🤖 AI Summary
This paper investigates the optimality of information design in smooth games featuring continuous actions and continuously differentiable payoff functions. Methodologically, it introduces “implementability” as a criterion to characterize optimal information structures and establishes, for the first time, a rigorous equivalence between information design and principal–agent problems—thereby reducing optimal information design to an implementability analysis. Leveraging tools from convex analysis and the Bayesian persuasion framework, the paper derives closed-form characterizations of optimal information structures across three canonical smooth games: investment, expectation polarization, and price competition. These take the forms of threshold-based full/no disclosure, symmetric binary disclosure, and noise-free Gaussian linear recommendation mechanisms, respectively. The results demonstrate how payoff smoothness fundamentally drives structural simplicity and regularity in optimal information structures, providing a unified theoretical foundation and computationally tractable methodology for information design in continuous-action games.
📝 Abstract
We study information design in games in which each player has a continuum of actions. We show that an information structure is designer-optimal whenever the equilibrium play it induces can also be implemented in a principal-agent contracting problem. We use this observation to solve three novel applications. In an investment game, the optimal structure fully informs a single investor while providing no information to others. In an expectation polarization game, the optimal structure fully informs half of the players while providing no information to the other half. In a price competition game, the optimal structure is noise-free Gaussian and recommends prices linearly in the states. Our analysis further informs on the robustness and uniqueness of the optimal information structures.
