The importance of randomization in resource assignment problems

In this paper, we consider problems involvinga central commander that must assign a pool of availableresources to two separate competitions. In each competition,a sub-colonel allocates its endowed resources from the assignmentagainst an opponent. We consider General Lottogames as the underlying model of competition. Here, we alsotake into account that the commander’s randomized resourceassignments cause the opponents to have uncertainty about thesub-commanders’ actual assigned endowments. We find thatrandomized assignments, which induce General Lotto gamesof incomplete and asymmetric information in the componentcompetitions, do not offer strategic advantages over deterministicones when the opponents have fixed resource endowments.However, this is not the case when the opponents have per-unitcosts to utilize resources. We find the optimal randomized assignmentstrategy can actually improve the commander’s payofftwo-fold when compared to optimal deterministic assignments