This talk focuses on non-cooperative differential game-theoretic models in both deterministic and stochastic settings to design incentive schemes for water users, geographically distributed across a river network, that reduce conflicts and water consumption. We propose solution methods for both convex and nonconvex decision problems and perform parametric analyses to examine how parameters influence the choice of solution methods and affect decision-making processes.
We propose a mean-field game (MFG) approach to study the dynamics of spatial agglomeration in a continuous space-time framework where trade across locations may follow a broad class of static gravity models. Forward-looking agents work and migrate in a two-dimensional geography and face idiosyncratic shocks. Equilibrium wages and prices depend on their common distribution and adjust statically according to the underlying trade model. We first prove the existence and uniqueness of the static trade equilibrium. We then prove the existence of dynamic equilibria. Finally, we apply our model to a simple circular geography to understand what the MFG theory can tell us about the forces driving agglomeration and dispersion in a dynamic setting.
The tragedy of the commons (TOTC, introduced by Hardin in 1968) states that individual incentives lead to the overuse of common pool resources (CPRs) which in turn may have detrimental future consequences that affect everyone involved negatively. However, in many real-life situations this outcome does not occur and researchers such as Nobel laureate Elinor Ostrom suggested that mutual restraint by individuals can be the preventing factor. In mean field games (MFGs), since individuals are insignificant and fully non-cooperative, the TOTC is inevitable. This indicates that MFG models should incorporate a mixture of selfishness and altruism to capture real-life situations that involve CPRs. Motivated by this, we explore different equilibrium notions to capture a blend of cooperative and non-cooperative behavior in the population. First, we introduce mixed individual MFGs and mixed population MFGs where we also include the CPRs. The former captures altruistic tendencies at the individual level, while the latter models a population that is a mixture of fully cooperative and non-cooperative individuals. For both cases, we briefly discuss the definitions and characterization of equilibrium using forward-backward stochastic differential equations. Later, we present a real-life inspired example of fishers where the fish stock serves as the CPR. We analyze the existence and uniqueness results and discuss the experimental findings.
