Babichenko, Yakov
[Verfasser:in];
Talgam-Cohen, Inbal
[Verfasser:in];
Xu, Haifeng
[Verfasser:in];
Zabarnyi, Konstantin
[Verfasser:in]
;
Yakov Babichenko and Inbal Talgam-Cohen and Haifeng Xu and Konstantin Zabarnyi
[Mitwirkende:r]
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Beschreibung:
The celebrated Bayesian persuasion model considers strategic communication between an informed agent (the sender) and uninformed decision makers (the receivers). The current rapidly-growing literature assumes a dichotomy: either the sender is powerful enough to communicate separately with each receiver (a.k.a. private persuasion), or she cannot communicate separately at all (a.k.a. public persuasion). We propose a model that smoothly interpolates between the two, by introducing a natural multi-channel communication structure in which each receiver observes a subset of the sender’s communication channels. This captures, e.g., receivers on a network, where information spillover is almost inevitable. Our main result is a complete characterization specifying when one communication structure is better for the sender than another, in the sense of yielding higher optimal expected utility universally over all prior distributions and utility functions. The characterization is based on a simple pairwise relation among receivers - one receiver information-dominates another if he observes at least the same channels. We prove that a communication structure M₁ is (weakly) better than M₂ if and only if every information-dominating pair of receivers in M₁ is also such in M₂. This result holds in the most general model of Bayesian persuasion in which receivers may have externalities - that is, the receivers' actions affect each other. The proof is cryptographic-inspired and it has a close conceptual connection to secret sharing protocols. As a surprising consequence of the main result, the sender can implement private Bayesian persuasion (which is the best communication structure for the sender) for k receivers using only O(log k) communication channels, rather than k channels in the naive implementation. We provide an implementation that matches the information-theoretical lower bound on the number of channels - not only asymptotically, but exactly. Moreover, the main result immediately implies some results of [Kerman and ...