*Result*: Optimizing platform subsidy strategies in the MaaS era: Employing a mixed equilibrium dynamic traffic assignment framework with route choice rights game.

*• Developed a UE-CN-SO mixed equilibrium DTA framework. • Constructed a route choice model considering the route choice rights game. • Formulated a platform subsidy optimization model for multi-platform game scenarios. • Designed an algorithm integrating simulation, NS, GP, ABC and other strategies. • Validated the performance of the DTA framework and the subsidy optimization model. In the era of Mobility as a Service (MaaS), urban transportation systems will include not only users of private MaaS platforms (like Uber and Lyft) and private vehicle users but also public MaaS platform users. This will create a mixed equilibrium state within the road network, where participants utilize varying route choice criteria such as User Equilibrium (UE), System Optimum (SO), and Cournot-Nash (CN). This complex scenario raises several scientific challenges: (1) Dynamic Traffic Assignment (DTA) in multi-platform gaming contexts, (2) assigning route choice rights while considering interrelationships between passengers and platforms, (3) accounting for travel time value heterogeneity among MaaS traveler types, and (4) optimizing platform subsidy strategies while assessing the overall impact of subsidies on route choice rights, mixed equilibrium networks, and platform revenues. Early research failed to integrate the dynamics, complexity, and competitive features of the MaaS network into a coherent co-optimization framework, resulting in a lack of systematic and practical solutions. This paper proposes a novel platform subsidy optimization method based on a UE-CN-SO mixed equilibrium DTA framework, employing a bi-level programming approach. The upper-level model optimizes platform subsidy strategies within a multi-platform game framework, aiming to maximize platform revenues. Subsidies are defined as time-varying Dynamic Discount Rate Schemes (DDRS) and Uniform Discount Rate Schemes (UDRS) on travel duration fees. By implementing these subsidies, the platform gains control over passengers' route choices, allowing it to guide travel in a way that maximizes platform revenue. The lower-level model is a simulation-based DTA model that determines the mixed equilibrium flow distribution, where each traveler type—UE, CN, and SO—optimizes its objective function (minimizing individual, platform, or system-wide costs). This process includes a route choice rights assignment mechanism and considers traveler time valuation heterogeneity. An algorithm integrating traffic simulation, Gradient Projection (GP), Neighborhood Search (NS), Artificial Bee Colony (ABC), and custom rules was developed. Through testing, our algorithm finds the optimal solution in 182 s less and 77 s less time compared to the traditional ABC algorithm and NS-SA algorithm, respectively, and the optimal objective function values are 2421 and 959 higher, respectively; the results of repeated tests are also more stable, as validated on the Sioux-Falls network. Numerical analysis validated the model's representation of mixed equilibrium, route choice rights, and traveler time valuation heterogeneity. Analysis results demonstrate that DDRS are significantly more effective than UDRS, improving platform revenue by 1.1 % more than UDRS in single-platform scenarios, and showing up to 7.29 % superior improvements in multi-platform games. Additionally, sensitivity analyses on the key parameters confirmed that our method can provide valuable support for demand management and platform decision-making in the MaaS era. [ABSTRACT FROM AUTHOR]

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