Knowing me, imagining you: Projection and overbidding in auctions

Breitmoser, Yves (2015): Knowing me, imagining you: Projection and overbidding in auctions.

Abstract

People overestimate the probability that others share their values or preferences. I introduce type projection equilibrium (TPE) to capture such projection in Bayesian games. TPE allows each player to believe his opponents share his type with intermediate probability \rho. After establishing existence, I address my main question: How does projection affect behavior in games? I analyze auctions and distribution games. In auctions, projection implies an increased sense of competition, which induces overbidding in all (first-price) auctions. In addition, it biases the perceived value distribution, which induces cursed bidding in common value auctions. Thus, projection induces a hitherto neglected bias in bidding. It is novel in that it explains behavior across conditions and it is independently founded in psychology. I test projection equilibrium in multiple ways on existing data and find that it substantially improves on alternative concepts, both in isolation and in addition to them. The findings are cross-validated by testing projection of social preferences in distribution games.

• Item Type: MPRA Paper
• Language: English
• Keywords: auctions, overbidding, winner's curse, projection, risk aversion, cursed equilibrium, level-k, social preferences
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D44 - Auctions

References

Aksoy, O. and Weesie, J. (2012). Beliefs about the social orientations of others: Aparametric test of the triangle, false consensus, and cone hypotheses. Journal of Experimental Social Psychology, 48(1):45–54.

Avery, C. and Kagel, J. (1997). Second-price auctions with asymmetric payoffs: An experimental investigation. Journal of Economics & Management Strategy, 6(3):573–603.

Bajari, P. and Hortacsu, A. (2005). Are structural estimates of auction models reasonable? evidence from experimental data. Journal of Political Economy, 113(4):703–741.

Bellemare, C., Kroger, S., and van Soest, A. (2008). Measuring inequity aversion in a heterogeneous population using experimental decisions and subjective probabilities. Econometrica, 76(4):815–839.

Bellemare, C., Sebald, A., and Strobel, M. (2011). Measuring the willingness to pay to avoid guilt: estimation using equilibrium and stated belief models. Journal of Applied Econometrics, 26(3):437–453.

Biernacki, C., Celeux, G., and Govaert, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(7):719–725.

Blanco, M., Engelmann, D., Koch, A. K., and Normann, H.-T. (2014). Preferences and beliefs in a sequential social dilemma: a within-subjects analysis. Games and Economic Behavior, 87(0):122–135.

Blanco, M., Engelmann, D., and Normann, H. T. (2011). A within-subject analysis of other-regarding preferences. Games and Economic Behavior, 72(2):321–338.

Bottom, W. P. and Paese, P. W. (1999). Judgment accuracy and the asymmetric cost of errors in distributive bargaining. Group Decision and Negotiation, 8(4):349–364.

Breitmoser, Y. (2012). Strategic reasoning in p-beauty contests. Games and Economic Behavior, 75(2):555–569.

Browne, M. (2000). Cross-validation methods. Journal of Mathematical Psychology, 44(1):108–132.

Camerer, C., Ho, T., and Chong, J. (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119(3):861–898.

Camerer, C. and Ho, T. H. (1999). Experience-weighted attraction learning in normal form games. Econometrica, 67(4):827–874.

Capra, C., Goeree, J., Gomez, R., and Holt, C. (1999). Anomalous behavior in a traveler’s dilemma? American Economic Review, 89(3):678–690.

Choi, S., Gale, D., and Kariv, S. (2008). Sequential equilibrium in monotone games: A theory-based analysis of experimental data. Journal of Economic Theory, 143(1):302–330.

Clement, R. W. and Krueger, J. (2002). Social categorization moderates social projection. Journal of Experimental Social Psychology, 38(3):219–231.

Conlin, M., O’Donoghue, T., and Vogelsang, T. J. (2007). Projection bias in catalog orders. The American Economic Review, 97(4):1217–1249.

Costa-Gomes, M., Crawford, V., and Iriberri, N. (2009). Comparing models of strategic thinking in Van Huyck, Battalio, and Beil’s coordination games. Journal of the European Economic Association, 7(2-3):365–376.

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.

Dyer, D., Kagel, J., and Levin, D. (1989). Resolving uncertainty about the number of bidders in independent private-value auctions: An experimental analysis. The RAND Journal of Economics, 20(2):268–279.

Engelmann, D. and Strobel, M. (2000). The false consensus effect disappears if representative information and monetary incentives are given. Experimental Economics, 3(3):241–260.

Engelmann, D. and Strobel, M. (2012). Deconstruction and reconstruction of an anomaly. Games and Economic Behavior, 76(2):678–689.

Erev, I. and Roth, A. (1998). Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. American Economic Review, 88(4):848–881.

Eyster, E. and Rabin, M. (2005). Cursed equilibrium. Econometrica, pages 1623–1672.

Fehr, E. and Schmidt, K. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114(3):817–868.

Fey, M., McKelvey, R., and Palfrey, T. (1996). An experimental study of constant-sum centipede games. International Journal of Game Theory, 25(3):269–287.

Filiz-Ozbay, E. and Ozbay, E. (2007). Auctions with anticipated regret: theory and experiment. American Economic Review, 97(4):1407–1418.

Frederick, S. (2012). Overestimating others' willingness to pay. Journal of Consumer Research, 39(1):1–21.

Galinsky, A. D. and Mussweiler, T. (2001). First offers as anchors: the role of perspective-taking and negotiator focus. Journal of personality and social psychology, 81(4):657.

Garvin, S. and Kagel, J. (1994). Learning in common value auctions: Some initial observations. Journal of Economic Behavior & Organization, 25(3):351–372.

Gilbert, D., Pinel, E., Wilson, T., Blumberg, S., and Wheatley, T. (1998). Immune neglect: a source of durability bias in affective forecasting. Journal of personality and social psychology, 75(3):617–638.

Goeree, J. and Holt, C. (2004). A model of noisy introspection. Games and Economic Behavior, 46(2):365–382.

Goeree, J., Holt, C., and Laury, S. (2002a). Private costs and public benefits: Unraveling the effects of altruism and noisy behavior. Journal of Public Economics, 83(2):255–276.

Goeree, J., Holt, C., and Palfrey, T. (2002b). Quantal response equilibrium and overbidding in private-value auctions. Journal of Economic Theory, 104(1):247–272.

Grable, J., Lytton, R., and O’Neill, B. (2004). Projection bias and financial risk tolerance. The Journal of Behavioral Finance, 5(3):142–147.

Grable, J., Lytton, R. H., O’neill, B., Joo, S.-H., and Klock, D. (2006). Risk tolerance, projection bias, vividness, and equity prices. The journal of investing, 15(2):68–74.

Güth, W. and Ivanova-Stenzel, R. (2003). Asymmetric auction experiments with (out) commonly known beliefs. Economics Letters, 80(2):195–199.

Haile, P. A., Hortacsu, A., and Kosenok, G. (2006). On the empirical content of quantal response equilibrium. American Economic Review.

Hey, J., Lotito, G., and Maffioletti, A. (2010). The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity. Journal of risk and uncertainty, 41(2):81–111.

Ho, T., Wang, X., and Camerer, C. (2008). Individual differences in ewa learning with partial payoff information. The Economic Journal, 118(525):37–59.

Hoch, S. J. (1987). Perceived consensus and predictive accuracy: The pros and cons of projection. Journal of Personality and Social Psychology, 53(2):221.

Iedema, J. and Poppe, M. (1995). Perceived consensus of one’s social value orientation in different populations in public and private circumstances. European Journal of Social Psychology, 25(5):497–507.

Kagel, J., Harstad, R., and Levin, D. (1987). Information impact and allocation rules in auctions with affiliated private values: A laboratory study. Econometrica, 55(6):1275–1304.

Kagel, J. and Levin, D. (1986). The winner’s curse and public information in common value auctions. American Economic Review, 76(5):894–920.

Kagel, J. and Levin, D. (1993). Independent private value auctions: Bidder behaviour in first-, second-and third-price auctions with varying numbers of bidders. The Economic Journal, 103(419):868–879.

Kagel, J. and Levin, D. (2002). Common value auctions and the winner’s curse. Princeton University Press.

Keane, M. and Wolpin, K. (2007). Exploring the usefulness of a nonrandom holdout sample for model validation: Welfare effects on female behavior. International Economic Review, 48(4):1351–1378.

Kliger, D. and Levy, O. (2008). Projection bias by investors: A market approach. Journal of Economic Behavior & Organization, 66(3):657–668.

Krueger, J. and Clement, R. W. (1994). The truly false consensus effect: an ineradicable and edocentric bias in social perception. Journal of personality and social psychology, 67(4):596–610.

Kurt, D. and Inman, J. J. (2013). Mispredicting others' valuations: Self-other difference in the context of endowment. Journal of Consumer Research, 40(1):78–89.

Loewenstein, G., O’Donoghue, T., and Rabin, M. (2003). Projection bias in predicting future utility. The Quarterly Journal of Economics, 118(4):1209–1248.

Madarász, K. (2012). Information projection: Model and applications. Review of Economic Studies, 79(3):961–985.

Madarász, K. (2013). Projection equilibrium: Communication and social investment. Unpublished manuscript.

McKelvey, R. and Palfrey, T. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior, 10(1):6–38.

McLachlan, G. and Peel, D. (2000). Finite Mixture Models. Wiley series in probability and statistics.

Messé, L. A. and Sivacek, J. M. (1979). Predictions of others’ responses in a mixed-motive game: Self-justification or false consensus? Journal of Personality and Social Psychology, 37(4):602.

Mullen, B., Atkins, J. L., Champion, D. S., Edwards, C., Hardy, D., Story, J. E., and Vanderklok, M. (1985). The false consensus effect: A meta-analysis of 115 hypothesis tests. Journal of Experimental Social Psychology, 21(3):262–283.

Nagel, R. (1995). Unraveling in guessing games: An experimental study. American Economic Review, 85(5):1313–1326.

Nagelkerke, N. J. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3):691–692.

Offerman, T., Sonnemans, J., and Schram, A. J. H. C. (1996). Value orientations, expectations and voluntary contributions in public goods. Economic Journal, 106(437):817–45.

Powell, M. (2006). The newuoa software for unconstrained optimization without derivatives. Large-Scale Nonlinear Optimization, pages 255–297.

Read, D. and Van Leeuwen, B. (1998). Predicting hunger: The effects of appetite and delay on choice. Organizational behavior and human decision processes, 76(2):189–205.

Ross, L., Greene, D., and House, P. (1977). The “false consensus effect”: An egocentric bias in social perception and attribution processes. Journal of Experimental Social Psychology, 13(3):279–301.

Shapiro, D., Shi, X., and Zillante, A. (2014). Level-k reasoning in a generalized beauty contest. Games and Economic Behavior.

Simonsohn, U. (2010). Weather to go to college. The Economic Journal, 120(543):270–280.

Stahl, D. and Wilson, P. (1995). On players’ models of other players: Theory and experimental evidence. Games and Economic Behavior, 10(1):218–254.

Tang, F. (2003). A comparative study on learning in a normal form game experiment. Journal of Economic Behavior and Organization, 50(3):385–390.

Train, K. (2003). Discrete choice methods with simulation. Cambridge Univ Press.

Turocy, T. (2008). Auction choice for ambiguity-averse sellers facing strategic uncertainty. Games and Economic Behavior, 62(1):155–179.

Weizsäcker, G. (2003). Ignoring the rationality of others: evidence from experimental normal-form games. Games and Economic Behavior, 44(1):145–171.

Wilcox, N. (2008). Stochastic models for binary discrete choice under risk: A critical primer and econometric comparison. In Cox, J. C. and Harrison, G. W., editors, Risk aversion in experiments, volume 12 of Research in experimental economics, pages 197–292. Emerald Group Publishing Limited.