\section{Related Works}

In this section, we review the related works in the field of cloud edge collaborative multi-star cooperative game strategy. We categorize the related works into several fields and analyze their strengths and weaknesses.

\paragraph{Consensus and Control in Multi-Agent Systems}
Several works have addressed the consensus and control issues in multi-agent systems. For instance, Li et al. \citep{li2016consensus} proposed a distributed observer-type consensus protocol based on relative output measurements. Wang et al. \citep{wang2022hybrid} addressed the leader-following consensus issue for continuous-time multi-agent systems with semi-Markov jump parameters. Liang et al. \citep{liang2021containment} utilized two kinds of classical control schemes to address the proposed synthesis problem of the containment control with respect to continuous-time semi-Markovian multi-agent systems with semi-Markovian switching topologies. These works provide theoretical foundations for the consensus and control in multi-agent systems.

\paragraph{Collaborative Computing in Edge-Cloud Systems}
Collaborative computing in edge-cloud systems has been extensively studied in recent years. Liu et al. \citep{liu2020coordinated} proposed a distributed cloud predictive control scheme to achieve desired coordination control performance and compensate actively for communication delays between the cloud computing nodes and between the agents. Liu et al. \citep{liu2017predictive} proposed a cloud predictive control scheme for networked multi-agent systems (NMASs) to achieve consensus and stability simultaneously and to compensate for network delays actively. Liu et al. \citep{liu2022coordinated} proposed a mist-fog-cloud predictive control scheme for the coordinated control of complex large-scale networked multi-agent systems. These works provide insights into the design of collaborative computing systems in edge-cloud environments.

\paragraph{Game Theory and Cooperative Game Strategy}
Game theory and cooperative game strategy have been widely used in the design of collaborative computing systems. Prasadu et al. \citep{prasadu2018implementing} proposed a non-cooperative game-based task scheduling and computing resource allocation algorithm NG_TSRA that can improve the average power efficiency of the cloud computing system. Moura et al. \citep{moura2019game} discussed relevant theoretical models that enable cooperation amongst the players in distinct ways through pricing or reputation and highlighted open problems. Bataineh et al. \citep{bataineh2021cloud} proposed a novel game theoretical model that consists of a mix of cooperative and competitive strategies. These works provide a theoretical basis for the design of game-theoretic models in collaborative computing systems.

\paragraph{Federated Learning and Multi-Agent Systems}
Federated learning and multi-agent systems have been combined to address various problems in cloud-edge collaborative computing. Fadlullah et al. \citep{fadlullah2022hcp} proposed a 2-stage federated learning algorithm among the UEs, UAVs/BSs, and HCP to collaboratively predict the content caching placement. Yang et al. \citep{yang2022output} presented a cloud-based control scheme for multi-agent systems and proved that the proposed scheme renders the MAS stable and achieves output consensus. Houda et al. \citep{houda2022when} designed a novel MEC-based framework to secure IIoT applications leveraging FL, called FedGame, and evaluated its accuracy against centralized ML/DL schemes while preserving the privacy of Industrial systems. These works provide insights into the integration of federated learning and multi-agent systems in cloud-edge collaborative computing.

\paragraph{IoT Systems and Multi-Server Offloading Strategy}
IoT systems and multi-server offloading strategy have been studied to optimize the performance of cloud-edge collaborative computing. Wang et al. \citep{wang2021multi} introduced a multi-server cooperative offloading strategy for IoT systems. Ananth et al. \citep{ananth2015cooperative} proposed a new job scheduling technique using the concepts of game theory and genetic algorithm to provide Pareto optimal solution using Non-dominated Sorting Genetic Algorithm II (NSGA II) and also concentrated on minimizing the deadline violation and makespan for the jobs submitted by the user. Kim et al. \citep{kim2021a} designed a novel DMCC resource sharing scheme for data offloading services that explores the mutual benefits of local and global MCC providers¡¯ interactions. These works provide insights into the design of IoT systems and multi-server offloading strategy in cloud-edge collaborative computing.

In summary, the related works in the field of cloud edge collaborative multi-star cooperative game strategy have been categorized into several fields, including consensus and control in multi-agent systems, collaborative computing in edge-cloud systems, game theory and cooperative game strategy, federated learning and multi-agent systems, and IoT systems and multi-server offloading strategy. These works provide theoretical foundations and practical insights into the design of cloud-edge collaborative computing systems.