3,144 research outputs found
Efficient Bayesian Learning in Social Networks with Gaussian Estimators
We consider a group of Bayesian agents who try to estimate a state of the
world through interaction on a social network. Each agent
initially receives a private measurement of : a number picked
from a Gaussian distribution with mean and standard deviation one.
Then, in each discrete time iteration, each reveals its estimate of to
its neighbors, and, observing its neighbors' actions, updates its belief using
Bayes' Law.
This process aggregates information efficiently, in the sense that all the
agents converge to the belief that they would have, had they access to all the
private measurements. We show that this process is computationally efficient,
so that each agent's calculation can be easily carried out. We also show that
on any graph the process converges after at most steps, where
is the number of agents and is the diameter of the network. Finally, we
show that on trees and on distance transitive-graphs the process converges
after steps, and that it preserves privacy, so that agents learn very
little about the private signal of most other agents, despite the efficient
aggregation of information. Our results extend those in an unpublished
manuscript of the first and last authors.Comment: Added coauthor. Added proofs for fast convergence on trees and
distance transitive graphs. Also, now analyzing a notion of privac
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
Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud
We focus on the following natural question: is it possible to influence the
outcome of a voting process through the strategic provision of information to
voters who update their beliefs rationally? We investigate whether it is
computationally tractable to design a signaling scheme maximizing the
probability with which the sender's preferred candidate is elected. We focus on
the model recently introduced by Arieli and Babichenko (2019) (i.e., without
inter-agent externalities), and consider, as explanatory examples, -voting
rule and plurality voting. There is a sharp contrast between the case in which
private signals are allowed and the more restrictive setting in which only
public signals are allowed. In the former, we show that an optimal signaling
scheme can be computed efficiently both under a -voting rule and plurality
voting. In establishing these results, we provide two general (i.e., applicable
to settings beyond voting) contributions. Specifically, we extend a well known
result by Dughmi and Xu (2017) to more general settings, and prove that, when
the sender's utility function is anonymous, computing an optimal signaling
scheme is fixed parameter tractable w.r.t. the number of receivers' actions. In
the public signaling case, we show that the sender's optimal expected return
cannot be approximated to within any factor under a -voting rule. This
negative result easily extends to plurality voting and problems where utility
functions are anonymous
Multi-Receiver Online Bayesian Persuasion
Bayesian persuasion studies how an informed sender should partially disclose
information to influence the behavior of a self-interested receiver. Classical
models make the stringent assumption that the sender knows the receiver's
utility. This can be relaxed by considering an online learning framework in
which the sender repeatedly faces a receiver of an unknown, adversarially
selected type. We study, for the first time, an online Bayesian persuasion
setting with multiple receivers. We focus on the case with no externalities and
binary actions, as customary in offline models. Our goal is to design no-regret
algorithms for the sender with polynomial per-iteration running time. First, we
prove a negative result: for any , there is no
polynomial-time no--regret algorithm when the sender's utility function
is supermodular or anonymous. Then, we focus on the case of submodular sender's
utility functions and we show that, in this case, it is possible to design a
polynomial-time no--regret algorithm. To do so, we introduce
a general online gradient descent scheme to handle online learning problems
with a finite number of possible loss functions. This requires the existence of
an approximate projection oracle. We show that, in our setting, there exists
one such projection oracle which can be implemented in polynomial time
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