Cheap Talk in Bilateral Trade

Abstract

A single seller offers one or more goods to a single buyer. The buyer’s values and the seller’s costs are private information. Each player has a commonly known prior over the other player’s value or cost, supported on a finite set. What is the optimal selling mechanism? We argue that, despite this question’s importance and apparent simplicity, prior work offers no satisfactory answer. If the seller simply chooses an optimal menu given her realized costs, she fails to exploit her informational advantage. At the other extreme, the optimal trade mechanism that satisfies IC/IR constraints for both parties fails in practice, as it conditions prices on the seller’s unknown costs in an unenforceable way. The seller’s realistic capabilities lie somewhere in between: she may leverage private information but lacks unlimited commitment power. To bridge this gap, we consider a solution concept built on the realistic assumption that the seller can commit to prices but nothing more. Similar—albeit technically distinct—solution concepts have been studied in the context of auctions with multiple buyers. Our concept proves surprisingly rich even with a single buyer. In our model, the buyer and seller engage in multiple rounds of cheap talk before the seller posts a menu of priced bundles. The buyer then purchases. We measure value as profit for the seller and consumer surplus for the buyer. We prove that, when there is only one good, such cheap talk cannot improve the welfare of either party. We then demonstrate that cheap talk can be useful when there are (1) multiple goods with additive costs and values, (2) multiple units of a single good with constant marginal cost and diminishing marginal value, (3) interdependent values for a single good, or (4) repeated play of a one-good game. We also show that multiple rounds of communication can yield strictly higher expected profit than a single round. Conceptually, these results show that in any extension beyond the canonical setting of one seller, one buyer, and one good, cheap talk creates value in bilateral trade. We discuss how realistic factors beyond our stripped-down model combine with cheap talk to enhance this value even further.