A Kind of N-Player Switching Game: Verification Approach
Guanxu Li, Jincan Song, Zhen Wu · 2025
In this paper, we consider a general class of two-regime switching games. For$N$-player game, we adopt a verification approach to characterize the Nash equilibria (NEs) of the game. For the limit situation of$N \rightarrow \infty$, we consider a suitable meanfield game (MFG) with optimal switching. We prove the optimality of NE solution to the MFG, which is an$\epsilon$-NE approximation to the$N$-player game. This kind of switching game can be used to solve trading game (buy and sell decisions) with large population whose equilibrium is influenced by overall behaviour of all players. We analyze in details and obtain explicit solutions.