Information Design Using Copulas

We propose an equivalent formulation of a two player information design problem in terms of choosing a copula, as opposed to choosing a joint distribution of a signal and the state variable. We then propose a copula based signal ordering which is both necessary and sufficient for the more informative signal to generate higher dispersion of the distribution of posteriors. Applications involving Bayesian persuasion with a continuous state variable, a buyer's incentives to acquire information and a seller's incentives to provide information in a bilateral trade setting, and the role of insider information in European and American call option valuations are presented.