A Duality Approach to Bayesian Persuasion

Piotr Dworczak

Stanford Graduate School of Business

Giorgio Martini

Stanford Graduate School of Business

May 27, 2016

Abstract:

We propose a duality approach for Bayesian Persuasion problems in which the preferences of the Sender depend only on the posterior mean. The problem reduces to finding «prices» for posterior means such that the Sender maximizes utility subject to a budget constraint (with endowment given by the prior distribution) and a feasibility constraint (the distribution of posterior means must be a mean-preserving spread of the prior). We use this approach to derive a sufficient condition for the optimality of monotone partitional signals. Two examples illustrate the method’s applicability to complex persuasion problems.

A Duality Approach to Bayesian Persuasion

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