Multi-agent systems are designed to concurrently accomplish a diverse set of tasks at unprecedented scale. Here, the central problems faced by a system operator are to decide (i) how to divide available resources amongst the agents assigned to tasks and (ii) how to coordinate the behavior of the agents to optimize the efficiency of the resulting collective behavior. The focus of this paper is on problem (i), where we seek to characterize the impact of the division of resources on the best-case efficiency of the resulting collective behavior. Specifically, we focus on a team Colonel Blotto game where there are two sub-colonels competing against a common adversary in a two battlefield environment. Here, each sub-colonel is assigned a given resource budget and is required to allocate these resources independent of the other sub-colonel. However, their success is dependent on the allocation strategy of both sub-colonels. The central focus of this manuscript is on how to divide a common pool of resources among the two sub-colonels to optimize the resulting best-case efficiency guarantees. Intuitively, one would imagine that the more balanced the division of resources, the worse the performance, as such divisions restrict the sub-colonels' ability to employ joint randomized strategies that tend to be necessary for optimizing performance guarantees. However, the main result of this paper demonstrates that this intuition is actually incorrect. A more balanced division of resources can offer better performance guarantees than a more centralized division. Hence, this paper demonstrates that the resource division problem is highly non-trivial in such enmeshed environments and worthy of significant future research efforts.
翻译:多试剂系统旨在以前所未有的规模同时完成一系列不同的任务。这里,系统操作员面临的中心问题是决定(一) 如何在分配任务的人员之间分配可用资源,以及(二) 如何协调代理人的行为,以优化由此产生的集体行为的效率。本文的重点是问题(一) 我们力求确定资源分配对由此产生的集体行为最佳办案效率的影响。具体地说,我们侧重于一个团队布洛托上校的游戏,其中有两个子阵列在两个战场环境中与共同对手竞争。在这里,每个分行都分配了一个特定的资源预算,并需要分配这些资源独立于其他分行之外。然而,它们的成功取决于两个分行的分配战略。本稿的中心重点是如何在两个分行之间分配共同的资源,以优化由此产生的最佳效率保证。直觉地说,人们会想象,资源分工更加平衡,更糟糕的是业绩,因为这样的分行将限制其他分行。它们的成功取决于两个分行的分配战略。本分行如何将更稳定地展示这种稳定的业绩。 如此,这样,最不精确的分行将使得这个分行的分行能够更稳定地展示这种不偏的成绩。