We study a buyer-seller problem of a novel good for which the seller does not yet know the production cost. A contract can be agreed upon at either the ex-ante stage, before learning the cost, or at the ex-post stage, when both parties will incur a costly delay, but the seller knows the production cost. We show that the optimal ex-ante contract for a profit-maximizing seller is a fixed price contract with an "at-will" clause: the seller can choose to cancel the contract upon discovering her production cost. However, sometimes the seller can do better by offering a guaranteed-delivery price at the ex-ante stage and a second price at the ex-post stage if the buyer rejects the first offer. Such a "limited commitment" mechanism can raise profits, allowing the seller to make the allocation partially dependent on the cost while not requiring it to be embedded in the contract terms. Analogous results hold in a model where the buyer does not know her valuation ex-ante and offers a procurement contract to a seller.

In persuasion problems where the receiver’s utility is single-peaked in a one-dimensional action, optimal signals are characterized by duality, based on a first-order approach to the receiver’s problem. A signal that pools at most two states in each realization is always optimal, and such pairwise signals are the only solutions under a non-singularity condition on utilities (the twist condition). Our core results provide conditions under which higher actions are induced at more or less extreme pairs of states, so that the induced action is single-dipped or single-peaked on each set of nested pairs of states. We also provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Methodologically, our proofs rely on a novel complementary slackness theorem for persuasion problems.

Two debaters address an audience by sequentially choosing their information strategies. We compare the setting where the second mover reveals additional information (constructive argumentation) with the setting where the second mover obfuscates the first mover's information (toxic argumentation). We reframe both settings as constrained optimization problems of the first mover. We show that when the preferences are zero-sum or risk neutral, constructive debates reveal the state, while toxic debates are completely uninformative. Moreover, constructive debates reveal the state under the assumption on preferences that capture autocratic regimes, whereas toxic debates are completely uninformative under the assumption on preferences that capture democratic regimes.