1,357 research outputs found
Algorithmic Aspects of Private Bayesian Persuasion
We consider a multi-receivers Bayesian persuasion model where an informed sender tries to persuade a group of receivers to take a certain action. The state of nature is known to the sender, but it is unknown to the receivers. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. This work studies the computation aspects of finding a signaling policy that maximizes the sender\u27s revenue.
We show that if the sender\u27s utility is a submodular function of the set of receivers that take the desired action, then we can efficiently find a signaling policy whose revenue is at least (1-1/e) times the optimal. We also prove that approximating the sender\u27s optimal revenue by a factor better than (1-1/e) is NP-hard and, hence, the developed approximation guarantee is essentially tight. When the sender\u27s utility is a function of the number of receivers that take the desired action (i.e., the utility function is anonymous), we show that an optimal signaling policy can be computed in polynomial time. Our results are based on an interesting connection between the Bayesian persuasion problem and the evaluation of the concave closure of a set function
Algorithmic Cheap Talk
The literature on strategic communication originated with the influential
cheap talk model, which precedes the Bayesian persuasion model by three
decades. This model describes an interaction between two agents: sender and
receiver. The sender knows some state of the world which the receiver does not
know, and tries to influence the receiver's action by communicating a cheap
talk message to the receiver.
This paper initiates the algorithmic study of cheap talk in a finite
environment (i.e., a finite number of states and receiver's possible actions).
We first prove that approximating the sender-optimal or the welfare-maximizing
cheap talk equilibrium up to a certain additive constant or multiplicative
factor is NP-hard. Fortunately, we identify three naturally-restricted cases
that admit efficient algorithms for finding a sender-optimal equilibrium. These
include a state-independent sender's utility structure, a constant number of
states or a receiver having only two actions
Access to Population-Level Signaling as a Source of Inequality
We identify and explore differential access to population-level signaling
(also known as information design) as a source of unequal access to
opportunity. A population-level signaler has potentially noisy observations of
a binary type for each member of a population and, based on this, produces a
signal about each member. A decision-maker infers types from signals and
accepts those individuals whose type is high in expectation. We assume the
signaler of the disadvantaged population reveals her observations to the
decision-maker, whereas the signaler of the advantaged population forms signals
strategically. We study the expected utility of the populations as measured by
the fraction of accepted members, as well as the false positive rates (FPR) and
false negative rates (FNR).
We first show the intuitive results that for a fixed environment, the
advantaged population has higher expected utility, higher FPR, and lower FNR,
than the disadvantaged one (despite having identical population quality), and
that more accurate observations improve the expected utility of the advantaged
population while harming that of the disadvantaged one. We next explore the
introduction of a publicly-observable signal, such as a test score, as a
potential intervention. Our main finding is that this natural intervention,
intended to reduce the inequality between the populations' utilities, may
actually exacerbate it in settings where observations and test scores are
noisy
Algorithmic Persuasion with Evidence
We consider a game of persuasion with evidence between a sender and a
receiver. The sender has private information. By presenting evidence on the
information, the sender wishes to persuade the receiver to take a single action
(e.g., hire a job candidate, or convict a defendant). The sender's utility
depends solely on whether or not the receiver takes the action. The receiver's
utility depends on both the action as well as the sender's private information.
We study three natural variations. First, we consider sequential equilibria of
the game without commitment power. Second, we consider a persuasion variant,
where the sender commits to a signaling scheme and then the receiver, after
seeing the evidence, takes the action or not. Third, we study a delegation
variant, where the receiver first commits to taking the action if being
presented certain evidence, and then the sender presents evidence to maximize
the probability the action is taken. We study these variants through the
computational lens, and give hardness results, optimal approximation
algorithms, as well as polynomial-time algorithms for special cases. Among our
results is an approximation algorithm that rounds a semidefinite program that
might be of independent interest, since, to the best of our knowledge, it is
the first such approximation algorithm for a natural problem in algorithmic
economics.Comment: 31 page
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