Optimal Auctions for Partially Rational Bidders

We investigate the problem of revenue optimal mechanism design [Myerson, 1981] under the context of the partial rationality model, where buyers randomize between two modes: rational and irrational. When a buyer is irrational (can be thought of as lazy), he acts according to certain fixed strategies, such as bidding his true valuation. The seller cannot observe the buyer’s valuation, or his rationality mode, but treat them as random variables from known distributions. The seller’s goal is to design a single-shot auction that maximizes her expected revenue. A minor generalization as it may seem, our findings are in sharp contrast to Myerson’s theory on the standard rational bidder case. In particular, we show that, even for the simplest setting with one buyer, direct value revelation loses generality. However, we do show that, in terms of revenue, the optimal value-revelation and type-revelation mechanisms are equivalent. In addition, the posted-price mechanism is no longer optimal. In fact, the more complicated the mechanism, the higher the revenue. For the case where there are multiple bidders with IID uniform valuations, we show that when the irrational buyers are truthful, first price auction yields more revenue than second price auction.