Learning How to Strategically Disclose Information
Raj Kiriti Velicheti Melih Bastopcu S. Rasoul Etesami Tamer Başar
Strategic information disclosure, in its simplest form, considers a game
between an information provider (sender) who has access to some private
information that an information receiver is interested in. While the receiver
takes an action that affects the utilities of both players, the sender can
design information (or modify beliefs) of the receiver through signal
commitment, hence posing a Stackelberg game. However, obtaining a Stackelberg
equilibrium for this game traditionally requires the sender to have access to
the receiver's objective. In this work, we consider an online version of
information design where a sender interacts with a receiver of an unknown type
who is adversarially chosen at each round. Restricting attention to Gaussian
prior and quadratic costs for the sender and the receiver, we show that
$\mathcal{O}(\sqrt{T})$ regret is achievable with full information feedback,
where $T$ is the total number of interactions between the sender and the
receiver. Further, we propose a novel parametrization that allows the sender to
achieve $\mathcal{O}(\sqrt{T})$ regret for a general convex utility function.
We then consider the Bayesian Persuasion problem with an additional cost term
in the objective function, which penalizes signaling policies that are more
informative and obtain $\mathcal{O}(\log(T))$ regret. Finally, we establish a
sublinear regret bound for the partial information feedback setting and provide
simulations to support our theoretical results.