Deterministic Refund Mechanisms

We consider a mechanism design setting with a single item and a single buyer who is uncertain about the value of the item. Both the buyer and the seller have a common model for the buyer's value, but the buyer discovers her true value only upon receiving the item. Mechanisms in this setting can be interpreted as randomized refund mechanisms, which allocate the item at some price and then offer a (partial and/or randomized) refund to the buyer in exchange for the item if the buyer is unsatisfied with her purchase. Motivated by their practical importance, we study the design of optimal deterministic mechanisms in this setting. We characterize optimal mechanisms as virtual value maximizers for both continuous and discrete type settings. We then use this characterization, along with bounds on the menu size complexity, to develop efficient algorithms for finding optimal and near-optimal deterministic mechanisms.