IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v180y2019icp336-367.html
   My bibliography  Save this article

Repeated implementation: A practical characterization

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053119300067
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2019.01.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jihong Lee & Hamid Sabourian, 2011. "Efficient Repeated Implementation," Econometrica, Econometric Society, vol. 79(6), pages 1967-1994, November.
    2. Kalai, Ehud & Ledyard, John O., 1998. "Repeated Implementation," Journal of Economic Theory, Elsevier, vol. 83(2), pages 308-317, December.
    3. Renou, Ludovic & Tomala, Tristan, 2015. "Approximate implementation in Markovian environments," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 401-442.
    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    5. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    6. 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.
    7. Chambers, Christopher P., 2004. "Virtual repeated implementation," Economics Letters, Elsevier, vol. 83(2), pages 263-268, May.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    13. 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.
    14. Lee, Jihong & Sabourian, Hamid, 2015. "Complexity and repeated implementation," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 259-292.
    15. 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.
    16. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    17. 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..
    18. Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
    19. Mezzetti, Claudio & Renou, Ludovic, 2017. "Repeated Nash implementation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    20. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Azacis, Helmuts & Vida, Péter, 2015. "Repeated Implementation," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 518, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    2. Lombardi, M. & Yoshihara, N., 2018. "Treading a fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Games and Economic Behavior, Elsevier, vol. 111(C), pages 203-216.
    3. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    4. Hayashi, Takashi & Lombardi, Michele, 2019. "One-step-ahead implementation," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 110-126.
    5. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2020. "Do coalitions matter in designing institutions?," Journal of Economic Theory, Elsevier, vol. 185(C).
    6. R Jain & V Korpela & M Lombardi, 2022. "Two-Player Rationalizable Implementation," Working Papers 202228, University of Liverpool, Department of Economics.
    7. Lombardi, Michele & Yoshihara, Naoki, 2016. "Partially-honest Nash Implementation with Non-connected Honesty Standards," Discussion Paper Series 633, Institute of Economic Research, Hitotsubashi University.
    8. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    9. Michele Lombardi & Naoki Yoshihara, 2017. "Treading a Â…fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Working Papers SDES-2017-14, Kochi University of Technology, School of Economics and Management, revised Aug 2017.
    10. Laslier, Jean-François & Núñez, Matías & Remzi Sanver, M., 2021. "A solution to the two-person implementation problem," Journal of Economic Theory, Elsevier, vol. 194(C).
    11. 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.
    12. Lee, Jihong & Sabourian, Hamid, 2015. "Complexity and repeated implementation," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 259-292.
    13. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    14. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    15. Corchón, Luis C., 2008. "The theory of implementation : what did we learn?," UC3M Working papers. Economics we081207, Universidad Carlos III de Madrid. Departamento de Economía.
    16. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    17. Mezzetti, Claudio & Renou, Ludovic, 2017. "Repeated Nash implementation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    18. Ashraf-Ball, Hezlin & Oswald, Andrew J. & Oswald, James I., 2009. "Hydrogen Transport and the Spatial Requirements of Renewable Energy," The Warwick Economics Research Paper Series (TWERPS) 903, University of Warwick, Department of Economics.
    19. Yi, Jianxin, 2011. "Implementation via mechanisms with transfers," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 65-70, January.
    20. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:180:y:2019:i:c:p:336-367. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.