On non-uniqueness in mean field games

Erhan Bayraktar and Xin Zhang

Papers from arXiv.org

Abstract: We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $\alpha^j$ plus a minimum jumping rate $\eta$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean field game equation may have multiple solutions if $\eta

Date: 2019-08, Revised 2020-03
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