We develop a method to recover primitives from data generated by artificial intelligence (AI) agents in strategic environments such as online marketplaces and auctions. Building on the design of leading online learning AIs, we assume that agents minimize their regret. Under asymptotic no regret, we show that the time average of play converges to the set of Bayes coarse correlated equilibrium (BCCE) predictions. Our econometric procedure is based on BCCE restrictions and convergence rates of regret-minimizing AIs. We apply the method to pricing data in a digital marketplace for used smartphones. We estimate sellers' cost distributions and find lower markups than in centralized platforms.

We study the role of information structures in mechanism design problems with limited commitment. In each period, a principal offers a ''spot'' contract to a privately informed agent without committing to future spot contracts, and the agent responds to the contract. In contrast to the classical approach in which the information structure is fixed, we allow for all admissible information structures. We represent the information structure as a fictitious mediator and re-interpret the model as a mechanism design problem by the mediator with commitment. The mediator collects the agent's private information and then, in each period, privately recommends the principal's spot contract and the agent's response in an incentive-compatible manner (both in truth-telling and obedience). We construct several examples to clarify why new equilibrium outcomes can arise once we allow for general information structures. We next develop a durable-good monopoly application. We show that trading outcomes and welfare consequences can substantially differ from those in the classical model with a fixed information structure. In the seller-optimal mechanism, the seller offers a discounted price to the high-valuation buyer only in the initial period, followed by the high, surplus-extracting price until some endogenous deadline, when the buyer's information is revealed and hence fully extracted. As a result, the Coase conjecture fails: even in the limiting case of perfect patience, the seller makes a positive surplus, and the trading outcome is not the first best. We also characterize mediated and unmediated implementation of the seller-optimal outcome.