  We consider the multi-sender persuasion problem: multiple players with
informational advantage signal to convince a single self-interested actor to
take certain actions. This problem generalizes the seminal Bayesian Persuasion
framework and is ubiquitous in computational economics, multi-agent learning,
and multi-objective machine learning. The core solution concept here is the
Nash equilibrium of senders' signaling policies. Theoretically, we prove that
finding an equilibrium in general is PPAD-Hard; in fact, even computing a
sender's best response is NP-Hard. Given these intrinsic difficulties, we turn
to finding local Nash equilibria. We propose a novel differentiable neural
network to approximate this game's non-linear and discontinuous utilities.
Complementing this with the extra-gradient algorithm, we discover local
equilibria that Pareto dominates full-revelation equilibria and those found by
existing neural networks. Broadly, our theoretical and empirical contributions
are of interest to a large class of economic problems.
