Non-zero-sum stopping games in continuous time

2015/08/17 by Zhou Zhou, Zhou, Zhou
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1508.03921

openalex publication_date 2015/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On a filtered probability space (Ω,F, (F_t)_t∈[0,∞], ℙ), we consider the two-player non-zero-sum stopping game uⁱ := 𝔼[Uⁱ(ρ,τ)], i=1,2, where the first player choose a stopping strategy ρ to maximize u¹ and the second player chose a stopping strategy τ to maximize u². Unlike the Dynkin game, here we assume that U(s,t) is F_{s\vee t}-measurable. Assuming the continuity of Uⁱ in (s,t), we show that there exists an ε-Nash equilibrium for any ε>0.

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