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<p>This paper is concerned with the <i>N</i>-player stochastic differential game of optimal switching. Both Nash equilibrium and social optima are studied and proven to have the same mean field limit. The authors prove the convergence of the value functions in the sense of viscosity solution, and show the limit of Nash equilibrium coincides with social optima as <i>N</i> → ∞. In virtue of the weak formulation, the limit problem is characterized by a weak mean field equilibrium, which corresponds to approximate solutions of <i>N</i>-player game. Moreover, the authors provide example and simulation to illustrate the connection between weak mean field equilibrium and <i>N</i>-player game.</p>

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N-Player Optimal Switching Game and Mean Field Limit: Nash Equilibrium and Social Optima

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Guanxu Li,
  • Zhen Wu

摘要

This paper is concerned with the N-player stochastic differential game of optimal switching. Both Nash equilibrium and social optima are studied and proven to have the same mean field limit. The authors prove the convergence of the value functions in the sense of viscosity solution, and show the limit of Nash equilibrium coincides with social optima as N → ∞. In virtue of the weak formulation, the limit problem is characterized by a weak mean field equilibrium, which corresponds to approximate solutions of N-player game. Moreover, the authors provide example and simulation to illustrate the connection between weak mean field equilibrium and N-player game.