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We consider a symmetric $n$-player nonzero-sum stochastic differential gamewith controlled jumps and mean-field type interaction among the players. Eachplayer minimizes some expected cost by affecting the drift as well as the jumppart of their own private state process. We consider the corresponding limitingmean-field game and, under the assumption that the latter admits a regularMarkovian solution, we prove that an approximate Nash equilibrium for the$n$-player game can be constructed for $n$ large enough, and provide the rateof convergence. This extends to a class of games with controlled jumpsclassical results in mean-field game literature. This paper complements ourprevious work, where in particular the existence of a mean-field game solutionwas investigated.

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