## 7 Review of Studies Related to Integration in the Context of Multi-Modal Mobility
### Review of Studies
Question: How to allocate costs and determine prices offered by operators according to user route choices and operator service choices in MaaS systems? Results: An algorithm was developed in [119] for a model proposed to allow travelers to make multi-modal trips offered by multiple operators to efficiently generate stability conditions. Application of the model to handle pricing responses of MaaS operators to technological and capacity changes, government acquisition, consolidation, and firm entry was demonstrated through computational experiments. Results showed that the solution time of the proposed algorithm is reduced by 98% on average. 18. Question: How to solve the vehicle dispatching service pricing and demand problem in MaaS?Results: In [120], a two-stage Stackelberg game under different pricing schemes was proposed for the vehicle dispatching service pricing and demand problem. Two different pricing schemes were considered, the independent pricing scheme (IPS) and the competitive pricing scheme (CPS). The vehicle supply-demand relationship and market competition among the modality switch points (MSPs) were also considered in the problem. The paradigm of leaders-followers is used with the MSPs as leaders to set their service pricing strategies first, and the passengers as the followers to determine their service demands. Due to the complexity of the dynamic MaaS market environment, a multi-agent deep reinforcement learning (MADRL) algorithm was developed to achieve the Nash equilibrium (NE) (the optimal pricing and demand strategies) of the formulated game. Convergence to the optimal solution by applying the proposed algorithm was analyzed. The results show that the proposed algorithm outperforms other benchmark schemes under both IPS and CPS in terms of maximizing MSPs' revenue and passengers' benefits. * Question: How to balance sustainability and profitability in electric Mobility-as-a-Service ecosystems by providing carbon emissions reduction incentives? Results: An ecosystem enabling platform to leverage carbon reduction funds to incentivize travelers to choose electric MaaS services was presented in [121]. A multi-leader multi-follower game model was proposed in [121] to model the interactions between multiple leaders and multiple followers, where leaders represent MaaS platforms and followers represents travelers. A leader competes with other leaders to maximize his/her profits by making bundle allocation/pricing decisions based on the levels of travelers' participation. A follower minimizes his/her travel costs based on determination of the participation levels for multiple MaaS platforms. An algorithm was developed to solve the proposed multi-leader multi-follower game. The convergence and robustness properties of the proposed algorithm were illustrated by experiments based on real-life data in Australia. For MaaS operators, the proposed method provides valuable insights into balancing profitability with environmental responsibility. * Questions: Can a MaaS system ensure that travelers and service operators will be better off in terms of welfare while maintain profitability of the platform? Does there exist a pricing scheme that can ensure stability condition under which operators and travelers of a MaaS system are willing to participate? Results: To answer these questions, [PERSON] and [PERSON] regarded a MaaS platform for a multi-model transportation network as an intermediary between travelers and service operators in the study [122]. The MaaS intermediary acquires capacity from the service operators and sells capacity to travelers to according to the origin-destination (OD) pairs of their trips. They proposed a model for the assignment problem and the pricing problem for the on-demand mobility services of a MaaS platform in which travelers can plan their trip flexibly. The authors conducted analysis for the many-to-many stable matching issue in a MaaS platform through decomposition of the original problem into an assignment problem and a pricing problem.