Observational Learning in Mean-Field Games with Imperfect Observations

Pawan Poojary*, Randall Berry

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

There are many settings in which agents learn from observing the actions of other agents. Bayesian observational learning models provide a framework for studying such situations and have been well-studied in settings where agents sequentially choose Bayes' optimal actions by learning from the actions of previous agents. Here, we consider such observational learning in a mean-field game setting, in which agents repeatedly choose actions over time to maximize an infinite horizon discounted pay-off. This pay-off depends on the underlying mean-field population state, which agents do not know and only have a prior common belief over it. At the end of each time-step, agents observe a common signal which is an imperfect observation of the mean-field action profile played in that time-step and use this to update their beliefs. We give a sequential decomposition of this game that enables one to characterize Markov perfect equilibria of the game. We then focus on a particular sub-class of these games which can be viewed as a mix of coordination/anti-coordination players. Using the sequential decomposition, we characterize the impact of varying the observation quality on the outcome of the game and show that this can exhibit non-monotonic behaviour, where in many instances, poorer observations lead to better expected total discounted pay-offs.

Original languageEnglish (US)
Title of host publication2023 59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9798350328141
DOIs
StatePublished - 2023
Event59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023 - Monticello, United States
Duration: Sep 26 2023Sep 29 2023

Publication series

Name2023 59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023

Conference

Conference59th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2023
Country/TerritoryUnited States
CityMonticello
Period9/26/239/29/23

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization

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