$\varepsilon$-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps

Understand

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players.

• Each player minimizes some expected cost by affecting the drift as well as the jump part of their own private state process.
• We consider the corresponding limiting mean-field game and, under the assumption that the latter admits a regular Markovian solution, we prove that an approximate Nash equilibrium for the $n$-player game can be constructed for $n$ large enough, and provide the rate of convergence.
• This extends to a class of games with controlled jumps classical results in mean-field game literature.