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The General Lotto game is a popular variant of the famous Colonel Blottogame, in which two opposing players allocate limited resources over manybattlefields. In this paper, we consider incomplete and asymmetric informationformulations regarding the resource budgets of the players. In particular, oneof the player's resource budget is common knowledge while the other player's isprivate. We provide complete equilibrium characterizations in the scenariowhere the private resource budget is drawn from an arbitrary Bernoullidistribution. We then show that these characterizations can be used to analyzea multi-stage resource assignment problem where a commander must decide how toassign resources to sub-colonels that compete against opponents in separateGeneral Lotto games. While optimal deterministic assignments have beencharacterized in the literature, we broaden the context by deriving optimal(Bernoulli) randomized assignments, which induce asymmetric information GeneralLotto games to be played. We demonstrate that randomizing can offer a four-foldimprovement in the commander's performance over deterministic assignments.

A General Lotto game with asymmetric budget uncertainty