Risk- & Regret-Averse Bidders in Sealed-Bid Auctions

Overbidding, bidding more than risk-neutral Bayesian Nash Equilibrium, is a widely observed phenomenon in virtually all experimental auctions. The scholars within the auction literature propose the risk-averse preference model to explain overbidding structurally. However, the risk-averse preference model predicts underbidding in such important classes of auctions as all-pay auctions. To solve this discrepancy, we construct a structural model of bidding behavior in sealed-bid auctions, one in which bidders may regret their decisions. Our model nests both risk-averse and regret-averse attitudes and aims to explain overbidding in a wider class of auctions. We first derive equilibrium first-order conditions, which are used for estimation and calibration analyses, and show monotonic increasing properties of equilibrium bidding functions. Second, we carry out structural estimation and calibration analyses based on experimental data from Kagel and Levin (1993) and Noussair and Silver (2006). With these structurally estimated parameters, we test the significance of bidders' risk-averse and regret-averse attitudes. The estimation results show that bidders exhibit weak risk-averse (close to risk-neutral) and strong regret-averse attitudes. Furthermore, regret-averse attitudes are significant when bidders anticipate losing. Calibration results demonstrate that our risk- and regret-averse model can explain overbidding across all of the above IPV auctions. Third, we simulate our model with the estimated parameters and obtain revenue rankings numerically. This allows us to confirm the revenue supremacy in all-pay auctions reported in experimental auction literature. We discuss extensions to asymmetric and Common-Value (CV) auctions in our online Appendix.