Certifiable Dominance: Unique Equilibrium Outcome in Persuasion Games with Binary Actions

Abstract

This paper studies equilibrium selection in persuasion games where the receiver's actions are binary, and discusses how to justify the most informative equilibrium as a reasonable consequence. In general, there exist multiple equilibria in this environment even if the sender's private information is fully certifiable, and the convention of focusing on the most informative equilibrium is followed without formal justification. However, we show that the existing selection criteria in the literature on strategic communication hardly justifies such a convention; in particular, these criteria might select the least informative equilibrium. We then suggest the notion of certifiable dominance, and show that the most informative equilibrium is uniquely selected by a perfect Bayesian equilibrium constructed using certifiably undominated strategies. This criterion could also uniquely select the most informative equilibrium when the sender's private information is partially certifiable.