Asymmetric Guessing Games

AKIN, ZAFER (2020): Asymmetric Guessing Games.

Abstract

This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing k>1 replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (k=1) imitates the strong player (k>1). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases discrepancy in choices (defined as the squared distance of choices from the winning number) in both games.

• Item Type: MPRA Paper
• Language: English
• Keywords: Guessing game, asymmetry, convergence, game theory, experimental economics
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C92 - Laboratory, Group Behavior

References

Agranov, M., Potamites, E., Schotter, A., and Tergiman, C. (2012). Beliefs and endogenous cognitive levels: An experimental study. Games and Economic Behavior, 75 (2), 449-463.

Akin, Z., and Urhan, U. B (2011). A Game Theoretic Approach to Model Financial Markets: Guessing Games. ISE Review, 12(47), 43-60.

Baethge, C. (2016). Performance in the beauty contest: How strategic discussion enhances team reasoning. Passauer Diskussionspapiere - Betriebswirtschaftliche Reihe, No. B-17-16, Universität Passau.

Benhabib, J., Duffy J., and Nagel R. (2019). (De)-Anchoring Beliefs in Beauty Contest Games. Working Paper.

Bosch-Domenech A., GarcÃ-a-Montalvo, J., Nagel, R. and Antoni, S. A. (2002). One, Two, (Three), Infinity: Newspaper and Lab Beauty-Contest Experiments. American Economic Review, Vol. 92, No 5, 1687-1701.

Bosch-Rosa, C., and Meissner, T. (2020). The one player guessing game: a diagnosis on the relationship between equilibrium play, beliefs, and best responses. Experimental Economics, 1-19.

Burchardi, K. B., and Penczynski, S. P. (2014). Out of your mind: Eliciting individual reasoning in one shot games. Games and Economic Behavior, 84, 39-57.

Camerer, Colin F. (2003). Behavioral Game Theory. Princeton University Press.

Chou, E., McConnell, M., Nagel, R., and Plott, Charles R. (2009). The control of game form recognition in experiments: Understanding dominant strategy failures in a simple two person guessing game. Experimental Economics, 12, 159-179.

Costa-Gomes, M.A. and Crawford, V.P. (2006). Cognition and behavior in two-player guessing games: An experimental study. American Economic Review, 96, 1737-1768.

Crawford, V.P., Costa-Gomes, M.A., and Iriberri, N. (2013). Structural models of non-equilibrium strategic thinking: Theory, evidence, and applications. Journal of Economic Literature, 51(1), 5-62.

Duffy, J. and Nagel, R. (1997). On the robustness of behavior in experimental “beauty contest” games. The Economic Journal, Vol. 107, 1684-1700.

Echenique, F., and Edlin, A. S. (2004). Mixed equilibria are unstable in games of strategic complements. Journal of Economic Theory, 118(1), 61-79.

Fischbacher, Urs, (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics 10(2), 171-178.

Fragiadakis, D. E., Knoepfle, D. T., and Niederle, M. (2013). Identifying predictable players: Relating behavioral types and subjects with deterministic rules. mimeo.

Grosskopf, B. and Nagel, R. (2008). The two-player beauty contest. Games and Economic Behavior, 62 (1), 93-99.

Grosskopf, B. and Nagel, R. (2009). Unraveling in two-player Guessing Games. Working Paper.

G{ü}th, W., Kocher, M. and Sutter, M. (2002). Experimental beauty contests with homogeneous and heterogeneous players and with interior and boundary equilibria. Economics Letters, Vol. 74, 219-228.

Hanaki, N., Koriyama, Y., Sutan, A., and Willinger, M. (2019). The strategic environment effect in beauty contest games. Games and Economic Behavior, 113, 587-610.

Heemeijer, P., Hommes, C., Sonnemans, J., and Tuinstra, J. (2009). Price stability and volatility in markets with positive and negative expectations feedback: An experimental investigation. Journal of Economic Dynamics and Control, 33(5), 1052-1072.

Heinemann, F., Nagel, R., and Ockenfels, P. (2009). Measuring strategic uncertainty in coordination games. The Review of Economic Studies, 76(1), 181-221.

Ho, T., Camerer, C., and Keith, W. (1998). Iterated dominance and iterated best response in experimental p-beauty-contests. American Economic Review, Vol. 88, 947-969.

Hoffman, E., McCabe, K., Shachat, K., and Smith, V. (1994). P, property rights, and anonymity in bargaining games. Games and Economic behavior, 7(3), 346-380.

Hommes, C., Sonnemans, J., Tuinstra, J., and Van de Velden, H. (2005). Coordination of expectations in asset pricing experiments. Review of Financial Studies, 18, 955- 980.

Hommes, C., Sonnemans, J., Tuinstra, J., and Van de Velden, H. (2008). Expectations and bubbles in asset pricing experiments. Journal of Economic Behavior and Organization, 67(1), 116-133.

Keynes, John Maynard (1936). The General Theory of Employment, Interest and Money. London: MacMillan.

Kocher, M., Straub, S., and Sutter, M. (2006). Individual or team decision-making - Causes and consequences of self-selection. Games and Economic Behavior, Vol. 56, 259-270.

Kocher, M. and Sutter, M (2005). The decision maker matters: individual versus group behavior in experimental beauty-contest games. The Economic Journal, 115 (500), 200–223.

Kocher, M., Sutter, M., and Wakolbinger, F. (2014). Social learning in beauty-contest games. Southern Economic Journal, 80(1), 586-613.

Kopányi, D., Rabanal, J. P., Rud, O. A., and Tuinstra, J. (2019). Can competition between forecasters stabilize asset prices in learning to forecast experiments?. Journal of Economic Dynamics and Control, 109, 103770.

Kovac, E., Ortmann, A., and Vojtek, M. (2008). Comparing guessing games with homogeneous and heterogeneous players: Experimental results and a CH explanation. Economics Bulletin, 3(9), 1-9.

Kirchler, M. (2009). Under-reaction to fundamental information and asymmetry in mispricing between bullish and bearish markets. An experimental study. Journal of Economic Dynamics and Control, 33(2), 491-506.

Liu, T. (2016). Heterogeneity in Guessing Games: An Experiment. Working Paper.

Lopez, R. (2001). On p-beauty contest integer games. UPF Economics and Business Working Paper No:608.

Mauersberger, F. and Nagel, R. (2018). Levels of reasoning in Keynesian Beauty Contests: a generative framework. In Handbook of computational economics (Vol. 4, 541-634). Elsevier.

McKelvey, Richard D., McLennan, Andrew M., and Turocy, Theodore L. (2016). Gambit: Software tools for game theory, Version 16.0.1. http://www.gambit-project.org.

Nagel, R. (1995). Unraveling in guessing games: an experimental study. American Economic Review, Vol. 85, 1313-1326.

Nagel, R. (2008). Experimental beauty contest games: levels of reasoning and convergence to equilibrium. Handbook of experimental economics results, 1, 391-410.

Nagel, R., Bühren, C., and Frank, B. (2017). Inspired and inspiring: Hervé Moulin and the discovery of the beauty-contest game. Mathematical Social Sciences, 90, 191–207.

Noussair, C., Robin, S., and Ruffieux, B. (2001). Price bubbles in laboratory asset markets with constant fundamental values. Experimental Economics, 4(1), 87-105.

Penczynski, S. P. (2016). Persuasion: An experimental study of team decision making. Journal of Economic Psychology, 56, 244-261.

Sbriglia, Patrizia. (2008). Revealing the depth of reasoning in p-beauty contest games. Experimental Economics, Vol. 11, No.2, 107-121.

Slonim, R. L. (2005). Competing Against Experienced and Inexperienced Players. Experimental Economics, Vol. 8, 55-75.

Smith, V. L., Suchanek, G. L., and Williams, A. W. (1988). Bubbles, crashes, and endogenous expectations in experimental spot asset markets. Econometrica, 1119-1151.

Sonnemans, J. and Tuinstra, J. (2010). Positive expectations feedback experiments and number guessing games as models of financial markets. Journal of Economic Psychology, 31(6), 964-984.

Stahl, Dale O. (1996). Boundedly rational rule learning in a guessing game. Games and Economic Behavior, Vol. 16, 303-330.

Sutter, M. (2005). Are four heads better than two? An experimental beauty-contest game with teams of different size. Economics Letters, Vol. 88 (1), 41-46.

Weber, Roberto A. (2003). Learning with no feedback in a competitive guessing game. Games and Economic Behavior, Vol. 44, 131-144.