Optimal selling strategies when buyers name their own prices

This paper models a name-your-own-price (NYOP) retailer who allows buyers to initiate their retail interactions by describing a product and submitting a binding bid for it. The buyers have an outside option to buy the same good for a commonly known posted price that also acts as an informative upper bound on the cost the NYOP retailer faces. We conceptualize a selling strategy of such an NYOP retailer to be the probability that a buyer's bid gets accepted. The selling strategy is a function of only the bid level; it does not depend on the particular realization of the retailer's procurement cost. Using mechanism-design techniques, we characterize the optimal selling strategy and the equilibrium bidding function that best responds to it. We show that the optimal strategy implements the first-best ex-post optimal mechanism: for every cost realization, the retailer can make as much profit as he would if he could learn his cost first and use the optimal mechanism contingent on it. The complexity involved in credibly communicating an entire bid-acceptance function to buyers can make the first-best strategy impractical in some real-world markets, so we also analyze several simpler NYOP strategies: setting a minimum bid, charging a participation fee, and accepting all bids above cost. We find that under many scenarios, the minimum-bid strategy dominates the other simpler strategies and achieves a majority of the maximal profit improvement available from the first best strategy. However, NYOP retailers in thin markets can do better by charging participation fees than by setting minimum bids.