广义纳什均衡问题中作为反馈设计的个性化激励
Personalized incentives as feedback design in generalized Nash equilibrium problems
AI总结：
针对势函数未知的稳态与时变非单调广义纳什均衡问题，提出两层半去中心化算法，由协调器学习伪梯度并设计个性化激励，实现均衡或可调误差近似。
摘要：
我们研究了智能体之间表现出对称交互的稳态和时变非单调广义纳什均衡问题，这类问题已知是势博弈。然而，正如实际情况中可能发生的那样，我们设想了一种无法获得底层势函数形式表达的场景，并设计了一种半去中心化的纳什均衡求解算法。在所提出的两层方案中，协调器迭代地整合智能体的反馈（可能是含噪且零星的）以学习智能体的伪梯度，随后为其设计个性化激励。在智能体一侧，它们接收这些个性化激励，计算扩展博弈的解，然后将反馈测量结果返回给协调器。在稳态情形下，如果协调器配备标准学习策略，我们的算法会返回纳什均衡；而在时变情形下，它返回的纳什均衡存在一个恒定但可调的误差。作为一个启发性应用，我们考虑了多家公司在出行即服务编排下提供的网约车服务，这对于处理企业间竞争和避免交通拥堵都是必要的，我们也采用该应用开展数值实验以验证我们的结果。
英文摘要：
We investigate both stationary and time-varying, nonmonotone generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision a scenario in which the formal expression of the underlying potential function is not available, and we design a semi-decentralized Nash equilibrium seeking algorithm. In the proposed two-layer scheme, a coordinator iteratively integrates the (possibly noisy and sporadic) agents' feedback to learn the pseudo-gradients of the agents, and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measurements to the coordinator. In the stationary setting, our algorithm returns a Nash equilibrium in case the coordinator is endowed with standard learning policies, while it returns a Nash equilibrium up to a constant, yet adjustable, error in the time-varying case. As a motivating application, we consider the ridehailing service provided by several companies with mobility as a service orchestration, necessary to both handle competition among firms and avoid traffic congestion, which is also adopted to run numerical experiments verifying our results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
