TY - JOUR
AU - Celli, Andrea
AU - Coniglio, Stefano
AU - Gatti, Nicola
PY - 2020/04/03
Y2 - 2022/01/20
TI - Private Bayesian Persuasion with Sequential Games
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 34
IS - 02
SE - AAAI Technical Track: Game Theory and Economic Paradigms
DO - 10.1609/aaai.v34i02.5557
UR - https://ojs.aaai.org/index.php/AAAI/article/view/5557
SP - 1886-1893
AB - <p>We study an information-structure design problem (a.k.a. a persuasion problem) with a <em>single</em> sender and <em>multiple</em> receivers with actions of <em>a priori</em> unknown types, independently drawn from action-specific marginal probability distributions. As in the standard <em>Bayesian persuasion</em> model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the much more expressive case in which the receivers interact in a <em>sequential game with imperfect information</em>, with utilities depending on the game outcome and the realized action types. After formalizing the notions of <em>ex ante</em> and <em>ex interim</em> persuasiveness (which differ by the time at which the receivers commit to following the sender's signaling scheme), we investigate the <em>continuous optimization</em> problem of computing a signaling scheme which maximizes the sender's expected revenue. We show that computing an optimal <em>ex ante</em> persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for <em>ex interim</em> persuasion, we show that, for games with two receivers, an optimal <em>ex ante</em> persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method.</p>
ER -