We propose a decentralized game-theoretic framework for dynamic task allocation problems for multi-agent systems. In our problem formulation, the agents' utilities depend on both the rewards and the costs associated with the successful completion of the tasks assigned to them. The rewards reflect how likely is for the agents to accomplish their assigned tasks whereas the costs reflect the effort needed to complete these tasks (this effort is determined by the solution of corresponding optimal control problems). The task allocation problem considered herein corresponds to a dynamic game whose solution depends on the states of the agents in contrast with classic static (or single-act) game formulations. We propose a greedy solution approach in which the agents negotiate with each other to find a mutually agreeable (or individually rational) task assignment profile based on evaluations of the task utilities that reflect their current states. We illustrate the main ideas of this work by means of extensive numerical simulations.

中文翻译：

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多代理系统动态任务分配问题的分散博弈论控制

我们为多代理系统的动态任务分配问题提出了一个分散的博弈论框架。在我们的问题表述中，代理的效用取决于与成功完成分配给他们的任务相关的回报和成本。奖励反映了代理完成分配任务的可能性，而成本反映了完成这些任务所需的努力（这种努力由相应的最优控制问题的解决方案决定）。此处考虑的任务分配问题对应于动态游戏，与经典的静态（或单动作）游戏公式相比，其解决方案取决于代理的状态。我们提出了一种贪婪的解决方案，其中代理相互协商，根据对反映其当前状态的任务效用的评估，找到一个双方都同意的（或个人合理的）任务分配配置文件。我们通过广泛的数值模拟来说明这项工作的主要思想。