2025/12/09 by Possamaï, Dylan, Rossato, Chiara
Decision Sciences · Economics, Econometrics and Finance · #Climate Change Policy and Economics #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #Theoretical Economics (econ.TH)
paper · doi:10.48550/arxiv.2512.08745
openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28
We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality principle no longer applies. To address this, we adopt a two-layer game-theoretic framework and seek sub-game--perfect Nash equilibria both at the intra-personal level, which accounts for time inconsistency, and at the inter-personal level, which captures strategic interactions among players. We first characterise sub-game--perfect Nash equilibria and the corresponding value processes of all players through a system of coupled backward stochastic differential equations. We then analyse the mean-field counterpart and its sub-game--perfect mean-field equilibria, described by a system of McKean-Vlasov backward stochastic differential equations. Building on this representation, we finally prove the convergence of sub-game--perfect Nash equilibria and their corresponding value processes in the N-player game to their mean-field counterparts.