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

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 resulting collective behavior in a best-case sense. We focus on a 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 resource budget and is required to independently allocate its assigned resources. However, the team’s success depends on the adversary’s response to the allocations 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. The main result of this paper establishes that performance is not monotonic in the division of resources to the sub-colonels. In particular, a more equitable division can offer better performance than a more centralized division. Hence, this paper demonstrates that the resource division problem is highly non-trivial and worthy of significant future research efforts.