Bayesian Persuasion under Bias Management
Kemal Ozbek
TL;DR
The paper develops a joint design framework for steering delegated choice via information design and bias management in a binary-state, two-action setup. It establishes an inner-outer decomposition: optimal bias is bang--bang at each posterior, while the outer information design uses concavification of an endogenous posterior value function that incorporates management and information costs. The analysis shows that information and management can be complements, substitutes, or both, with regime changes and discontinuities driven by cost parameters and the shape of the posterior value function. These results yield intuitive regimes (pooling, informative signaling, or no management) and two key thresholds guiding when information or management becomes valuable, offering nuanced policy guidance on subsidizing information versus governance or enforcement in practical settings. Overall, the framework highlights the interdependent nature of belief-based and rule-based steering tools and provides a tractable approach to quantify their joint effects and policy implications.
Abstract
A principal delegates choice to an agent whose decision depends on both beliefs and tastes. The principal can steer the delegated decision using two costly instruments: (i) an information policy that determines a Bayes--plausible distribution of posteriors, and (ii) a bias-management policy that shifts the agent's effective taste. We study a binary-state, two-action, convex hull of two benchmark tastes specialization with posterior-separable information costs. The analysis admits an inner--outer decomposition: optimal bias management is bang--bang (either no intervention or the minimal intervention needed to flip the agent's action), while the optimal information policy is characterized by concavification of an endogenous posterior value function that already incorporates optimal management and information costs. This structure clarifies how information acquisition and bias management interact; they can be complements, substitutes, or both depending on the primitives of the model. Information changes which posteriors are realized and hence where management is used; management reshapes the curvature and kinks of the posterior value function and hence the marginal value of information. The model delivers regime classifications for pooling vs. informativeness and for management at different posteriors within informative signals, and highlights how comparative statics can be monotone or non-monotone depending on how concavification contact points move with costs.