# Bayesian Persuasion: Reduced Form Approach

*Juuso Toikka* (),
*Akhil Vohra* () and
*Rakesh Vohra* ()

Additional contact information

Juuso Toikka: University of Pennsylvania

Akhil Vohra: University of Cambridge

Rakesh Vohra: University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

**Abstract:**
We introduce reduced form representations of Bayesian persuasion problems where the variables are the probabilities that the receiver takes each of her actions. These are simpler objects than, say, the joint distribution over states and actions in the obedience formulation of the persuasion problem. This can make a difference in computational and analytical tractability which we illustrate with two applications. The first shows that with quadratic receiver payoffs, the worst-case complexity scales with the number of actions and not the number of states. If |A |and |S | denote the number of actions and states respectively, the worst case complexity of the obedience formulation is O(|A |2.5 max{|A |2.5,|S |2.5}). The worst case complexity of the reduced form representation is O(|A |3). In the second application, the reduced form leads to a simple greedy algorithm to determine the maximum value a sender can achieve in any cheap talk equilibrium.

**Keywords:** Bayesian Persuasion; Information Design; Mechanism Design; Duality (search for similar items in EconPapers)

**JEL-codes:** C6 D82 D83 (search for similar items in EconPapers)

**Pages:** 38 pages

**Date:** 2022-06-28

**New Economics Papers:** this item is included in nep-des, nep-gth and nep-mic

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

https://economics.sas.upenn.edu/system/files/worki ... per%20Submission.pdf (application/pdf)

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:pen:papers:22-018

Access Statistics for this paper

More papers in PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania 133 South 36th Street, Philadelphia, PA 19104. Contact information at EDIRC.

Bibliographic data for series maintained by Administrator ().