Scalable, Stochastic and Spatiotemporal Game Theory for Real-World Human Adversarial Behavior

Work Synopsis: The contribution of Prof. D'Orsogna's group at CSUN to the MURI proposal will be to merge stochastic methodologies and game theoretical modeling within the context of criminal and insurgent behavior. We will especially focus on new scenarios such as the introduction of probabilistic strategies, fluctuations, irrational or conditioned choices within games as well as non-simultaneous decision making in the context of partial information or including memory effects. Starting from the relevant sociological considerations, individual player games will be constructed and analyzed. Spatial information will also be included so that communication and information exchanges do not occur uniformly in space. Once the discrete system is thoroughly analyzed, the limit of a large number of players will be taken, so as to construct mean-field games, resulting in PDE or ODE systems of equations. Such methods have been successfully applied within Economics and Finance so much so that mean-field games are a rapidly growing branch of applied mathematics. We expect to develop interesting mathematical results, useful for practical applications, in collaboration with Drs. Short and Bertozzi at UCLA, to be compared and contrasted with on-field data and sociological input from Dr. Brantingham at UCLA, behavioral analysis from experiments to be designed in close collaboration with Dr. McBride from UCI, and with more formal studies and possible extensions towards operations research and optimization methods to be implemented in conjunction with Drs. Tambe and Maheswaran at USC. Logistics: CSUN is an undergraduate, Hispanic-serving institution located in close proximity to both UCLA and USC. It will serve as a host location for MURI events for collaborators, researchers and undergraduate workshops.