Optimal Selling Mechanisms on Incentive Graphs∗

We present a model highlighting one advantage of negotiation over posted prices from the seller’s perspective. In the process, we develop a general methodology for studying mechanism design with weaker incentive constraints. To do so, we introduce the notion of an incentive graph, which encodes the relevant constraints. This construction is relevant when agents possess hard evidence, when they partake in a specific form of costly signaling, or when they are boundedly rational. In such settings, we show that the optimal selling mechanism involves price discrimination and study the form which this price discrimination takes. When the incentive graph has a tree structure, we offer a complete solution. Our solution involves an adaptation of the classic notion of a virtual valuation as in Myerson (1981) to a tree. We show that for acyclic graphs, all allocations are incentive compatible, but nevertheless, the revenue maximizing mechanism is in many ways similar to that found in the classic analysis. JEL Classification: D44, D82.