Private Bayesian Persuasion with Sequential Games

Abstract

We study an information-structure design problem (a.k.a. a persuasion problem) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal probability distributions. As in the standard Bayesian persuasion 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 sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ by the time at which the receivers commit to following the sender's signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender's expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method.

Preplay Communication in Multi-Player Sequential Games: An Overview of Recent Results

“…Celli et al [12] examine information-structure design problems as a means of forcing coordination towards a certain objective. More precisely, they start from the usual scenario where a mediator can communicate action recommendations to players before the beginning of a sequential game.…”

“…Specifically, the mediator is able to observe more information than the other players. Celli et al [12] pose the following question: can the mediator exploit the information asymmetry to coordinate players' behavior toward a favorable outcome?…”

“…This problem can be accurately modeled via the Bayesian persuasion framework [26]. Celli et al [12] investigate private persuasion problems with multiple receivers interacting in a sequential game, and study the continuous optimization problem of computing a private signaling scheme which maximizes the sender's expected utility. The authors show how to address sequential, multi-receiver settings algorithmically via the notion of ex ante persuasive signaling scheme, where the receivers commit to following the sender's recommendations having observed only the signaling scheme.…”

Algorithmic Information Design in Multi-Player Games: Possibility and Limits in Singleton Congestion

“…Thus unsurprisingly, it has attracted much algorithmic studies, particularly in the challenging situation of multi-receiver persuasion [18]. Much algorithmic investigation has been devoted to the special case with no inter-agent externalities [19,20,21,22,23], i.e., a receiver's utility is not affected by other receivers' actions. This restriction is certainly not ideal, but does come with a reason.…”

“…(i.e., private signaling). This turns out to be more tractable: optimal private signaling admits polynomial time algorithm so long as the sender's objective function can be efficiently maximized [20,22] but becomes NP-hard otherwise [19].…”