Selling mechanisms for a financially constrained buyer

We study implementability and revenue equivalence for selling mechanisms in a model where a seller has multiple items to allocate, and a buyer has private valuations and private budgets. We provide necessary and sufficient conditions for selling mechanisms to be incentive compatible and ex-post budget feasible for the buyer and derive the revenue equivalence principle in the presence of private budgets. Our conditions are based on a novel network approach that exploits the difference between unrestricted incremental values —the minimal value difference between an item assigned to the buyer by the seller and another alternative— and restricted incremental values —the minimal value difference between the assigned item and the alternative when the buyer can actually afford the alternative, given her financial disposition. We derive properties of incentive compatible, budget feasible prices, and illustrate our approach in a multi-item allocation problem with a convex type space.