The Division of Assets in Multiagent Systems: A Case Study in Team Blotto Games

TL;DR

This paper investigates how dividing resources among agents in a multi-agent team affects their collective efficiency, revealing that more balanced resource divisions can surprisingly lead to better performance guarantees in adversarial settings.

Contribution

It characterizes the impact of resource division on efficiency in a team Colonel Blotto game, showing that balanced divisions can outperform centralized ones, challenging common intuitions.

Findings

More balanced resource divisions can improve efficiency guarantees.

Resource division impacts strategic performance in adversarial multi-agent settings.

The problem is highly non-trivial and warrants further research.

Abstract

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.