The Sumo Coach Problem

We address the problem of optimal allocation of non-divisible resource bundles to a set of interconnected contests. For this purpose, we study a modification of the Colonel Blotto Game called the Tennis Coach Problem. We devise a thoroughly probabilistic method of payoff representation and fully characterize equilibria in the arising games. We further formalize the idea of strategic team training in a comparative static setting. The problem applies to several distinct economic interactions but seems to be most prevalent in team sports with individual matches as, for instance, in Tennis and Sumo