发表机构
Elmore Family School of Electrical and Computer Engineering, Purdue University; Michigan State University（普渡大学埃尔莫电气与计算机工程学院; 密歇根州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对时间与协调成本受限的系统中奖励率最大化问题，提出奖励率拥塞博弈，通过Dinkelbach变换转化为势博弈，并设计复制者--Dinkelbach动力学实现社会奖励率优化，在连续任务分配中验证了收敛性。
AI 中文摘要
奖励率是信息物理系统和机器人系统中的关键性能指标，在这些系统中，时间、工作负载和协调成本是限制性资源。我们引入了奖励率拥塞博弈，其中智能体旨在最大化每单位执行时间的奖励。直接的奖励率博弈通常不是一个精确势博弈。我们开发了一个基于Dinkelbach的框架，在该框架中，对于每个固定的Dinkelbach参数，变换后的博弈是一个精确势博弈。这产生了一个势级Dinkelbach迭代，当内部势最大化问题被全局求解时，该迭代在最优势奖励率处有限终止。我们还提供了一个充分条件，在该条件下，变换后博弈的均衡是原始奖励率博弈的均衡。为了优化总体性能，我们引入了边际外部性修正，使修正后的势与Dinkelbach变换的社会奖励率目标一致，从而能够优化社会奖励率。最后，我们为奖励率群体博弈开发了连续时间的复制者--Dinkelbach动力学，将快速复制者动力学与缓慢的奖励率更新耦合。我们建立了固定参数复制者动力学的收敛性、简化Dinkelbach动力学的全局渐近和局部指数稳定性，以及对于足够慢的Dinkelbach更新的耦合系统的局部指数稳定性。该框架在一个连续任务分配问题上得到了说明。
英文摘要
Reward rate is a key performance criterion in cyber-physical and robotic systems where time, workload, and coordination costs are limiting resources. We introduce reward-rate congestion games, where agents seek to maximize reward per unit execution time. The direct reward-rate game is generally not an exact potential game. We develop a Dinkelbach-based framework in which, for every fixed Dinkelbach parameter, the transformed game is an exact potential game. This yields a potential-level Dinkelbach iteration that terminates finitely at the optimal potential reward rate when the inner potential maximization problem is solved globally. We also provide a sufficient condition under which an equilibrium of the transformed game is an equilibrium of the original reward-rate game. To optimize aggregate performance, we introduce marginal externality corrections that make the corrected potential coincide with the Dinkelbach-transformed social reward-rate objective, thereby enabling optimization of the social reward rate. Finally, we develop a continuous-time replicator--Dinkelbach dynamics for reward-rate population games coupling fast replicator dynamics with a slow reward-rate update. We establish convergence of the fixed-parameter replicator dynamics, global asymptotic and local exponential stability of the reduced Dinkelbach dynamics, and local exponential stability of the coupled system for sufficiently slow Dinkelbach updates. The framework is illustrated on a continuous task-allocation problem.
