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 price discrimination is certain—that is, the items are always offered to bidders at their highest losing bids—bidders can predict it, and it results in revenue loss for the seller. This dissertation hence allows the seller to randomize his strategy. It examines a similar, more general problem: a seller has k items. They are sold to n bidders in a two-stage game. The first stage is a sealed-bid private-value 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 dissertation 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 analyzes item scarcity and two types of auction mechanisms for the first stage: first-price auction and second-price auction. It tests the approach on real eBay data, and a rational bidding tool is implemented to illustrate the practical use of this model on eBay. This dissertation’s use of randomized seller strategies and genetic algorithm simulations is unique in the study of the second-chance offer.