具有随机动态稳定性的机制设计系统方法
A Systematic Approach to Mechanism Design with Stochastic Dynamic Stability
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中文总结 AI 辅助
针对带策略智能体的资源分配问题，提出带LMI支付函数的激励机制及VS-PBR算法，在苏福尔斯交通网络验证其效率，可实现社会福利最大化且具动态稳定性。
中文摘要 AI 辅助
我们考虑具有策略智能体的资源分配问题，这些智能体拥有私人随机满意度函数和局部约束。为实现全局最优解，我们提出一种激励机制，该机制会在智能体之间诱导出一个博弈。对于该机制的支付函数，我们采用线性矩阵不等式（LMI）方法构造了一族二次函数，该函数在诱导博弈的唯一纳什均衡（NE）上实现社会福利最大化结果，同时确保预算平衡和个体理性。此外，我们提出了一种带Krasnoselskij迭代的去中心化可变样本量近端最佳响应（VS-PBR）算法，其中智能体仅可获得聚合信息。该算法具有动态稳定性，因为已证明其在均方意义下收敛到博弈的纳什均衡。随后，我们在苏福尔斯市交通网络上研究了该机制的效率，其中电动汽车（EV）用户共同选择目的地和路线。
英文摘要
We consider a resource allocation problem with strategic agents that have private stochastic satisfaction functions and local constraints. To achieve a global optimal solution, we propose an incentive mechanism that induces a game among the agents. For the payment function of the mechanism, we construct a family of quadratic functions using the linear matrix inequality (LMI) approach that implements the social welfare maximizing outcome on the unique Nash equilibrium (NE) of the induced game while ensuring budget balance and individual rationality. Moreover, we propose a decentralized variable sample-size proximal best-response (VS-PBR) algorithm with Krasnoselskij iteration where only aggregate information is available to the agents. The algorithm is dynamically stable, as it is proven to converge in the mean-square sense to the NE of the game. The efficiency of the mechanism is then investigated on the Sioux Falls City transportation network, where electric vehicle (EV) users jointly select their destination and route.
