Finite State Graphon Mean Field Games

Regular seminar of the Department of Mathematics
11 October 2023
Start time 
5:00 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room "1" (Povo 0) e via Zoom (please contact to get the code)
Departmento of Mathematics
Target audience: 
University community
UniTrento students
Contact person: 
Prof. Luigi Amedeo Bianchi, Prof. Stefano Bonaccorsi, Prof. Michele Coghi
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3898-1980
Nicola Fraccarolo (University of Trento)


In this work we will talk about stochastic games on large graphs, where the players no longer interact with each other symmetrically. To encode this information, the concept of graphon is employed. Graphons are the natural continuum limits for dense interaction matrices.
Mathematically, a graphon is a symmetric measurable function $W : [0, 1]^2 \to [0,1]$, with $W(u, v)$ representing the interaction between vertices players $u$ and $v$.
We consider continuous-time controlled dynamics on finite states: we write the dynamics of the $N$-player game as a system of stochastic differential equations driven by independent stationary Poisson random measures. Under a set of fairly general assumptions, we derive the existence of both relaxed and nonrelaxed controls, while uniqueness is proven under the Lasry-Lions monotonicity conditions.
This talk is based on joint research with Luca Di Persio (University of Verona, Italy) and Francesco Giuseppe Cordoni (University of Trento, Italy).