## 2 Related Work
### Game Theory for Network Slicing
In the cooperative gaming setting, the proposed Nash bargaining scheme is more effective. Instead of maximizing the social welfare or utility sum of all participants, some studies focus on the guarantee of profit for service providers. For example, a profitable auction-based approach for multi-domain network service orchestration in 5G networks is proposed for increasing the profit of service providers, while keeping the QoS requirements [46]. Another type of design objective is the stability of the game theory-based solution. A stable solution is one that is accepted by all the participants and no violation would appear. For example, a hierarchical auction and dynamic programming-based resource allocation algorithm is proposed for achieving a stable solution in 5G radio access network slicing [47]. Table 2 presents the summary of existing game theory-based access control mechanisms as well as our differences with them. Compared with existing game theory-based solutions for multi-domain network slicing admission control, this work is the first to model the cooperation and competition among different network service providers simultaneously and the previous solutions no longer hold for this new and more realistic scenario. Most of the previous studies only consider a non-cooperative case or a cooperative case. Even for the only one exception that both cases are considered, they are  
seen as two different problems with two solutions [45]. This work is also the first to consider both terrestrial and satellite networks for providing a multi-domain network service simultaneously, based on SDN and network slicing techniques. The satellite network is featured with its global connectivity ability powered by inter-satellite links regardless of the terrestrial obstacles. Our mechanism is designed for boosting the competition and cooperation between satellite and terrestrial networks, especially those operating LEO constellations with limited budgets and willing to provide commercial services, and achieving a win-win-win result for satellite network service providers, terrestrial network service providers, and end users. As the main beneficiary, satellite network service providers can be involved in the telecommunication market, which was previously dominated by terrestrial network service providers. The users have more options for their data transmission missions or Internet connections [48]. The whole market can be more efficient for all participants with the asymptotic maximum gain from trade and the terrestrial network service providers which would also benefit from our mechanism. For the implementation of game theory-based solutions, distributed ledger technologies have been proven to be the ideal choice with trust, security, transparency, and traceability abilities [49]. The Microsoft Confidential Consortium Framework platform is leveraged to provide a privacy-preserving multi-domain network slice orchestration architecture and a bilateral evaluation mechanism based on game theory is proposed to guarantee fairness and quality-of-experience (QoE) by suppressing malicious behaviors during multi-domain network slice orchestration [50]. Ethereum is used as another blockchain-based solution to deploy multi-domain network slices [51]. Since the internal topology information is usually a commercial secret and network service providers are not willing to reveal such private information [23], it is difficult and impractical to deploy our proposed mechanism in a centralized approach. Instead, a decentralized approach is preferred for deploying our mechanism in the near future, e.g., with blockchains after the software-defined satellite networks become mature and commercialized [52]. As indicated in the literature, a careful design of the auction mechanism and strict regulations are required for mitigating drawbacks and risks such as multi-round auction overhead, biased bidding, and cheating [53].