2016/05/17 by Rani Basna, Basna, Rani, Astrid Hilbert +3
Decision Sciences · Physics and Astronomy · Economics, Econometrics and Finance · #Game Theory and Applications #Advanced Thermodynamics and Statistical Mechanics #Economic theories and models
paper · pdf · doi:10.48550/arxiv.1605.05073
We investigate mean-field games from the point of view of a large number of\nindistinguishable players which eventually converges to infinity. The players\nare weakly coupled via their empirical measure. The dynamics of the states of\nthe individual players is governed by a non-autonomous pure jump type semi\ngroup in a Euclidean space, which is not necessarily smoothing. Investigations\nare conducted in the framework of non-linear Markov processes. We show that the\nindividual optimal strategy results from a consistent coupling of an optimal\ncontrol problem with a forward non-autonomous dynamics. In the limit as the\nnumber N of players goes to infinity this leads to a jump-type analog of the\nwell-known non-linear McKean-Vlasov dynamics. The case where one player has an\nindividual preference different from the ones of the remaining players is also\ncovered. The two results combined reveal an epsilon-Nash Equilibrium for the\nN-player games.\n