We consider General Lotto games of asymmetric information where one player's resource endowment is randomly assigned one of two possible values, and the assignment is not revealed to the opponent. We completely characterize the Bayes-Nash equilibria for two such formulations -- namely, one in which the opponent's endowment is fixed and common knowledge, and another where the opponent has a per-unit cost to utilize resources. We then highlight the impact these characterizations have on resource allocation problems involving a central commander that decides how to assign available resources to two sub-colonels competing in separate Lotto games against respective opponents. We find that randomized assignments, which induce the Bayesian game interactions, 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, and four-fold in settings where the commander also pays a per-unit cost for resources.

中文翻译：

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具有不对称预算不确定性的通用乐透游戏

我们考虑不对称信息的 General Lotto 游戏，其中一个玩家的资源禀赋被随机分配两个可能值之一，并且分配不会透露给对手。我们完全描述了两种这样的公式的贝叶斯-纳什均衡——即，一种是对手的禀赋是固定的和常识，另一种是对手有单位成本来利用资源。然后，我们强调这些特征对资源分配问题的影响，涉及中央指挥官决定如何将可用资源分配给在不同乐透游戏中与各自对手竞争的两个副上校。我们发现引起贝叶斯博弈交互的随机分配，当对手拥有固定的资源禀赋时，不提供优于确定性优势的战略优势。但是，当对手具有利用资源的单位成本时，情况并非如此。我们发现，与最佳确定性分配相比，最佳随机分配策略实际上可以将指挥官的回报提高两倍，在指挥官还为资源支付单位成本的情况下，可以提高四倍。