A Simple Proof of Strong Duality in the Linear Persuasion Problem

The Persuasion Duality

“…2 In the special case when the objective function depends only on a finite set of moments of the posterior distribution (for example, the expected state), we show that the price function on the space of moments is a convex function that is greater than the objective function (Section 4). This result generalizes the duality results established by Kolotilin (2018), Dworczak and Martini (2019), and Dizdar and Kováč (2019). We comment on the precise relationship to these papers in Section 7.…”

“…The results of this paper generalize some existing results in the persuasion literature. The linear persuasion problem in which the objective function depends only on the expected onedimensional state has received special attention (see, for example, Gentzkow and Kamenica, 2016, Kolotilin et al, 2017, Kolotilin, 2018, Dworczak and Martini, 2019, and Dizdar and Kováč, 2019. Linear persuasion is the special case of moment persuasion when ω ∈ R and m(ω) = ω.…”

“…8 See Appendix A. That last condition can be significantly relaxed in more specific instances of the problem, as in Dworczak and Martini (2019) or Dizdar and Kováč (2019). lies above V on ∆(Ω).…”

“…In Appendix A, we show that the moment persuasion problem is regular if v is Lipschitz continuous. Other authors have identified weaker sufficient conditions on v in the case when ω ∈ R and m(ω) = ω (see especially Dizdar and Kováč, 2019).…”

“…1 Although conceptually attractive, concavification is not always a tractable approach. Thus, several recent papers (see Kolotilin, 2018, Dworczak and Martini, 2019, Galperti and Perego, 2018, and Dizdar and Kováč, 2019 used duality theory to characterize the optimal signal.…”