## 1 Introduction
For example, study [27] introduces game theory based flight control algorithms run by each autonomous UAV to satisfy the need of speedy and dynamic adjustments to swarm operations. Study [28] addresses the cooperation problem in underwater acoustic sensor network (UASN) using game theory-based clustering scheme to balance network energy consumption. Study [29] presents a real-time implementation of a multi-agent-based game theory model for microgrid market operations to monitor, control, and perform the reverse auction process of distributed energy resources (DER). In addition, as more complex systems recently emerged in the real world, networked game theory also gained prominence and showed great potential for application in socio-ecological systems [30], networked systems [31], project management [32], etc., but surprisingly, relatively little study has focused on implementing game theory in DEOS. Moreover, dynamic scheduling which focuses on quick response to emergency observation requests, is also a practical issue for EOS applications. [PERSON] et al. [33] listed four key dynamic elements that can make an impact on change of satellite scheduling plan, namely, mission observation opportunity changes, resource changes, new mission insertion, and scheduling parameter changes, but they did not propose any related models or algorithms. Other related studies seem to reveal a major concern regarding this problem, which is how to consider the adjustability brought by those dynamic elements to the initial plan. Some researchers [34; 35] have implemented a complete reprogramming algorithm to solve this problem, but the new plan generated is greatly different from the original one, which may create conflict with the executed missions in progress and lead to waste of time and resources. [PERSON] [16] proposed a multi-satellite dynamic mission scheduling model and used a dynamic scheduling algorithm based on mission priority. When a new mission arrives, this approach will respectively conduct insert, reallocation, and replacement operations to reschedule the plan according to mission priority. Other similar works [36; 37; 38] propose some mechanisms or strategies to solve the dynamic scheduling problem; overall, these methods reduce the complexity of the dynamic adjustment and maintain the stability of the initial scheduling plan, but the efficiency and scalability can be further improved. The overall goal of this paper is to design a distributed mission scheduling architecture that can meet the mission-level scheduling needs of heterogeneous multi-satellite earth observation system in both static and dynamic environments. Specifically, we see each satellite as a rational player and convert the satellite mission scheduling into a cooperative game. Aiming at finding a near global optimal solution in a decentralized way, this paper presents a distributed mission scheduling model, which guarantees convergence to a Nash equilibrium. Moreover, we propose a distributed mission scheduling algorithm along with two improved optimization algorithms for satellite mission scheduling in both static and dynamic environments. Finally, case studies are presented to demonstrate the effectiveness of the proposed methods.