We consider a symmetric n-player nonzero-sum stochastic differential game with jump–diffusion dynamics and mean-field type interaction among the players. Under the assumption of existence of a regular Markovian solution for the corresponding limiting mean-field game, we construct an approximate Nash equilibrium for the n-player game for n large enough, and provide the rate of convergence. This extends to a class of games with jumps classical results in mean-field game literature. This paper complements our previous work Benazzol et al. (2017) on the existence of solutions of mean-field games for jump–diffusions.
ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps [epsilon-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps] / C. Benazzoli, L. Campi, L. Di Persio. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 154(2019 Nov). [10.1016/j.spl.2019.05.021]
ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps [epsilon-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps]
L. CampiSecondo
;
2019
Abstract
We consider a symmetric n-player nonzero-sum stochastic differential game with jump–diffusion dynamics and mean-field type interaction among the players. Under the assumption of existence of a regular Markovian solution for the corresponding limiting mean-field game, we construct an approximate Nash equilibrium for the n-player game for n large enough, and provide the rate of convergence. This extends to a class of games with jumps classical results in mean-field game literature. This paper complements our previous work Benazzol et al. (2017) on the existence of solutions of mean-field games for jump–diffusions.File | Dimensione | Formato | |
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