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Lucky Numbers in Simple Games

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  • Irenaeus Wolff

Abstract

Simple game structures such as coordination, discoordination, hide-and seek, and Colonel-Blotto games have been used to model a wide range of economically relevant situations. Yet, Nash-equilibrium, and alternative theories that have been proposed in the literature, notoriously fail to explain observed behaviorinthesegames. Thispaperproposesabounded-rationalityapproachinwhich players lexicographically employ team reasoning, choose ‘lucky numbers’ (the choice they would pick in a lottery), and randomise uniformly. This three-step procedure is able to organise the data across many diferent frames for coordination, discoordination, and hide-and-seek games. Moreover, it predicts three general regularities that bear out on the existing data and additional data from a Colonel-Blotto game and a Rock-Paper-Scissors-type of game.

Suggested Citation

  • Irenaeus Wolff, 2017. "Lucky Numbers in Simple Games," TWI Research Paper Series 107, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    • Handle: RePEc:twi:respas:0107
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    1. Maya Bar-Hillel, 2015. "Position Effects in Choice from Simultaneous Displays: A Conundrum Solved," Discussion Paper Series dp678, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Vincent P. Crawford & Uri Gneezy & Yuval Rottenstreich, 2008. "The Power of Focal Points Is Limited: Even Minute Payoff Asymmetry May Yield Large Coordination Failures," American Economic Review, American Economic Association, vol. 98(4), pages 1443-1458, September.
    3. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 833-861, April.
    4. Nicholas Bardsley & Judith Mehta & Chris Starmer & Robert Sugden, 2010. "Explaining Focal Points: Cognitive Hierarchy Theory "versus" Team Reasoning," Economic Journal, Royal Economic Society, vol. 120(543), pages 40-79, March.
    5. Wolff, Irenaeus, 2016. "Elicited salience and salience-based level-k," Economics Letters, Elsevier, vol. 141(C), pages 134-137.
    6. 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.
    7. Arad, Ayala & Rubinstein, Ariel, 2012. "Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game," Journal of Economic Behavior & Organization, Elsevier, vol. 84(2), pages 571-585.
    8. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    9. Dominik Bauer & Irenaeus Wolff, 2018. "Biases in Beliefs: Experimental Evidence," TWI Research Paper Series 109, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    10. 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.
    11. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    12. Eliaz, Kfir & Rubinstein, Ariel, 2011. "Edgar Allan Poe's riddle: Framing effects in repeated matching pennies games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 88-99, January.
    13. Vincent P. Crawford, 2003. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," American Economic Review, American Economic Association, vol. 93(1), pages 133-149, March.
    14. Mehta, Judith & Starmer, Chris & Sugden, Robert, 1994. "The Nature of Salience: An Experimental Investigation of Pure Coordination Games," American Economic Review, American Economic Association, vol. 84(3), pages 658-673, June.
    15. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
    16. Scharlemann, Jorn P. W. & Eckel, Catherine C. & Kacelnik, Alex & Wilson, Rick K., 2001. "The value of a smile: Game theory with a human face," Journal of Economic Psychology, Elsevier, vol. 22(5), pages 617-640, October.
    17. Timo Heinrich & Irenaeus Wolff, 2012. "Strategic Reasoning in Hide-and-Seek Games: A Note," Working Paper Series of the Department of Economics, University of Konstanz 2012-11, Department of Economics, University of Konstanz.
    18. Broseta, Bruno & Costa-Gomes, Miguel & Crawford, Vincent P., 2000. "Cognition and Behavior in Normal-Form Games: An Experimental Study," University of California at San Diego, Economics Working Paper Series qt0fp8278k, Department of Economics, UC San Diego.
    19. Simon, Jonathan, 1998. "An Analysis of the Distribution of Combinations Chosen by UK National Lottery Players," Journal of Risk and Uncertainty, Springer, vol. 17(3), pages 243-276, December.
    20. Sugden, Robert, 1995. "A Theory of Focal Points," Economic Journal, Royal Economic Society, vol. 105(430), pages 533-550, May.
    21. Yang, Zili, 2011. "“Lucky” numbers, unlucky consumers," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 40(5), pages 692-699.
    22. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    23. Rubinstein, Ariel, 1999. "Experience from a Course in Game Theory: Pre- and Postclass Problem Sets as a Didactic Device," Games and Economic Behavior, Elsevier, vol. 28(1), pages 155-170, July.
    24. Irenaeus Wolff & Dominik Bauer, 2018. "Elusive Beliefs: Why Uncertainty Leads to Stochastic Choice and Errors," TWI Research Paper Series 111, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    25. 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.
    26. Ayala Arad & Ariel Rubinstein, 2012. "The 11-20 Money Request Game: A Level-k Reasoning Study," American Economic Review, American Economic Association, vol. 102(7), pages 3561-3573, December.
    27. Ireneaus Wolff, 2016. "Elicited Salience and Salience-Based Level-k," TWI Research Paper Series 103, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    28. 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.
    29. Shane Frederick, 2005. "Cognitive Reflection and Decision Making," Journal of Economic Perspectives, American Economic Association, vol. 19(4), pages 25-42, Fall.
    30. Penczynski, Stefan P., 2016. "Strategic thinking: The influence of the game," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 72-84.
    31. 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.
    32. Groseclose, Tim & Snyder, James M., 1996. "Buying Supermajorities," American Political Science Review, Cambridge University Press, vol. 90(2), pages 303-315, June.
    33. Shaun Hargreaves Heap & David Rojo Arjona & Robert Sugden, 2014. "How Portable Is Level‐0 Behavior? A Test of Level‐k Theory in Games With Non‐Neutral Frames," Econometrica, Econometric Society, vol. 82(3), pages 1133-1151, May.
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    Cited by:

    1. Folli, Dominik & Wolff, Irenaeus, 2022. "Biases in belief reports," Journal of Economic Psychology, Elsevier, vol. 88(C).
    2. Dominik Bauer & Irenaeus Wolff, 2018. "Biases in Beliefs: Experimental Evidence," TWI Research Paper Series 109, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    3. Bauer, Dominik & Wolff, Irenaeus, 2019. "Biases in Beliefs," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203601, Verein für Socialpolitik / German Economic Association.

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    Keywords

    Bounded Rationality; Level-k; Salience; Heuristic; Hide & Seek; Discoordination; Rock-Paper-Scissors; Colonel Blotto; Representativeness;
    All these keywords.

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