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To err is human: Implementation in quantal response equilibria

Listed author(s):
  • Tumennasan, Norovsambuu

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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File URL: http://www.sciencedirect.com/science/article/pii/S0899825612001522
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 77 (2013)
Issue (Month): 1 ()
Pages: 138-152

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Handle: RePEc:eee:gamebe:v:77:y:2013:i:1:p:138-152
DOI: 10.1016/j.geb.2012.10.004
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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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," Review of Economic Studies, Oxford University Press, 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. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
  6. Kfir Eliaz, 2002. "Fault Tolerant Implementation," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 589-610.
  7. 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.
  8. 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.
  9. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 757-775.
  10. Cabrales, Antonio, 1999. "Adaptive Dynamics and the Implementation Problem with Complete Information," Journal of Economic Theory, Elsevier, vol. 86(2), pages 159-184, June.
  11. 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.
  12. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  13. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 885-915.
  14. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1998. "Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction," Journal of Political Economy, University of Chicago Press, vol. 106(4), pages 828-853, August.
  15. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  16. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
  17. 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.
  18. 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.
  19. 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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