Economic Theory and Experimental Seminar - Juan Carlos Carbajal (University of New South Wales)

*** Please note the change of venue to room 315 for this seminar. ***

Title: Selling Mechanisms for a Financially Constrained Buyer

Abstract: A seller has multiple items to allocate. A buyer has private information about her values for these items and demands at most one of them; in addition, the buyer is financially constrained. A selling mechanism specifies a collection of non-linear prices, given that the buyer’s types (pairs of valuation and budget) are private information. Focusing on mechanisms that never generate a deficit for the seller, we provide necessary and sufficient conditions for selling mechanisms to be prior free incentive compatible and ex post budget feasible for the buyer. These conditions inform the construction of the incentive compatible prices. We use a novel flow network approach to incentive compatibility that also takes care of budget feasibility, exploiting a subtle difference between unrestricted incremental values —i.e., the minimal value difference between an item assigned to the buyer by the mechanism and another alternative— and restricted incremental values —i.e., the minimal value difference between the assigned item and the alternative when the buyer can actually afford the alternative, given her financial position. We derive important properties on prices for any given allocation function that is implementable without deficits, and illustrate the usefulness of our approach in two settings: (i) a multi-item allocation problem with a convex type space; and (ii) a revenue maximization problem when the seller has two identical objects to allocate and the buyer’s valuation may exhibit complementarities between the objects.