Abstract: Against the backdrop of increasing urban traffic congestion and mounting environmental pressure, improving travel efficiency and optimizing resource allocation have become critical issues that urban transportation systems urgently need to address. As an emerging mobility mode, car-sharing demonstrates potential advantages in enhancing vehicle utilization and alleviating resource constraints. However, during the early stage of development, car-sharing systems typically face challenges such as insufficient supply, low user adoption rates,and unstable policy incentives. The evolution of these systems is influenced not only by market supply and demand dynamics but also by the interactions among multiple agents, including the government, operators,and travelers. The strategic decisions of these agents are interdependent and generate dynamic feedback through payoff structures, rendering the system evolution complex and path-dependent.
To systematically investigate the mechanisms through which multi-agent behavior influences the evolution of car-sharing systems, this study develops a tripartite evolutionary game model involving the government, car-sharing operators,and travelers under the framework of bounded rationality. In the model, the government, as the regulatory authority, chooses between regulation and non-regulation by comprehensively considering factors such as regulatory costs, subsidy expenditures,and environmental benefits. Operators, as service providers, decide between large-scale operations and small-scale operations, balancing the trade-off between service network coverage and operational cost inputs. Their strategic choices directly determine the service capacity and market competitiveness of the car-sharing system. Travelers, as demand-side participants, determine whether to switch from private car usage to car-sharing based on the relative travel utility between the two mobility modes, with their behavioral choices serving as a key variable on the demand side of the system. Based on these settings, this study constructs a tripartite payoff matrix, specifying the payoff expressions for each agent under different strategy combinations. The proportions of agents adopting different strategies are introduced as state variables, and replicator dynamic equations are derived to characterize the evolution of strategy proportions over time.
To further reveal the underlying mechanisms of system evolution, this study applies evolutionary stability theory to solve the equilibrium points of the system. On this basis, the Jacobian matrix is constructed to systematically analyze the stability conditions of each equilibrium point, determining whether they qualify as evolutionary stable strategies based on the signs of the eigenvalues. This process identifies possible evolutionary stable states under various parameter configurations. To examine the impact of key parameters on evolutionary trajectories, numerical simulations are conducted, focusing on core variables such as subsidy levels, cost-related parameters,and travel utility differences. By setting different parameter values, the convergence paths and stable states under various parameter combinations are systematically compared, visually presenting the dynamic adjustment process of agent strategies over time.
The findings reveal that under different parameter conditions, the system can converge to multiple evolutionary stable states, reflecting the interactive nature and dynamic feedback mechanisms among the strategies of the government, operators,and travelers. Notably, when the government adopts a regulatory strategy, operators expand their service scale, and travelers shift their travel mode, the system can reach a relatively ideal stable equilibrium. In this state, a virtuous interaction is formed among policy support, service supply,and user demand, with the strategies of the three parties aligning to collectively drive the system toward efficient operation. Under other parameter configurations, the system may converge to alternative equilibria, such as scenarios where the government refrains from regulation, operators control costs without expansion, or travelers do not shift from private cars. These outcomes correspond to varying behavioral patterns and system operation states, reflecting systemic challenges arising from insufficient policy incentives or immature market development.
From the perspective of parameter effects, subsidy levels influence both the government’s payoff structure and operators’ decision-making, thereby shaping the evolutionary trajectory of the system. When subsidy levels are maintained within a reasonable range, operators are more inclined to expand service scale to capture policy support, and the government’s net benefit from adopting a regulatory strategy remains positive, enhancing the stability of this strategy. However, when subsidy levels become excessively high, the government’s net benefits decline due to increased subsidy expenditures, weakening the stability of the regulatory strategy and potentially leading to a shift toward non-regulation. Travel utility differences directly affect travelers’ strategic choices: when the relative utility of car-sharing compared to private cars increases, travelers will be more likely to shift toward car-sharing. This change in traveler behavior further influences the strategies of operators and the government through the payoff structure: a higher proportion of travelers shifting to car-sharing expands market demand, incentivizing operators to expand service scale while also strengthening the government’s motivation to implement regulatory policies, thereby affecting the overall evolutionary direction of the system.
Based on the above analysis, this study suggests that in the process of policy formulation, subsidy levels should be reasonably determined under fiscal constraints to avoid excessive pressure on government revenues while ensuring that subsidies effectively incentivize operators to expand service scale. Furthermore, efforts should be made to improve the travel utility of car-sharing relative to private cars by enhancing service quality, optimizing pricing strategies and improving supporting infrastructure, thereby effectively guiding travelers toward mode shifts and further influencing the strategic choices of the government and operators, so as to form a positive feedback mechanism. This study provides a systematic analytical framework for understanding multi-agent interactions in car-sharing systems and offers theoretical foundations and practical references for policy design and system optimization.

Key words: car-sharing, three-side game, regulation policy, evolutionary game

摘要： 针对共享汽车发展初期供给不足、用户转化率偏低及政策激励效果不稳定等问题,本文从多主体互动视角出发,构建政府、共享汽车运营商与出行者三方演化博弈模型,刻画有限理性条件下各主体策略的动态调整过程。在建立收益函数与复制动态方程的基础上,结合数值仿真分析关键参数对系统演化路径及稳定结果的影响。研究表明,三方策略之间存在显著联动关系,系统在不同参数条件下可收敛至不同稳定状态,其中政府实施规制、运营商扩大规模、出行者选择转移为理想的稳定均衡状态。研究结果发现,补贴水平对系统演化具有显著调节作用,适度补贴有助于强化政府规制激励并促进运营扩张,但补贴过高会削弱政府收益。出行效用差异是驱动用户选择与系统演化的关键因素,提升共享汽车出行效用能够有效促进需求转移,并推动系统向良性均衡状态演化。

关键词: 共享汽车, 三方博弈, 政策规制, 演化博弈