Knowing me, imagining you: Projection and overbidding in auctions
Introduction
The false consensus bias is the tendency to assume that one's own opinions, preferences and values are typical and shared by others. Following Ross et al. (1977), such “projection” has been confirmed in many experiments (Mullen et al., 1985) and shown to persist even if subjects are provided with factually contradicting information (Krueger and Clement, 1994). Thus, projection is of intuitive relevance in all choices under incomplete information—not just in the non-strategic environments on which the psychological literature traditionally focuses, but also in strategic interactions. Existing studies of projection in “games” focus on games with one-sided incomplete information. Loewenstein et al. (2003) study projection of utility onto future selves, finding that it explains anomalies in purchases of durable goods, and Madarász (2012) studies projection of information from an informed player to an uninformed one, which explains the hindsight bias in agency problems. The present paper provides a comprehensive analysis of projection in a class of games with two-sided incomplete information, auctions.
Auctions are widely analyzed games with two-sided incomplete information about individual object values. I introduce a model of type projection where players may overestimate the probability that their opponents share their type—i.e. their signal about the object value—ranging from zero projection (the original Bayesian case) to full projection (disregarding all prior information).2 The degree of projection is denoted by . In equilibrium, players anticipate their opponent types' actual strategies, but overestimating the probability that opponents share their type, they perceive competition to be fiercer than it is and they wrongly update their estimate of the object value conditional on winning. This generates the behavioral phenomena observed in bidding across conditions, and based on my theoretical and econometric analysis, I argue that type projection, as predicted by a host of psychological evidence, captures bidding fairly comprehensively and substantially better than existing models.
The basic idea is simple. Type-projecting bidders project their signals about the object value. This builds on psychological evidence showing that object values indeed are projected, e.g. in bargaining (Bottom and Paese, 1999; Galinsky and Mussweiler, 2001) and in consumption decisions (Frederick, 2012; Kurt and Inman, 2013). As for auctions, consider bidding to buy a house. Projecting bidders neglect competitors whose values are vastly inferior, against whom they surely win, and competitors whose values are vastly superior, against whom they surely lose. They focus on competitors with similar values, trying to ensure winning against them. This focus increases the sense of competition and obscures the perceived value distribution. The former induces overbidding in any first-price auction, essentially to avoid “loser regret”, and the latter weakens Bayesian updating in any common value auction (the Winner's Curse).
That is, the robust psychological finding of (type) projection already implies the main behavioral phenomena in auctions, and in addition, it correctly predicts a number of more subtle findings that are incompatible with existing models. For example, in private value auctions, projecting bidders overbid as they overestimate the share of opponents with similar values. They outbid them to increase the probability of winning. In contrast, risk aversion emphasizes a trade-off between increasing winning probability and increasing conditional profit. Following Engelbrecht-Wiggans (1989), the former relates to loser regret (regret of losers if they could have won profitably) and the latter relates to winner regret (regret of winners if they could have won with lower bids). Filiz-Ozbay and Ozbay (2007) find that subjects do not trade off these regrets but focus on loser regret. This focus contradicts risk aversion and is implied by type projection. At the individual level, I find that subjects randomize consistently and use left-skewed mixed strategies, which also contradicts risk aversion and is predicted by type projection equilibrium.
Analyzing common value auctions, I similarly find that subjects randomize consistently and that they overbid more with common values than with private values. Again, both observations are implied by type projection and not implied by existing models such as risk aversion or cursed equilibrium (Eyster and Rabin, 2005).3 This range of observations uniquely predicted by type projection, and considering that projection is a robust phenomenon known to affect behavior under incomplete information, raises the question to which degree projection can be considered a robust, potentially comprehensive explanation of bidding in auctions.4 To answer this question, I conduct a structural analysis of data from seven experiments. The data set forms the union of the data sets analyzed in seminal structural analyses of bidding, which limits data selection effects in favor of type projection. In addition, merging multiple data sets allows me to assess whether models are precise (in-sample) and reliable (out-of-sample).
Both features are desirable in behavioral and empirical analysis, but reliability will be of particular relevance here. To clarify, let me briefly review existing results. Goeree et al. (2002b) and Bajari and Hortacsu (2005) show that risk aversion captures bidding in private value auctions, Filiz-Ozbay and Ozbay (2007) and Engelbrecht-Wiggans and Katok (2007) observe loser regret, Eyster and Rabin (2005) observe cursedness in common value auctions, and Crawford and Iriberri (2007) observe limited depth of reasoning in either condition. That is, the results vary enormously between studies. The main reason appears to relate to the identifying assumptions on strategic beliefs, which range from naive beliefs (level-1) over Nash beliefs (equilibrium without anticipating errors) to rational expectations. To reconcile these results, such specific assumptions on belief formation should therefore be avoided. I introduce a concept based on quantal response equilibrium (McKelvey and Palfrey, 1995) that nests the three belief models above and endogenizes the assumption on belief formation. While this solves one problem, Haile et al. (2008) suspect that generalized forms of QRE may overfit and lack robustness themselves. The data used here allow me to directly address this issue by evaluating robustness, i.e. the accuracy of predictions across experiments.5 In addition, this analysis verifies whether the models are applicable across data sets, e.g. in (future) analyses of different data.
The results corroborate the compatibility with psychological intuition and stylized facts. Type projection indeed captures behavior well, both descriptively (in-sample) and in particular predictively (out-of-sample). Further, inexperienced subjects tend to underestimate the rationality of others, though not in the way predicted by level-k. As subjects gain experience, their beliefs approach rational expectations, the precision in maximizing utility increases, subject heterogeneity becomes significant, and yet, the degree of projection remains largely constant (around 0.5). Thus, type projection appears to be a robust facet of behavior, and in the analyzed auctions, it is comprehensive in the sense that neither risk aversion nor cursedness capture facets of behavior incompatible with projection. The results have policy implications, as the projection bias is reduced when subjects are educated explicitly (Engelmann and Strobel, 2012), which enables efficiency gains, and they have implications for behavioral and empirical work. For, type projection intuitively factors in all symmetric Bayesian games, and thus needs to be controlled for in analyses of social preferences under anonymity (for related evidence, see Blanco et al., 2014), and as it fits robustly across private and common values, it promises to capture field auctions which tend to be hybrid (Haile, 2001; Goeree and Offerman, 2002).
Section 2 introduces the model of type projection and analyzes type projection in auctions. Section 3 introduces the data sets and evaluates type projection's basic predictions. Section 4 contains the structural analysis of bidding. Section 5 concludes. The appendix contains technical material, the supplementary material provides robustness checks.
Section snippets
Basic definitions of auctions and projection
There are n symmetric bidders, denoted as , and each bidder gets a signal . Signals may be correlated. A bidder's expectation of the object value conditional on signal x is , the expectation conditional on both the own signal x and the highest opponent signal y is . The density of the highest opponent signal y conditional on the own signal x is . A pure strategy is a function mapping signals x to bids . Unless stated otherwise, I focus on first-price
Testing the qualitative predictions
I re-analyze seven experiments. Pooling data from multiple experiments reduces the risk of misinterpreting model adequacy due to data selection and the fallacy to overfitting by assessing predictive adequacy across experiments. Evaluating predictive adequacy additionally clarifies to which degree the results obtained here may be helpful in (future) analyses of different data sets. Finally, pooling auctions under varying information conditions (IPV, APV and CV) allows me to examine robustness to
Structural analysis
As shown in the previous section, type projection equilibrium captures bidding in auctions substantially better than existing models. This yields the joint hypothesis that (i) type projection captures biases in computation of expected payoffs and (ii) equilibrium captures the beliefs of subjects. I will refer to (i) as a statement about the payoff structure and to (ii) as a statement about the belief structure. A structural analysis allows me to disentangle these statements and thus to clarify
Conclusion
This paper introduces type projection equilibrium as a model of bidding in auctions. Type projection was an ex-ante plausible candidate to be behaviorally relevant, as it is robustly observed in psychological research and intuitively applies to all (symmetric) Bayesian games, such as auctions. Yet, despite the large amounts of studies dedicated to either, auctions in economics and projection in psychology, the only published paper suggesting a potential link between bidding and projection
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Biases in belief reports
2022, Journal of Economic PsychologyCitation Excerpt :Joachim Krueger describes the consensus effect in a general but simple way: “People by and large expect that others are similar to them” (Krueger, 2007 p. 1). The basic idea has been studied in many different contexts under many different names: [false-]consensus effect (Dawes & Mulford, 1996; Marks & Miller, 1987; Mullen et al., 1985; Ross et al., 1977), perspective taking (Epley et al., 2004), social projection (Krueger, 2007, 2013), type projection (Breitmoser, 2015), evidential reasoning (al-Nowaihi & Dhami, 2015) or self-similarity bias (Rubinstein & Salant, 2016). Engelmann and Strobel (2012) convincingly demonstrate that the consensus effect exists, but only as long as no representative information about others is available.
Own experience bias in evaluating the efforts of others
2020, Journal of Economic Behavior and OrganizationCitation Excerpt :Extensive evidence shows that people are biased in overweighting own experience because of, for example, hindsight bias (e.g. Christensen-Szalanski and Willham (1991); Hoffrage et al. (2000)), overconfidence (e.g. Dunning et al. (1990)), the availability heuristic (e.g. Tversky and Kahneman (1973, 1974)), and anchoring (Furnham and Boo, 2011). Moreover, a growing literature shows evidence of projection bias, a bias towards assuming that others are similar to oneself (e.g. Ross et al. (1977); Mullen et al. (1985); Krueger and Clement (1994); Breitmoser (2019)). Our work introduces a new theoretical model of own experience bias and confirms that such biases can be developed in a laboratory setting.
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I thank the editor, the advisory editor, two anonymous referees, Friedel Bolle, Jana Friedrichsen, Paul Heidhues, Matthias Lang, Theo Offerman, Sebastian Schweighofer-Kodritsch, Jean-Robert Tyran, Felix Weinhardt, Georg Weizsäcker, seminar audiences in Berlin, Nottingham and Regensburg, and conference participants in Montreal (ESWC 2015) and Münster (VfS Jahrestagung, 2015) for helpful comments. Financial support of the DFG (BR 4648/1 and CRC TRR 190) is greatly appreciated.