The notation and definitions.

This paper investigates a signal online channel green hotel supply chain comprising a green small and medium-sized hospitality enterprise (GSMHE) responsible for offline electronic Word-of-Mouth (e-WOM) promotion and green service efforts, and an online travel agency (OTA) engaged in online e-WOM promotion activities. Both offline and online e-WOM efforts significantly contribute to the overall e-WOM level of the green hotel supply chain. Due to the inherent characteristic of reviews posting, the impacts of these efforts on e-WOM exist time lags. Therefore, this study aims to explore the influence of time lags and examine the feasibility of a cooperative program in this context. This paper develops a differential game model that incorporates time lags. By analyzing and comparing the equilibrium strategies and profits under three scenarios, we demonstrate that a cost-sharing model can be successfully implemented when specific relationships regarding the time lags of the GSMHE are satisfied.