplete information setup. In particular, it is shown that in this case efficiency is sufficient to ensure the characterization part of repeated implementation. For the existence part, incentive compatibility is sufficient but not necessary. In the case of interdependent values, existence can also be established with an intuitive condition stipulating that deviations can be detected by at least one agent other than the deviator. Our incomplete information analysis can be extended to incorporate the notion of ex post equilibrium.

Suggested Citation

  • Lee, J. & Sabourian, H., 2009. "Efficient Repeated Implementation," Cambridge Working Papers in Economics 0948, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:0948
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    Cited by:

    1. Renou, Ludovic & Tomala, Tristan, 2015. "Approximate implementation in Markovian environments," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 401-442.
    2. Lee, Jihong & Sabourian, Hamid, 2015. "Complexity and repeated implementation," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 259-292.
    3. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    4. Ghosh, Sambuddha & Han, Seungjin, 2012. "Repeated Contracting in Decentralised Markets," Microeconomics.ca working papers seungjin_han-2012-12, Vancouver School of Economics, revised 02 May 2013.
    5. Kóczy Á., László, 2012. "Elméleti játékok, 2012. 8th Spain-Italy-Netherlands Meetings on Game Theory (SING8)
      [Theoretical Games 2012. The 8th Spain-Italy-Netherlands Meeting on Game Theory (SING8)]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 1257-1261.

    More about this item

    Keywords

    Repeated implementation; Nash implementation; Bayesian implementation; Ex post implementation; Efficiency; Incentive compatibility; Identifiability;

    JEL classification:

    • A13 - General Economics and Teaching - - General Economics - - - Relation of Economics to Social Values
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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