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To err is human: Implementation in quantal response equilibria

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  • Tumennasan, Norovsambuu

Abstract

We study the implementation problem when players are prone to make mistakes. To capture the idea of mistakes, Logit Quantal Response Equilibrium (LQRE) is used, and we consider a case in which players are almost rational, i.e., the sophistication level of players approaches infinity. We show that quasimonotonicity, a small variation of Maskin monotonicity, and no worst alternative are the necessary conditions for restricted Limit LQRE (LLQRE) implementation. Moreover, these conditions are sufficient for both restricted and unrestricted LLQRE implementations if there are at least three players and if at least one player has a state-independent worst alternative.

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  • Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    • Handle: RePEc:eee:gamebe:v:77:y:2013:i:1:p:138-152
    DOI: 10.1016/j.geb.2012.10.004
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    1. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    2. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    3. Jacob K. Goeree & Thomas R. Palfrey & Brian W. Rogers & Richard D. McKelvey, 2007. "Self-Correcting Information Cascades," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 733-762.
    4. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    7. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
    8. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 2001. "Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium," Games and Economic Behavior, Elsevier, vol. 34(2), pages 177-199, February.
    9. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    10. 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.
    11. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June.
    12. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    13. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    14. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 885-915.
    15. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1998. "Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 225-250, Springer.
    16. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
    17. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
    18. 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.
    19. 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.
    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.
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    Cited by:

    1. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    2. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    3. Ivan S Menshikov & Alexsandr V Shklover & Tatiana S Babkina & Mikhail G Myagkov, 2017. "From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-17, November.
    4. Alexander L. Brown & Rodrigo A. Velez, 2019. "Empirical bias and efficiency of alpha-auctions: experimental evidence," Papers 1905.03876, arXiv.org, revised Jul 2020.
    5. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    6. Rodrigo A. Velez & Alexander L. Brown, 2019. "Empirical strategy-proofness," Papers 1907.12408, arXiv.org, revised Jul 2020.
    7. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    8. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
    9. Kendall, Ryan, 2021. "Sequential competitions with a middle-mover advantage," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
    10. Xiaochuan Huang & Takehito Masuda & Yoshitaka Okano & Tatsuyoshi Saijo, 2014. "Cooperation among behaviorally heterogeneous players in social dilemma with stay or leave decisions," Working Papers SDES-2014-7, Kochi University of Technology, School of Economics and Management, revised Feb 2015.
    11. Edward Cartwright & Anna Stepanova, 2017. "Efficiency in a forced contribution threshold public good game," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1163-1191, November.
    12. Kimya, Mert, 2017. "Nash implementation and tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 102(C), pages 138-146.
    13. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    14. 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.
    15. Rodrigo A. Velez & Alexander L. Brown, 2018. "Empirical Equilibrium," Papers 1804.07986, arXiv.org, revised Jul 2020.
    16. Changping Zhao & Yecheng Wang & Tianxiang Zhang & Qingbo Huang & Yu Gong, 2019. "The Game Simulation of “The Belt and Road” Economic and Trade Network Based on the Asymmetric QRE Model," Sustainability, MDPI, vol. 11(12), pages 1-17, June.
    17. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    18. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.

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    More about this item

    Keywords

    Implementation; Mechanisms; Bounded rationality; Quantal response equilibria;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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