Bayesian Group Decisions: Algorithms and Complexity

05/12/2017
by   Ali Jadbabaie, et al.
0

We address the computations that Bayesian agents undertake to realize their optimal actions, as they repeatedly observe each other's actions, following an initial private observation. We use iterated eliminations of infeasible signals (IEIS) to model the thinking process as well as the calculations of a Bayesian agent in a group decision scenario. We show that IEIS runs in exponential time; however, when the group structure is a partially ordered set, the Bayesian calculations simplify and polynomial-time computation of the Bayesian recommendations is possible. We next shift attention to the case where agents reveal their beliefs (instead of actions) at every decision epoch. We analyze the computational complexity of the Bayesian belief formation in groups and show that it is NP-hard. We also investigate the factors underlying this computational complexity and show how belief calculations simplify in special network structures or cases with strong inherent symmetries. We finally give insights about the statistical efficiency (optimality) of the beliefs and its relations to computational efficiency.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/23/2018

Beliefs and Expertise in Sequential Decision Making

This work explores a sequential decision making problem with agents havi...
07/09/2020

Bribery and Control in Stable Marriage

We initiate the study of external manipulations in Stable Marriage by co...
03/14/2019

A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

We study a setting where a group of agents, each receiving partially inf...
01/30/2013

A Hybrid Algorithm to Compute Marginal and Joint Beliefs in Bayesian Networks and Its Complexity

There exist two general forms of exact algorithms for updating probabili...
01/05/2015

Inverse Renormalization Group Transformation in Bayesian Image Segmentations

A new Bayesian image segmentation algorithm is proposed by combining a l...
06/09/2021

Bayesian Persuasion in Sequential Decision-Making

We study a dynamic model of Bayesian persuasion in sequential decision-m...
02/26/2020

Feasible Joint Posterior Beliefs

We study the set of possible joint posterior belief distributions of a g...