Lot-Sizing in sequential auctions while learning bid and demand distributions

Sellers often need to decide lot-sizes in sequential, multi-unit auctions, where bidder demand and bid distributions are not known in their entirety. We formulate a Bayesian Markov decision process (MDP) to study a profit maximization problem in this setting. We assume that the number of bidders is Poisson distributed with a Gamma prior on its mean, and that the bid distribution is categorical with a Dirichlet prior. The seller updates these beliefs using data collected over auctions while simultaneously making lot-sizing decisions until all inventory is depleted. Exact solution of our Bayesian MDP is intractable. We propose and numerically compare three approximation methods via extensive numerical simulations.