Subjective Probabilities in Games: An Application to the Overbidding Puzzle*

Abstract

This article illustrates how the joint elicitation of subjective probabilities and preferences may help us understand behavior in games. We conduct an experiment to test whether biased probabilistic beliefs may explain overbidding in first-price auctions. The experimental outcomes indicate that subjects underestimate their probability of winning the auction, and indeed overbid. When provided with feedback on the precision of their predictions, subjects learn to make better predictions, and to curb significantly overbidding. The structural estimation of different behavioral models suggests that biased probabilistic beliefs are a driving force behind overbidding, and that risk aversion plays a lesser role than previously believed. Copyright � (2009) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

A penny for your thoughts: a survey of methods for eliciting beliefs

“…(1926) suggests to minimize distortions arising from risk preferences by paying small stakes. However, Armantier and Treich (2013) prove that this does not necessary solve the problem. Paying small stakes only reduces biases when subjects display increasing relative risk aversion, and worsens it for decreasing relative risk aversion.…”

“…For example, under the QSR a risk averse subject should submit reports that are biased away from extreme outcomes in order to minimize losses. Using the QSR, Offerman et al (2009) and Armantier and Treich (2013) provide evidence that subjects do indeed report beliefs that are consistent with such a strategy.…”

Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem

“…Various answers have been proposed, as in e.g., Armantier and Treich (2009), Rogers, Camerer and Palfrey (2009) and Camerer, Nunnari and Palfrey (2016). 2 Although making these modifications shows that assuming heterogeneity in agents' traits considerably improves the model's goodness-of-fit, it does not address the question of when one should indeed forego the assumption of homogeneous agents.…”

“…3 We also note a subtle difference between empiricists and experimentalists regarding the definition of unobserved heterogeneity in the structural analysis of game-theoretic models. The former define it as information that is available to agents but not to the researcher (Paarsch and Hong, 2006) whereas the latter assume that the researcher is aware of this information and uses it to assess the model's explanatory power (e.g., Armantier andTreich, 2009, and. See Kirman (2006) for an overview of the role of heterogeneity in economics and Branch and McGough (2018) for a discussion of the role of heterogeneous expectations in macroeconomics.…”

“…from the same distribution as her/his (which is private information). Armantier and Treich (2009) study a setting where agents (bidders in first-price auctions) know that their private traits (i.e., agents' risk aversion and probability misperception) are i.i.d. from some commonly known bivariate distribution.…”