PhD Proposal: An Approximation Framework for Large-scale Spatial Games

Game theoretic modeling paradigms such as Evolutionary Games and Mean Field Games(MFG) are increasingly used to model a variety of multi-agent systems in which the agentsinteract in a game theoretic fashion. However, both modeling paradigms have unique issuesthat can make them difficult to analyze in closed form when applied to spatial domains. On onehand, spatial EGT models are difficult to evaluate mathematically and both simulations andapproximations run into accuracy issues and tractability issues. On the other hand, MFG modelsare not typically formulated to deal with domains where agents have strategies and physicallocations. Furthermore, any MFG approach for controlling strategy evolution on spatial domainsneed also address the accuracy and efficiency challenges in the evaluation of its forwarddynamics.In this work, we propose a new modeling paradigm and approximation technique termedBayesian-MFG for large-scale multi-agent games on spatial domains. The new framework liesat an intersection of techniques drawn from spatial evolutionary games and mean field games.Furthermore, using this framework, we present a method for incorporating Bayesian networkapproximations 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 forproblems with distinct strategy and spatial components. Alongside this, we have developedBayesian network approximations for spatial evolutionary games to address the accuracy issuesfaced by pair-MFG and other lower order models. Our plan for future work is to combine thepair-MFG and Bayesian Network approximations into a unified framework as well as to improvethe computational efficiency and accuracy of the Bayesian network approximations so that theunified framework can be effectively applied to a variety of control problems in domains such asreaction-diffusion equations, network security, and social modeling.

Examining Committee

Chair:

Dr. Dana Nau

Department Representative:

Dr. Aravind Srinivasan

Members:

Dr. Rina Dechter