Well-Posedness for Mean Field Games with Finite State and Action Space

The main purpose of this paper is to investigate the well-posedness for mean field game with finite state and action space (FSASMFG) by using nonlinear analysis methods. First, we set up the bounded rationality model of the FSASMFG in the topological space. Next, we study some sufficient conditions of generalized strong well-posedness (GS-wp) and strong well-posedness (S-wp) for a class of FSASMFGs. Finally, we give some characterizations of GS-wp and S-wp for FSASMFGs with the help of set-valued analysis methods. These new results presented in the paper develop and improve the corresponding conclusions in the recent literature.