Keep them guessing: The value of randomized resource assignments in General Lotto games

In this paper, we consider a class of problems where a commander must decide how to assign costly resources to independent sub-colonels. Each sub-colonel engages in competition against an opponent, where it is tasked with allocating its assigned resources towards multiple battlefields. The commander's performance is measured by the cumulative rewards attained by the sub-colonels. Here, we consider General Lotto games, a popular variant of the well-known Colonel Blotto game, as the underlying model of competition. While optimal deterministic assignments have been characterized in this context, we completely characterize optimal randomized assignments. Randomizing induces informational asymmetries in each competition, where the opponents become uncertain about the sub-colonels' actual assigned endowments. We find that randomized assignments can give up to a four-fold performance improvement over deterministic ones, when there are costs associated with utilizing resources. When there are no associated costs, randomization does not offer any performance improvements. In order to characterize the optimal randomized assignments, we provide a complete and novel equilibrium analysis of the underlying incomplete and asymmetric information General Lotto games induced from randomized assignments.