Breitmoser, Yves (2010): Hierarchical Reasoning versus Iterated Reasoning in p-Beauty Contest Guessing Games.
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This paper analyzes strategic choice in p-beauty contests. We first show that it is not generally a best reply to guess the expected target value (accounting for the own weight) even in games with n>2 players and that iterated best response sequences are not unique even after perfect/cautious refinement. This implies that standard formulations of ``level-k'' models are neither exactly nor uniquely rationalizable by belief systems based on iterated best response. Second, exact modeling of iterated reasoning weakens the fit considerably and reveals that equilibrium types dominate the populations. We also show that ``levels of reasoning'' cannot be measured regardless of the underlying model. Third, we consider a ``nested logit'' model where players choose their level. It dispenses with belief systems between players and is rationalized by a random utility model. Besides being internally consistent, nested logit equilibrium fits better than three variants of the level-k model in standard data sets.
|Item Type:||MPRA Paper|
|Original Title:||Hierarchical Reasoning versus Iterated Reasoning in p-Beauty Contest Guessing Games|
|Keywords:||logit equilibrium, hierarchical response, level-k, beauty contest|
|Subjects:||C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
|Depositing User:||Yves Breitmoser|
|Date Deposited:||13. Jan 2010 14:44|
|Last Modified:||18. Feb 2013 21:42|
Amemiya, T. (1978). On a two-step estimation of a multivariate logit model. Journal of Econometrics, 8(1):13–21.
Anderson, S. and De Palma, A. (1992). Multiproduct firms: a nested logit approach. The Journal of Industrial Economics, pages 261–276.
Anderson, S., Goeree, J., and Holt, C. (1998a). Rent seeking with bounded rationality: An analysis of the all-pay auction. Journal of Political Economy, 106(4):828.
Anderson, S., Goeree, J., and Holt, C. (1998b). A theoretical analysis of altruism and decision error in public goods games. Journal of Public Economics, 70(2):297– 323.
Arcidiacono, P. and Jones, J. (2003). Finite mixture distributions, sequential likelihood and the em algorithm. Econometrica, 71(3):933–946. Bernheim, B. (1984). Rationalizable strategic behavior. Econometrica, 52(4):1007– 1028.
Bierlaire, M. (2006). A theoretical analysis of the cross-nested logit model. Annals of operations research, 144(1):287–300. Bosch-Domenech, A., Montalvo, J., Nagel, R., and Satorra, A. (2002). One, two,(three), infinity,. . . : Newspaper and lab beauty-contest experiments. American Economic Review, 92(5):1687–1701.
Breitmoser, Y., Tan, J., and Zizzo, D. (2009). Understanding perpetual r&d races. Economic Theory (forthcoming).
Camerer, C., Ho, T., and Chong, J. (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119(3):861–898.
Costa-Gomes, M., Crawford, V., and Broseta, B. (2001). Cognition and behavior in normal-form games: An experimental study. Econometrica, 69(5):1193–1235.
Crawford, V. and Iriberri, N. (2007). Level-k auctions: Can a nonequilibrium model of strategic thinking explain the winner’s curse and overbidding in private-value auctions? Econometrica, 75(6):1721–1770.
Daly, A. and Zachary, S. (1978). Improved multiple choice models. In Determinants of Travel Choice, pages 335–357. Teakfield. 26
De Giorgi, E. and Reimann, S. (2008). The a-beauty contest: Choosing numbers, thinking intervals. Games and Economic Behavior, 64(2):470–486.
Haile, P., Hortacsu, A., and Kosenok, G. (2008). On the empirical content of quantal response equilibrium. American Economic Review, 98(1):180–200.
Ho, T., Camerer, C., and Weigelt, K. (1998). Iterated dominance and iterated best response in experimental "p-beauty contests". American Economic Review, 88(4):947–969.
Kübler, D. and Weizsäcker, G. (2004). Limited depth of reasoning and failure of cascade formation in the laboratory. Review of Economic Studies, 71(2):425–441.
Lee, B. (1999). Calling patterns and usage of residential toll service under self selecting tariffs. Journal of Regulatory economics, 16(1):45–82.
Luce, R. (1959). Individual choice behavior. Wiley New York.
Luce, R. (1977). The choice axiom after twenty years. Journal of Mathematical Psychology, 15(3):215–233. McFadden, D. (1978). Modelling the choice of residential location. In Karlqvist, A.,
Lundqvist, L., Snickars, F., and Weibull, J., editors, Spatial interaction theory and planning models, pages 75–96. North Holland: Amsterdam.
McFadden, D. (1981). Structural discrete probability models derived from theories of choice. In Manski, C. and McFadden, D., editors, Structural analysis of discrete data with econometric applications. MIT Press Cambridge, Mass.
McFadden, D. (1984). Econometric analysis of qualitative response models. Handbook of econometrics, 2:1395–1457.
McKelvey, R. and Palfrey, T. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior, 10(1):6–38.
McKelvey, R. and Palfrey, T. (1998). Quantal response equilibria for extensive form games. Experimental Economics, 1(1):9–41. 27
Nagel, R. (1995). Unraveling in guessing games: An experimental study. American Economic Review, 85(5):1313–1326.
Pearce, D. (1984). Rationalizable strategic behavior and the problem of perfection. Econometrica, 52(4):1029–1050.
Peel, D. and MacLahlan, G. (2000). Finite mixture models.
Rogers, B., Palfrey, T., and Camerer, C. (2009). Heterogeneous quantal response equilibrium and cognitive hierarchies. Journal of Economic Theory, 144(4):1440– 1467.
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2):461–464.
Selten, R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4(1):25–55.
Shaw, W. and Ozog, M. (1999). Modeling overnight recreation trip choice: application of a repeated nested multinomial logit model. Environmental and Resource Economics, 13(4):397–414.
Stahl, D. (1996). Boundedly rational rule learning in a guessing game. Games and Economic Behavior, 16(2):303–330.
Stahl, D. and Haruvy, E. (2008). Level-n bounded rationality in two-player two-stage games. Journal of Economic Behavior and Organization, 65(1):41–61.
Stahl, D. and Wilson, P. (1995). On players’ models of other players: Theory and experimental evidence. Games and Economic Behavior, 10(1):218–254.
Train, K. (2003). Discrete choice methods with simulation. Cambridge Univ Pr.
Train, K., McFadden, D., and Ben-Akiva, M. (1987). The demand for local telephone service: A fully discrete model of residential calling patterns and service choices. The Rand Journal of Economics, pages 109–123. 28
Turocy, T. (2005). A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence. Games and Economic Behavior, 51(2):243–263.
Tversky, A. (2004). Preference, Belief, and Similarity: Selected Writings. MIT Press.
Weizsäcker, G. (2003). Ignoring the rationality of others: evidence from experimental normal-form games. Games and Economic Behavior, 44(1):145–171.
Wen, C. and Koppelman, F. (2001). The generalized nested logit model. Transportation Research Part B, 35(7):627–641.
Whitten, G. and Palmer, H. (1996). Heightening comparativists’ concern for model choice: Voting behavior in great britain and the netherlands. American Journal of Political Science, 40(1):231–260. 29