Speaker:  Gokce Dayanikli, Assistant Professor at the University of Illinois Urbana-Champaign, Department of Statistics.

Title:  Cooperation, Competition, and Common Pool Resources in Mean Field Games

Abstract: The tragedy of the commons (TOTC, introduced by Hardin, 1968) states that the 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 have analyzed the reasons why it may not happen (such as mutual restraint by consensus may occur or laws controlling the usage may exist). 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 focuses on fully non-cooperative setup as in mean field games or fully cooperative setup as in mean field control. Motivated by the 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. Later, 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 results and discuss the numerical results. (This is a joint work with Mathieu Lauriere.)