Sequential Auctions with Synergies in the Presence of More Than Two Objects

We examine a model of sequential English auction in which, the objects being auctioned share synergetic relationships (complementarity and substitutability) between them. We incorporate more than two objects into the model, which allows for the possibility of both types of synergies to co-occur. We divide the objects being auctioned into categories, where a category is defined as the collection of substitutable items. Additionally, inter-category objects are treated as complements. Bidders demand one unit from each category and aim to create a bundle of intercategory/complementary objects. We find out all possible outcomes of the game, and for each outcome, we find optimal bidding strategies, equilibrium selling prices, bidders’ expected profits, and seller’s expected revenue. We observe a decreasing price trend in one of the possible outcomes. We also discover the possibility of false bidding when certain assumptions of the model are violated.