4.7 Article

Decision Making in Star Networks With Incorrect Beliefs

Journal

IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 69, Issue -, Pages 6221-6236

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2021.3123891

Keywords

Decision making; Standards; Bayes methods; Stochastic processes; Sociotechnical systems; Labeling; Error probability; Social decision making; distributed detection; cumulative prospect theory

Funding

  1. National Science Foundation [CCF-1717530]

Ask authors/readers for more resources

This study focuses on a Bayesian binary decision-making problem in star networks, revealing the surprising result that incorrect beliefs could lead to a smaller risk for the fusion agent. Additionally, it is found that the optimal risk of the fusion agent converges to zero exponentially fast as the number of local agents grows.
Consider a Bayesian binary decision-making problem in star networks, where local agents make selfish decisions independently, and a fusion agent makes a final decision based on aggregated decisions and its own private signal. In particular, we assume all agents have private beliefs for the true prior probability, based on which they perform Bayesian decision making. We focus on the Bayes risk of the fusion agent and counterintuitively find that incorrect beliefs could achieve a smaller risk than that when agents know the true prior. It is of independent interest for sociotechnical system design that the optimal beliefs of local agents resemble human probability reweighting models from cumulative prospect theory. We also consider asymptotic characterization of the optimal beliefs and fusion agent's risk in the number of local agents. We find that the optimal risk of the fusion agent converges to zero exponentially fast as the number of local agents grows. Furthermore, having an identical constant belief is asymptotically optimal in the sense of the risk exponent. For additive Gaussian noise, the optimal belief turns out to be a simple function of only error costs and the risk exponent can be explicitly characterized.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available