We leverage a new algorithm for numerically solving Colonel Blotto games to gain insight into a version of the game where players have different types of resources. Specifically, the winner of a battlefield is a function of a multi-dimensional allocation vector of each player. Our main focus is on the potential benefits of fractionation, which we define as the degree to which a player can quantize its resources. When players only have one type of resource, we show that the benefits to fractionation are in general, greatest in resource poor environments and against aggregated adversaries. We then extend the model to include random dropout and show that fractionation increases robustness to failure in resource poor environments but not resource rich environments. Finally, we show that when players have different types of resources, the benefits of fractionation are no longer mitigated by an increase in the total force size. Since many real-world resource allocation problems are multi-dimensional, our results illustrate the importance of analyzing multi-resource Blotto games in tandem with the traditional specification.

我们利用一种新算法来对上校式Blotto游戏进行数值求解，以深入了解玩家拥有不同类型资源的游戏版本。具体而言，战场的获胜者是每个玩家的多维分配向量的函数。我们的主要重点是分馏的潜在利益，我们将其定义为玩家可以量化其资源的程度。当参与者只有一种类型的资源时，我们证明了分拆带来的好处通常是最大的，这在资源贫乏的环境中以及对抗聚集的对手时是最大的。然后，我们将模型扩展为包括随机丢弃，并表明在资源贫乏的环境中（而非资源贫乏的）环境中，分馏提高了对故障的鲁棒性。最后，我们证明了当玩家拥有不同类型的资源时，总力大小的增加不再消除分馏的好处。由于许多现实世界中的资源分配问题是多维的，因此我们的结果说明了与传统规范一道分析多资源Blotto游戏的重要性。