## 2 Related Work
### Game Theory for Network Slicing  
In recent years, game theory has been proven to be an effective tool for solving various problems in satellite-terrestrial integrated networks which involve user participation and strategic behaviors. For example, to balance the utilities of the network operator and IoT users, a game theory-based mode selection and dynamic pricing scheme is proposed in ref. [34] to maximize the average throughput and reduce the delay, in which the network operator adopts the Stackelberg game strategy and the users adopt the evolutionary game strategy. Various auctions are further proposed as potential solutions for resource allocation, spectrum sharing, edge computing, and handover in satellite-terrestrial integrated networks. A second-price auction-based traffic offloading mechanism is proposed to achieve the symmetric Bayesian equilibrium and obtain the maximum expected utility of the mobile network operator [35]. To minimize the difference between the allocated and required data rate, a double auction-based resource allocation scheme is proposed in ref. [36], in which the utilities of both the network operator and users are maximized. A double auction mechanism is also used in the satellite mobile edge computing to optimize the rationality of resource allocation by considering successful trades and social welfare [37]. A multi-round auction-based resource allocation scheme is proposed to maximize the user sanctification when allocating the satellite network resource to ground users by considering the satellite network operator as the seller and the ground users as the buyers [38]. To achieve the effective and efficient secondary relay selection, a Vickery auction is introduced in the cognitive hybrid satellite-terrestrial overlay networks with non-orthogonal multiple access as a solution by distinct sub-time slot allocation for a one shot in terms of a distributed manner [39; 40; 41]. A deep-learning-based auction design approach is proposed in ref. [42] to achieve a trustworthy handover in LEO satellite network, in which a distributed and scalable auction can be applied to guarantee optimal revenue and enable self-configurable operations for adapting various conditions. Taking the privacy-preserving requirement into consideration, game theory has been an ideal tool for designing potential solutions in multi-domain network slicing service provision problems with different objectives, e.g., maximizing social welfare, maximizing profit for service providers only, and achieving a stable solution. The most frequently used objective in the literature is the maximization of social welfare, which is defined as the sum of the utilities from all participants. For example, an iterative double-auction mechanism is proposed for multi-domain network service provision with an SDN-based infrastructure, in which social welfare is maximized while keeping the truthful bidding property [43]. The iterative auction game approach is also used in ref. [44] for the multi-domain network slicing in mobile networks and the proposed distributed privacy-saving mechanism converges to the optimal solution within only a few (less than 10) iterations. The many-to-one matching game theory framework is used for associating a slice user with an access point in a tier and an infrastructure provider in the multi-tier multi-domain network slicing scenario, with the aim of maximizing the transformed utility [10]. Then, a recursive distributed backtracking technique is leveraged to find the optimal solution and outperforms the genetic algorithm-based and static slicing resource allocation schemes. Both incentive-driven broker competition (i.e., non-cooperative gaming) and market share-based broker bargain (i.e., cooperative gaming) cases are considered for end-to-end light path provisioning across multiple domains in the multi-domain software-defined elastic optical network [45]. In the competitive gaming setting, the Nash equilibrium result is outperformed by an effective bidding strategy based on the kernel density estimation.