Communications in Information and Systems

Volume 21 (2021)

Number 4

Master adjoint systems in mean-field-type games

Pages: 623 – 650



Hamidou Tembine (Learning and Game Theory Lab, Paris, France)


This article presents mean-field-type games with both atomic and non-atomic decision-makers.We establish sufficiency conditions for equilibria in state-and-mean-field-type feedback strategies using Bellman systems in the space of measures. We then derive master adjoint systems. The computation of the equilibrium system is illustrated in variance-aware games with heterogeneous decisionmakers.

Research supported in part by U.S. Air Force Office of Scientific Research under grant number FA9550-17-1-0259.

Received 23 May 2020

Published 4 June 2021