(MFG) are increasingly used to model a variety of multi-agent systems in which the agents
interact in a game theoretic fashion. However, both modeling paradigms have unique issues
that can make them difficult to analyze in closed form when applied to spatial domains. On one
hand, spatial EGT models are difficult to evaluate mathematically and both simulations and
approximations run into accuracy issues and tractability issues. On the other hand, MFG models
are not typically formulated to deal with domains where agents have strategies and physical
locations. Furthermore, any MFG approach for controlling strategy evolution on spatial domains
need also address the accuracy and efficiency challenges in the evaluation of its forward
In this work, we propose a new modeling paradigm and approximation technique termed
Bayesian-MFG for large-scale multi-agent games on spatial domains. The new framework lies
at an intersection of techniques drawn from spatial evolutionary games and mean field games.
Furthermore, using this framework, we present a method for incorporating Bayesian network
approximations of forward dynamics found in spatial games into a control problem framework.
We have already developed Pair-MFG, a model for defining an pair level approximate MFG for
problems with distinct strategy and spatial components. Alongside this, we have developed
Bayesian network approximations for spatial evolutionary games to address the accuracy issues
faced by pair-MFG and other lower order models. Our plan for future work is to combine the
pair-MFG and Bayesian Network approximations into a unified framework as well as to improve
the computational efficiency and accuracy of the Bayesian network approximations so that the
unified framework can be effectively applied to a variety of control problems in domains such as
reaction-diffusion equations, network security, and social modeling.
Vincent Hsiao is a Ph.D. student in the Department of Computer Science
at the University of Maryland, advised by Prof. Dana Nau. His research focuses on improving algorithms for the game theoretic modeling, approximation, and control of spatial multi-agent systems.