Self-interested behavior in sharing economies often leads to inefficient aggregate outcomes compared to a centrally coordinated allocation, ultimately harming users. Yet, centralized coordination removes individual decision power. This issue can be addressed by designing rules that align individual preferences with system-level objectives. Unfortunately, rules based on conventional monetary mechanisms introduce unfairness by discriminating among users based on their wealth. To solve this problem, in this paper, we propose a token-based mechanism for congestion games that achieves efficient and fair dynamic resource allocation. Specifically, we model the token economy as a continuous-time dynamic game with finitely many boundedly rational agents, explicitly capturing their evolutionary policy-revision dynamics. We derive a mean-field approximation of the finite-population game and establish strong approximation guarantees between the mean-field and the finite-population games. This approximation enables the design of integer tolls in closed form that provably steer the aggregate dynamics toward an optimal efficient and fair allocation from any initial condition.

翻译：在共享经济中，自利行为往往导致相比集中协调分配更低的整体效率，最终损害用户利益。然而集中协调会剥夺个体的决策权。通过设计能协调个体偏好与系统目标的规则可解决此问题。但基于传统货币机制的规则会因用户财富差异产生歧视性不公平。为解决该问题，本文提出一种面向拥塞博弈的令牌机制，实现高效公平的动态资源分配。具体而言，我们将令牌经济建模为具有有限数量有限理性智能体的连续时间动态博弈，明确刻画其演化策略修正动力学。我们推导了有限群体博弈的均场近似，并建立了均场与有限群体博弈间的强近似保证。该近似使得我们能以闭式形式设计整数通行费，从任意初始状态出发均可可靠地将聚合动力学引导至最优高效公平分配。