Discrete Rule Learning and the Bidding of the Sexes

Shachat, Jason and Wei, Lijia (2013): Discrete Rule Learning and the Bidding of the Sexes.

Abstract

We present a hidden Markov model of discrete strategic heterogeneity and learning in first price independent private values auctions. The model includes three latent bidding rules: constant absolute mark-up, constant percentage mark-up, and strategic best response. Rule switching probabilities depend upon a bidder's past auction outcomes. We apply this model to a new experiment that varies the number of bidders, the auction frame between forward and reverse, and includes the collection of saliva samples - used to measure subjects' sex hormone levels. We find the proportion of bidders following constant absolute mark-up increases with experience, particularly when the number of bidders is large. The primary driver here is subjects' increased propensity to switch strategies when they experience a loss (win) reinforcement when following a strategic (heuristic) rule. This affect is stronger for women and leads them spend more time following boundedly rational rules. We also find women in the Luteal and Menstrual phases of their menstrual cycle bid less aggressively, in terms of surplus demanded, when following the best response rule. This combined with spending more time following simple rules of thumbs explains gender differences in earnings.

• Item Type: MPRA Paper
• Language: English
• Keywords: private value auction; discrete heterogeneity; learning; gender difference; hidden Markov model; laboratory experiment
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; 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; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions

References

Albert, James H and Siddhartha Chib (1993), “Bayesian analysis of binary and polychotomous response data.” Journal of the American Statistical Association, 88, 669–679.

Baumol, William J. and Richard E. Quandt (1964), “Rules of thumb and optimally imperfect decisions.” The American Economic Review, 54, 23–46.

Blinder, Alan S (1973), “Wage discrimination: reduced form and structural estimates.” Journal of Human resources, 436–455.

Casari, Marco, John C. Ham, and John H. Kagel (2007), "Selection bias, demographic effects, and ability effects in common value auction experiments.” American Economic Review, 97, 1278–1304.

Chen, Yan, Peter Katuk, and Emre Ozdenoren (2013), “Why can’t a woman bid more like a man?” Games and Economic Behavior, 77, 181 – 213.

Crawford, Vincent P. and Nagore Iriberri (2007), “Level-k auctions: can a nonequilibrium model of strategic thinking explain the winner’s curse and overbidding in private-value auctions?” Econometrica, 75, 1721–1770.

Erev, Ido and Alvin E. Roth (1998), “Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria.” American Economic Review, 88, 848–81.

Filardo, Andrew I. and Stephen F. Gordon (1998), “Business cycle durations.” Journal of Econometrics, 85, 99–123.

Fischbacher, Urs (2007), “z-tree: Zurich toolbox for ready-made economic experiments.” Experimental Economics, 10, 171–178.

Geman, Stuart and Donald Geman (1987), “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images.” In Readings in computer vision: issues, problems, principles, and paradigms (Martin A. Fischler and Oscar Firschein, eds.), 564–584, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.

Geweke, John (1991), “Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments.” Staff Report 148, Federal Reserve Bank of Minneapolis.

Gill, David and Victoria Liza Prowse (2012), “Gender differences and dynamics in competition: the role of luck.” MPRA Paper, University Library of Munich, Germany.

Goeree, Jacob and Charles A. Holt (2002), “Quantal response equilibrium and overbidding in private-value auctions.” Journal of Economic Theory, 104, 247–272.

Greiner, Ben (2004), “An online recruitment system for economic experiments.” In Forschung und wissenschaftliches Rechnen (Kurt Kremer and Volker Macho, eds.), volume 63 of Ges. fur Wiss. Datenverarbeitung, 79–93, GWDG Bericht.

Guth, Werner, Radosveta Ivanova-Stenzel, Manfred Konigstein, and Martin Strobel (2003), “Learning to bid - an experimental study of bid function adjustments in auctions and fair division games.” Economic Journal, 113, 477–494.

Holt, Charles A (1980), “Competitive bidding for contracts under alternative auction procedures.” The Journal of Political Economy, 433–445.

Isaac, Mark, Svetlana Pevnitskaya, and Kurt S. Schnier (2012), “Individual behavior and bidding heterogeneity in sealed bid auctions where the number of bidders is unknown.” Economic Inquiry, 50, 516–533.

Kagel, John H (1995), “Auctions: a survey of experimental research.” In The Handbook of Experimental Economics (Alvin E Roth and John H Kagel, eds.), first edition, chapter 7, 501 – 585, Princeton University Press, Princeton, NJ.

Kagel, John H and Dan Levin (1993), “Independent private value auctions: bidder behaviour in first-, second-and third-price auctions with varying numbers of bidders.” The Economic Journal, 868–879.

Kagel, John H and Dan Levin (2011), “Auctions: a survey of experimental research, 1995–2010.” Manuscript, Ohio State University.

Kirchkamp, Oliver and J. Philipp Reiss (2008), "Heterogeneous bids in auctions with rational and markdown bidders - theory and experiment.” Jena Economic Research Papers 2008-066, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.

McKelvey, Richard D and Thomas R Palfrey (1995), “Quantal response equilibria for normal form games.” Games and economic behavior, 10, 6–38.

Neugebauer, Tibor and Reinhard Selten (2006), “Individual behavior of first-price auctions: The importance of information feedback in computerized experimental markets.” Games and Economic Behavior, 54, 183–204.

Oaxaca, Ronald (1973), “Male-female wage differentials in urban labor markets.” International Economic Review, 14, 693–709.

Pearson, Matthew and Burkhard C. Schipper (2013), “Menstrual cycle and competitive bidding.” Games and Economic Behavior, 78, 1 – 20.

Schipper, Burkhard (2012), “Sex hormones and competitive bidding.” Working Papers 128, University of California, Davis, Department of Economics.

Selten, Reinhard and Joachim Buchta (1998), “Experimental sealed bid first price auctions with directly observed bid functions.” In Games and Human Behavior: Essays in Honor of Amnon Rapoport (David V. Budescu, Ido Erev, and Rami Zwick, eds.), chapter 5, 79–102,Lawrence Erlbaum Ass., Mahwah (NJ).

Shachat, Jason and Lijia Wei (2012), “Procuring commodities: first-price sealed-bid or english auctions?” Marketing Science, 31, 317–333.

Vickrey, William (1961), “Counterpeculation, auctions, and competitive sealed tenders.” Journal of Finance, 16, 8–37.

Zhou, Yuanzhong, Chengliang Xiong, Ping Yin, Xuejun Shang, Sheng Wei, Hong Liu, Guohui Liu, Xueyi Wang, Meimei Zhang, Xinwei Li, Huangtao Guan, Dunzheng Xiao, Xuebing Pang, Ning Ren, and Min Wang (2009), “Survey of status and requirement about sexual behavior and contraception among unmarried college/university students in china.” Journal of Huazhong University of Science and Technology (Medical Sciences), 38, 561–580.