Projection of Private Values in Auctions

Abstract

We explore how taste projection—the tendency to overestimate how similar others’ tastes are to one’s own—affects bidding in auctions. In first-price auctions with private values, taste projection leads bidders to exaggerate the intensity of competition and, consequently, to overbid—irrespective of whether values are independent, affiliated, or (a)symmetric. Moreover, the optimal reserve price is lower than the rational benchmark, and decreasing in the extent of projection and the number of bidders. With an uncertain common-value component, projecting bidders draw distorted inferences about others’ information. This misinference is stronger in second-price and English auctions, reducing their allocative efficiency compared to first-price auctions. (JEL D11, D44, D82, D83)

Dutch vs. first-price auctions with expectations-based loss-averse bidders

“…If λ g = 1, then ( 16) has an interior solution (as the left-hand side of ( 16) is larger than the righthand side at t r = t, and vice versa at t r = t). Using (17) we see that for λ g = 1, we have that…”

“…In addition, using (16) it is straightforward to see that if N → ∞, and thus f 1 (t r ) → 0, the optimal t * r is in the interior. Using (17) we see that, if N → ∞, the optimal reserve price, r * , satisfies r…”

“…Fix a symmetric and increasing bidding strategy, β I : [t, t] → R + . Moreover, fix r and the implied t r , to be determined shortly, and consider a type-t bidder who mimics a larger type t > t. 17 With a slight abuse of notation, denote her expected payoff by EU ( t, t); this is given by…”

“…Using data from first-price and all-pay auctions, Eisenhuth and Ewers (2020) obtain an estimate for Λ g of 0.42 (with a standard error of 0.16); similarly, using data from a BDM-like auction, Banerji and Gupta (2014) obtain an estimate for Λ g of 0.283 (with a standard error of 0.08). 17 Recall that we are interested in characterizing the Preferred Personal Equilibrium (PPE). As shown by Balzer and Rosato (2021), in such equilibrium the bidders' upward incentive constraints are the binding ones.…”

Worst‐case equilibria in first‐price auctions

“…The idea that bidders form a valuation‐dependent belief and best reply to their competitors' strategies given this belief within a mental model is related to the work of Gagnon‐Bartsch, Pagnozzi, and Rosato (2021), who consider bidders with beliefs biased toward their own valuations. This assumption captures the idea that bidders overestimate how similar their tastes are to others'.…”