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A cognitive hierarchy model of behavior in the action commitment game

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  • Daniel Carvalho
  • Luís Santos-Pinto

Abstract

We apply the cognitive hierarchy model of Camerer et al. (Q J Econ 119(3):861–898, 2004 )—where players have different levels of reasoning—to Huck et al. (Games Econ Behav 38:240–264, 2002 ) discrete version of Hamilton and Slutsky (Games Econ Behav 2:29–46, 1990 ) action commitment game—a duopoly with endogenous timing of entry. We show that, for an empirically reasonable average number of thinking steps, the model rules out Stackelberg equilibria, generates Cournot outcomes including delay, and outcomes where the first mover commits to a quantity higher than Cournot but lower than Stackelberg leader. We show that a cognitive hierarchy model with quantal responses can explain the most important features of the experimental data on the action commitment game in ( 2002 ). In order to gauge the success of the model in fitting the data, we compare it to a noisy Nash model. We find that the cognitive hierarchy model with quantal responses fits the data better than the noisy Nash model. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Daniel Carvalho & Luís Santos-Pinto, 2014. "A cognitive hierarchy model of behavior in the action commitment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 551-577, August.
  • Handle: RePEc:spr:jogath:v:43:y:2014:i:3:p:551-577
    DOI: 10.1007/s00182-013-0395-5
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    1. Miguel Fonseca & Wieland Müller & Hans-Theo Normann, 2006. "Endogenous timing in duopoly: experimental evidence," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 443-456, October.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    4. Saloner, Garth, 1987. "Cournot duopoly with two production periods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 183-187, June.
    5. Asen Ivanov & Dan Levin & James Peck, 2009. "Hindsight, Foresight, and Insight: An Experimental Study of a Small-Market Investment Game with Common and Private Values," American Economic Review, American Economic Association, vol. 99(4), pages 1484-1507, September.
    6. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    7. Santos-Pinto, Luís, 2008. "Making sense of the experimental evidence on endogenous timing in duopoly markets," Journal of Economic Behavior & Organization, Elsevier, vol. 68(3-4), pages 657-666, December.
    8. Huck, Steffen & Muller, Wieland & Normann, Hans-Theo, 2002. "To Commit or Not to Commit: Endogenous Timing in Experimental Duopoly Markets," Games and Economic Behavior, Elsevier, vol. 38(2), pages 240-264, February.
    9. Rogers, Brian W. & Palfrey, Thomas R. & Camerer, Colin F., 2009. "Heterogeneous quantal response equilibrium and cognitive hierarchies," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1440-1467, July.
    10. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    11. 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.
    12. Huck, Steffen & Muller, Wieland & Normann, Hans-Theo, 2001. "Stackelberg Beats Cournot: On Collusion and Efficiency in Experimental Markets," Economic Journal, Royal Economic Society, vol. 111(474), pages 749-765, October.
    13. Harless, David W. & Camerer, Colin F., 1995. "An error rate analysis of experimental data testing Nash refinements," European Economic Review, Elsevier, vol. 39(3-4), pages 649-660, April.
    14. Robson, Arthur J, 1990. "Duopoly with Endogenous Strategic Timing: Stackelberg Regained," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 263-274, May.
    15. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental "Hide-and-Seek" Games," American Economic Review, American Economic Association, vol. 97(5), pages 1731-1750, December.
    16. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    17. Robert Östling & Joseph Tao-yi Wang & Eileen Y. Chou & Colin F. Camerer, 2011. "Testing Game Theory in the Field: Swedish LUPI Lottery Games," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 1-33, August.
    18. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    19. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    20. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
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    More about this item

    Keywords

    Action commitment game; Thinking steps; Cognitive hierarchy; C72; D43; L13;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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