FRE Special Seminar: Charles Bertucci & Gökçe Dayanikli
This event is free, but registration is required.
Gökçe Dayanikli
Title
Cooperation, Competition, and Common Pool Resources in Mean Field Games
Abstract
The tragedy of the commons (TOTC, introduced by Hardin, 1968) states that individual incentives will result in overusing common pool resources which in turn may have detrimental future consequences that affect everyone negatively. However, in many real-life situations, this does not happen and researchers such as the Nobel Prize winner Elinor Ostrom suggested mutual restraint by individuals can be the preventing factor. In mean field games (MFGs), since individuals are insignificant and non-cooperative, the TOTC is inevitable. This shows that mean field game models should incorporate a mixture of selfishness and altruism to model real-life situations that include common pool resources. However, commonly in the literature, mean field models either focus on fully non-cooperative setup as in mean field games, or fully cooperative setup as in mean field control. Motivated by real-life situations, in this talk, we will discuss different equilibrium notions to capture the mixture of cooperative and non-cooperative behavior in the population. To do this, we will introduce and discuss mixed individual MFGs and mixed population MFGs where we will also add the common pool resources in the models. The former captures the altruistic tendencies at the individual level and the latter models a population that is a mixture of fully cooperative and non-cooperative individuals. For both cases, we will discuss definitions and characterization of equilibrium with the forward-backward stochastic differential equations. In the talk, we will discuss two examples: the first one is a linear-quadratic example (without a common pool resource) where we can reduce the equilibrium characterization to solving ODEs and the second one is a real-life inspired example where we model fishers where the fish stock is modeled as the common pool resource. In these examples, we analyze the existence and uniqueness of results and discuss the numerical results. (This is joint work with Mathieu Lauriere.)
Bio
Gökçe Dayanıklı is an Assistant Professor of Statistics at the University of Illinois Urbana-Champaign where she is also an Affiliate Assistant Professor at the Department of Industrial & Enterprise Systems Engineering and an Affiliate at Carl R. Woese Institute for Genomic Biology. Before joining UIUC, she worked as a term assistant professor at Columbia University, Department of Statistics. She completed her Ph.D. in Operations Research & Financial Engineering at Princeton University where she was the recipient of the School of Engineering and Applied Science Award for Excellence. During Fall 2021, she was a visiting graduate researcher at the Institute for Mathematical and Statistical Innovation (IMSI) to participate in the "Distributed Solutions to Complex Societal Problems" program. Broadly, she is interested in Mean Field Games & Control, Stackelberg games, and Graphon Games applications, extensions, theory, and solutions. Her work is supported by National Science Foundation.
Charles Bertucci
Title
On some recent developments on HJB equations on the space of probability measure
Abstract
In this talk, I will overview some recent progress on HJB equations in the space of probability measures. I will focus on difficulties arising in the definition of viscosity solutions and the establishment of a proper comparison principle. I will comment on the difference between a notion of viscosity solution involving super-differentials, and one involving smooth test functions, namely through recent results on approximation of the squared Wasserstein distance that we obtain with Pierre-Louis Lions.
Bio
Charles Bertucci is a CNRS researcher who has been working at École Polytechnique since 2019. His work is at the meeting point of analysis, probabilities, and optimization. He is a specialist in mean-field games and Hamilton-Jacobi-Bellman equations. He works on both theoretical and modeling aspects, namely in economics, finance, or telecommunications.