Learning is Revelation in Disguise: Improved Regret and Equivalence Results for Dynamic Pricing

We study dynamic pricing where a seller repeatedly interacts with a strategic, non-myopic buyer who has a fixed private valuation and discounts future utility. Prior work focused exclusively on posted-price mechanisms, which only extract binary accept/reject signals. For our first result, we show that menu mechanisms-offering allocation-payment contracts are able to achieve $O(T_\gamma \log T_\gamma)$ regret, where $T_\gamma$ is the buyer's effective discounted time horizon, improving all prior bounds. Our second contribution is more conceptual in nature. The problem of dynamic pricing sits at the intersection of two paradigms: adaptive learning in computer science / machine learning and revelation-principle-based mechanism design in economics-yet their relationship has remained unclear. We establish a fundamental equivalence: indirect learning mechanisms and direct revelation mechanisms achieve identical optimal regret. The adaptive, data-driven algorithms of online learning and explicit type elicitation are two languages towards solving the same problem; hence, learning is revelation in disguise.