IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v158y2015ipap259-292.html
   My bibliography  Save this article

Complexity and repeated implementation

Author

Listed:
  • Lee, Jihong
  • Sabourian, Hamid

Abstract

This paper examines the problem of repeatedly implementing an efficient social choice function when the agents' preferences evolve randomly. We show that the freedom to set different mechanisms at different histories can give the planner an additional leverage to deter undesirable behavior even if the mechanisms are restricted to be simple and finite. Specifically, we construct a history-dependent sequence of simple mechanisms such that, with minor qualifications, every pure subgame perfect equilibrium delivers the correct social choice at every history, while every mixed equilibrium is strictly Pareto-dominated. More importantly, when faced with agents with a preference for less complex strategies at the margin, the (efficient) social choice function can be repeatedly implemented in subgame perfect equilibrium in pure or mixed strategies. Our results demonstrate a positive role for complexity considerations in mechanism design.

Suggested Citation

  • Lee, Jihong & Sabourian, Hamid, 2015. "Complexity and repeated implementation," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 259-292.
    • Handle: RePEc:eee:jetheo:v:158:y:2015:i:pa:p:259-292
    DOI: 10.1016/j.jet.2015.05.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053115000800
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2015.05.002?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. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, vol. 42(2), pages 382-386, August.
    2. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    3. Geoffroy de Clippel, 2012. "Behavioral Implementation," Working Papers 2012-6, Brown University, Department of Economics.
    4. Jacob Glazer & Ariel Rubinstein, 2014. "Complex Questionnaires," Econometrica, Econometric Society, vol. 82(4), pages 1529-1541, July.
    5. Jihong Lee & Hamid Sabourian, 2011. "Efficient Repeated Implementation," Econometrica, Econometric Society, vol. 79(6), pages 1967-1994, November.
    6. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, vol. 139(1), pages 353-359, March.
    7. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    8. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
    9. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    10. Ken Binmore & Michele Piccione & Larry Samuelson, "undated". "Evolutionary Stability in Alternating-Offers Bargaining Games," ELSE working papers 041, ESRC Centre on Economics Learning and Social Evolution.
    11. Binmore, Ken & Piccione, Michele & Samuelson, Larry, 1998. "Evolutionary Stability in Alternating-Offers Bargaining Games," Journal of Economic Theory, Elsevier, vol. 80(2), pages 257-291, June.
    12. Saran, Rene, 2011. "Menu-dependent preferences and revelation principle," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1712-1720, July.
    13. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107, Elsevier.
    14. 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.
    15. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    16. Lee, Jihong & Sabourian, Hamid, 2007. "Coase theorem, complexity and transaction costs," Journal of Economic Theory, Elsevier, vol. 135(1), pages 214-235, July.
    17. Kalai, E & Neme, A, 1992. "The Strength of a Little Perfection," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 335-355.
    18. Douglas Gale & Hamid Sabourian, 2005. "Complexity and Competition," Econometrica, Econometric Society, vol. 73(3), pages 739-769, May.
    19. 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.
    20. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    21. 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.
    22. Kalyan Chatterjee & Hamid Sabourian, 2000. "Multiperson Bargaining and Strategic Complexity," Econometrica, Econometric Society, vol. 68(6), pages 1491-1510, November.
    23. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    24. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    25. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    26. Geoffroy de Clippel, 2014. "Behavioral Implementation," American Economic Review, American Economic Association, vol. 104(10), pages 2975-3002, October.
    27. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    28. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    29. 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.
    30. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    31. Sabourian, Hamid, 2004. "Bargaining and markets: complexity and the competitive outcome," Journal of Economic Theory, Elsevier, vol. 116(2), pages 189-228, June.
    32. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    33. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    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. Āzacis, Helmuts & Vida, Péter, 2019. "Repeated implementation: A practical characterization," Journal of Economic Theory, Elsevier, vol. 180(C), pages 336-367.

    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. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    2. 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.
    3. 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.
    4. 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.
    5. T. Hayashi & R. Jain & V. Korpela & M. Lombardi, 2023. "Behavioral strong implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1257-1287, November.
    6. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2020. "Do coalitions matter in designing institutions?," Journal of Economic Theory, Elsevier, vol. 185(C).
    7. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    8. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    9. 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.
    10. 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.
    11. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    12. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    13. Ortner, Juan, 2015. "Direct implementation with minimally honest individuals," Games and Economic Behavior, Elsevier, vol. 90(C), pages 1-16.
    14. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.
    15. Koray, Semih & Yildiz, Kemal, 2018. "Implementation via rights structures," Journal of Economic Theory, Elsevier, vol. 176(C), pages 479-502.
    16. Lombardi, Michele & Yoshihara, Naoki, 2016. "Partially-honest Nash Implementation with Non-connected Honesty Standards," Discussion Paper Series 633, Institute of Economic Research, Hitotsubashi University.
    17. 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.
    18. Bierbrauer, Felix & Netzer, Nick, 2016. "Mechanism design and intentions," Journal of Economic Theory, Elsevier, vol. 163(C), pages 557-603.
    19. Philippe Aghion & Drew Fudenberg & Richard Holden & Takashi Kunimoto & Olivier Tercieux, 2012. "Subgame-Perfect Implementation Under Information Perturbations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(4), pages 1843-1881.
    20. George F. N. Shoukry, 2019. "Outcome-robust mechanisms for Nash implementation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 497-526, March.

    More about this item

    Keywords

    Complexity; Repeated implementation; Efficiency; Finite mechanisms; Mixed strategies; Subgame perfect equilibrium;
    All these keywords.

    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
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

    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:158:y:2015:i:pa:p:259-292. 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.