Geodesic
Mean field games based on the stable-like processes
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 4, pp. 33-65

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We investigate the mean field games of $N$ agents based on the nonlinear stable-like processes. The main result of the paper is in the statement that any solution of the limiting mean field consistency equation generates a $1/N$-Nash equilibrium for the approximating game of $N$ agents.
Keywords: stable-like processes, kinetic equation, forward-backward system, dynamic law of large numbers, rates of convergence, tagged particle, $\varepsilon$-Nash equilibrium. 
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     author = {Vassili N. Kolokoltsov and Marianna S. Troeva and Wei Yang},
     title = {Mean field games based on the stable-like processes},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {33--65},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_4_a2/}
}
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Vassili N. Kolokoltsov; Marianna S. Troeva; Wei Yang. Mean field games based on the stable-like processes. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 4, pp. 33-65. http://geodesic.mathdoc.fr/item/MGTA_2013_5_4_a2/