Incomplete and Asymmetric Information in General Lotto Games

In this article, we consider incomplete and asymmetric information formulations of the General Lotto game, which describes two opposing players that strategically allocate limited resources over multiple contests. In particular, we consider scenarios where one of the player's resource budget is common knowledge while the other player's is private. Our main contribution provides complete equilibrium characterizations in the scenario where the private resource budget is drawn from a Bernoulli distribution. We then leverage these characterizations to analyze a resource assignment problem where a commander must decide how to assign resources to subcolonels that compete against opponents in separate General Lotto games. While optimal deterministic policies have previously been characterized in the literature, we broaden the context by deriving optimal randomized policies, which induce asymmetric information General Lotto games. Leveraging our equilibrium characterizations, we demonstrate that randomization can offer a fourfold improvement in the commander's performance over the optimal deterministic assignments.