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Repeated implementation: A practical characterization

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  • Āzacis, Helmuts
  • Vida, Péter

Abstract

We characterize the social choice functions that are repeatedly implementable. The necessary and sufficient condition is formulated in terms of the equilibrium payoff set of an associated repeated game. It follows that the implementability of a function can be tested numerically by approximating the equilibrium payoff set. Additionally, with the help of our characterization, we demonstrate that an efficient function is implementable if and only if it satisfies a weaker version of Maskin monotonicity. As an application, we prove that utilitarian social choice functions are implementable by showing that continuation payoff promises effectively play the role of side-payments, which are needed for implementation in static setups.

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  • Āzacis, Helmuts & Vida, Péter, 2019. "Repeated implementation: A practical characterization," Journal of Economic Theory, Elsevier, vol. 180(C), pages 336-367.
    • Handle: RePEc:eee:jetheo:v:180:y:2019:i:c:p:336-367
    DOI: 10.1016/j.jet.2019.01.002
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    1. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    2. Renou, Ludovic & Tomala, Tristan, 2015. "Approximate implementation in Markovian environments," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 401-442.
    3. Jihong Lee & Hamid Sabourian, 2011. "Efficient Repeated Implementation," Econometrica, Econometric Society, vol. 79(6), pages 1967-1994, November.
    4. Lee, Jihong & Sabourian, Hamid, 2015. "Complexity and repeated implementation," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 259-292.
    5. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    6. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    7. Kalai, Ehud & Ledyard, John O., 1998. "Repeated Implementation," Journal of Economic Theory, Elsevier, vol. 83(2), pages 308-317, December.
    8. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
    9. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April.
    10. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    11. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    12. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    13. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    14. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    15. Dilip Abreu & Benjamin Brooks & Yuliy Sannikov, 2016. "A "Pencil Sharpening" Algorithm for Two Player Stochastic Games with Perfect Monitoring," Working Papers 78_2016, Princeton University, Department of Economics, Econometric Research Program..
    16. Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
    17. Chambers, Christopher P., 2004. "Virtual repeated implementation," Economics Letters, Elsevier, vol. 83(2), pages 263-268, May.
    18. Mezzetti, Claudio & Renou, Ludovic, 2017. "Repeated Nash implementation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    19. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    20. Laffont, Jean-Jacques & Maskin, Eric, 1982. "Nash and dominant strategy implementation in economic environments," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 17-47, June.
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    Cited by:

    1. Helmuts Āzacis, 2020. "Repeated implementation with overlapping generations of agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 275-299, August.

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    More about this item

    Keywords

    Repeated implementation; Dynamic monotonicity; Efficiency; Repeated games; Sufficient and necessary conditions;
    All these keywords.

    JEL classification:

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

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