Thus, in order to compute the equilibrium value functions in asynchronous games, we use an approach similar to that of \(Q\)-learning. We show here that although the other computing techniques cannot be directly applied, the \(Q\)-learning technique to compute the equilibrium value functions for asynchronous games works very well. As is well known, game theory has been widely used in economics and many other disciplines including political science, management, and finance, among others. It is increasingly being used in computer science as well. Game theory in economics is widely used in a variety of fields but is especially important in industrial organization and the study of markets with a small number of large firms such as oligopolies. Important sources for this literature can be found, among others, in [9; 10; 11]. Game theory is also being widely applied to deal with various challenges in lots of fields in computer science, such as cybersecurity, blockchains, and smart cities. In terms of cybersecurity, [PERSON] et al. [12] outlined the applications of game theory in networks, especially game models, including the cooperative model, the Static Prisoner's Problem, the Static Zero-Sum Game, and Min-Max Q and Nash-Q: [PERSON] et al. [13] established a zero-sum hybrid stochastic game model to design multiple strategies for a system under various types of attacks to balance the security overhead and control the system cost; in addition, [PERSON] et al. [14] summarized recent papers using game-theoretic methods in cybersecurity and divided them into six categories according to their application scenarios, namely, physical layer security, self-organized network security, intrusion detection, privacy preservation, the economics of cybersecurity, and cloud computing security. With the emergence of blockchain technology in recent years, game theory has also come to play an important role in studying security issues, mining management issues, and applications on the blockchain as discussed by [PERSON] et al. [15]. [PERSON] and [PERSON] [16] proposed a decentralized consensus protocol, integrating a game-theoretic model to reward honest validators and punish dishonest or lazy ones. In addition, by deploying different game models based on whether devices are resource-rich or resource-constrained, [PERSON] and [PERSON] [17] proposed the proof-of-game (PoG) consensus algorithm to balance the computational efficiency and the security level of protecting blockchain networks from selfish miners and majority attacks. In the study by [PERSON] et al. [18], transactions between blockchain providers, cyber insurers, and users were modeled as a two-stage Stackelberg game, balancing the service requirements of users, the cost and security level of the blockchain, and the profits of insurance companies. In addition, game theory concepts and machine learning techniques were used by [PERSON] [19] to monitor blockchain networks to prevent collusion in decentralized systems, thereby making the system as fair as possible. When it comes to the application of game theory in smart city research, here we mainly discuss three representative subareas, the Internet of Things (IoT), smart grids, and mobile crowdsensing. Focusing on UAV-assisted IoT communication networks, [PERSON] et al. [20] used a dynamic evolutionary game to solve access competition among UAV swarms and a non-cooperative game to address the bandwidth allocation problem for UAVs. [PERSON] et al. [21] proposed a reputation management scheme based on evolutionary game theory for the Internet of Vehicles, where attacks from malicious users could be effectively reduced by filtering out low-reputation users. In addition, [PERSON] et al. [22] proposed a multi-criteria intelligent scheduling method for IoT services in fog computing environments, using matching game theory to derive scheduling decisions for smart fog and IoT devices to ensure the low latency of services and effective utilization of fog node resources.