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ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps

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  • Benazzoli, Chiara
  • Campi, Luciano
  • Di Persio, Luca

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.

Suggested Citation

  • Benazzoli, Chiara & Campi, Luciano & Di Persio, Luca, 2019. "ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:21
    DOI: 10.1016/j.spl.2019.05.021
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    References listed on IDEAS

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    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    2. Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
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