In this paper, we formulate a hybrid version of the two-stage procedure for the utility maximization problem of a consumer proposed by Green (1964). In particular, we replace the second stage of this procedure with a problem of expenditure minimization. Under the assumption of homogeneous...

We present a unified duality approach to Bayesian persuasion. The optimal dual variable, interpreted as a price function on the state space, is shown to be a supergradient of the concave closure of the objective function at the prior belief. Strong duality holds when the objective function is...