Bayesian Persuasion with State-Dependent Quadratic Cost Measures

Muhammed O. Sayin, Tamer Basar

Research output: Contribution to journalArticlepeer-review


In this article, we address Bayesian persuasion between a sender and a receiver with state-dependent quadratic cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the sender while the sender signals strategically in order to control the receiver's estimate in a certain way. Such a scheme could model, e.g., deception and privacy, problems in multiagent systems. Existing solution concepts are not viable since here the receiver has continuous action space. We show that for finite state spaces, optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. We then establish its strong duality to a copositive program. To exemplify the effectiveness of this equivalence result, we adopt sequential polyhedral approximation of completely positive cones and analyze its performance numerically. We also quantify the approximation error for a quantized version of a continuous distribution and show that a semi-definite program relaxation of the equivalent problem could be a benchmark lower bound for the sender's cost for large state spaces.

Original languageEnglish (US)
Pages (from-to)1241-1252
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Mar 1 2022
Externally publishedYes


  • Aerospace electronics
  • Bayes methods
  • Bayesian persuasion
  • Copositive Programming
  • Deception
  • Nash equilibrium
  • Optimization
  • Privacy
  • Receivers
  • Signaling
  • Stackelberg games
  • Symmetric matrices
  • signaling
  • privacy
  • copositive programming
  • deception

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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