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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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    Cited by:

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    2. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    3. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    4. 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.
    5. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
    6. Rodrigo A. Velez & Alexander L. Brown, 2018. "Empirical Equilibrium," Papers 1804.07986, arXiv.org, revised Jul 2020.
    7. 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.
    8. 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.
    9. 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.
    10. Alexander L. Brown & Rodrigo A. Velez, 2019. "Empirical bias and efficiency of alpha-auctions: experimental evidence," Papers 1905.03876, arXiv.org, revised Jul 2020.
    11. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    12. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    13. 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).
    14. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    15. 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.
    16. Rodrigo A. Velez & Alexander L. Brown, 2019. "Empirical strategy-proofness," Papers 1907.12408, arXiv.org, revised Jul 2020.
    17. 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.
    18. Kimya, Mert, 2017. "Nash implementation and tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 102(C), pages 138-146.

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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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