First-price Sealed-bid Auctions with Smoothly Ambiguity-Averse Bidders

We analyze first-price sealed-bid auctions with independent private values in which bidders are uncertain about the distribution of their opponents’ valuations and have smooth ambiguity preferences. We characterize the unique non- decreasing symmetric equilibrium, whose bidding function solves a nonlinear ordinary differential equation with an endogenous ambiguity-adjusted distribution. Bids increase in ambiguity aversion, lie between the Bayesian benchmarks generated by the least and most competitive candidate priors, and converge to the maxmin benchmark. Under constant relative ambiguity aversion (CRAA), the equilibrium biding function is explicit. We also compare auction formats. Under an ex ante predictive criterion, the second-price auction dominates under ambiguity neutrality, but sufficiently strong ambiguity aversion reverses the ranking. Under a model-based criterion, the first- price auction performs better in less competitive environments and worse in more competitive ones, while compressing the range of possible revenues. Bidder preferences also depend on ambiguity attitudes: CRAA bidders weakly prefer the second-price auction, whereas bidders with increasing absolute ambiguity aversion weakly prefer the first-price auction.