International Society of Dynamic Games

Dynamic Games and Applications Seminar

A mean field game theory of spatial dynamics in economic geography

Nov 13, 2025   11:00 AM — 12:00 PM (Montreal time)

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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.

(with Raouf Boucekkine and Quentin Petit)

Dynamic Games and Applications Seminar

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

Nov 6, 2025   11:00 AM — 12:00 PM (Montreal time)

Zoom webinar link

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.

(Joint work with Mathieu Lauriere.)

Dynamic Games and Applications Seminar

Properties of guaranteed cost equilibrium in scalar infinite horizon linear quadratic differential games

Oct 30, 2025 11:00 AM — 12:00 PM (Montreal time)

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We consider infinite-horizon linear-quadratic differential games (LQDGs) with a state-feedback information structure and guaranteed cost equilibrium (GCE) as the solution concept. Once the players reach a GCE, no player has an incentive to deviate from the equilibrium strategy, as each has achieved a desired upper bound on her cost. In this work, we provide conditions for the existence of a GCE in scalar LQDGs and investigate the related welfare properties. Furthermore, we specialize these results to symmetric and two-player scenarios.

(with Aniruddha Roy)