🤖 AI Summary
This study addresses the problem of robust information structure design in settings where agents’ utility coefficients are unknown. It introduces Calibrated Bayesian Correlated Equilibrium (Cal-BCE) as a solution concept and establishes a revelation principle and a joint decentralization theorem tailored to environments with utility uncertainty, elucidating how distinct risk criteria constrain cross-agent action covariances. Within a linear-quadratic-Gaussian framework, the authors leverage Hadamard invertibility conditions and employ second-order cone and semidefinite programming techniques to reformulate the original nonconvex problem into a convex optimization form incorporating probabilistic and Conditional Value-at-Risk (CVaR) constraints. Empirical experiments using 15 industry ETFs demonstrate that probability-based optimization enhances average welfare, while CVaR-based optimization strengthens tail-risk protection, revealing a clear trade-off between the two objectives.
📝 Abstract
This paper studies information design when the designer lacks precise knowledge of agents' payoff coefficients. The Calibrated Bayes Correlated Equilibrium (Cal-BCE) is introduced as a solution concept that augments the Bayes correlated equilibrium with a corrector policy preserving incentive compatibility under the designer's structural uncertainty, adapting its revelation principle to this setting. The design problem is nonconvex in general, but under a linear-quadratic-Gaussian structure it admits convex second-order cone and semidefinite reformulations under two-sided probabilistic and conditional value-at-risk (CVaR) constraints, with feasibility guaranteed by a Hadamard invertibility condition. A joint decentralization theorem shows that both designs cap cross-agent action covariances, the CVaR design more tightly at a common tolerance; but because the formulations operate at design-specific feasibility thresholds, the realized ordering is calibration-dependent. Experiments on fifteen sector ETFs confirm the trade-off: the probabilistic design attains higher mean welfare and the CVaR design better tail protection, with neither dominating outright.