The importance of randomization in resource assignment problems

In this paper, we consider problems involving a central commander that must assign a pool of available resources to two separate competitions. In each competition, a sub-colonel allocates its endowed resources from the assignment against an opponent. We consider General Lotto games as the underlying model of competition. Here, we also take into account that the commander’s randomized resource assignments cause the opponents to have uncertainty about the sub-commanders’ actual assigned endowments. We find that randomized assignments, which induce General Lotto games of incomplete and asymmetric information in the component competitions, do not offer strategic advantages over deterministic ones when the opponents have fixed resource endowments. However, this is not the case when the opponents have per-unit costs to utilize resources. We find the optimal randomized assignment strategy can actually improve the commander’s payoff two-fold when compared to optimal deterministic assignments.