Auctions and Differential Pricing: Optimal Seller and Bidder Strategies in Second-chance Offers

The second chance offer is a common seller practice on eBay. It consists of price discrimination against the losing bidder, who is offered an identical item at the value of his or her highest bid. Prior work has shown that, if the goods are private-value goods and price discrimination is certain, rational bidders can anticipate it and accordingly modify their bidding strategies; this results in revenue loss for the seller. This paper hence examines the impact of randomized price discrimination. It examines a similar, more general problem: a seller has k items of the private-value good. They are sold to N bidders in a two-stage game. The first stage is a sealed-bid first-price auction with N bidders. The second stage is a take-it-or-leave-it offer to each of k − 1 losing bidders; randomized between a fixed-price offer and a second-chance offer. Showing that analytic techniques do not provide complete solutions because bidding strategies are not always monotonic increasing, this paper uses genetic algorithm simulations to determine the Bayesian (near-Nash) equilibrium strategies for bidders and sellers, for N = 8 and different values of k. It finds that price discrimination is beneficial to the seller when k is small, as item scarcity increases competition among bidders. The paper’s use of randomized seller strategies and genetic algorithm simulations is unique in the study of the second-chance offer.