Optimal Bidding Strategies in Non-Sealed Bid Online Auctions of Common Products with Quantity Uncertainty

We consider non-sealed bid online auctions of common products with quantity uncertainty. Both first-price (also known as pay-as-you-bid) and uniform-price auctions are considered. In these auctions, all bidders have the same valuation of the products but may have different demand quantities. The number of units being auctioned can be random with a known and common distribution. Each bidder decides on a bidding price to maximize her profit. We derive Nash equilibrium solutions, i.e., bidders' optimal bidding strategies, and the resulting market clearing prices.