We consider a class of incomplete-information Colonel Blotto games in which N ≥ 2 agents are engaged in (N + 1) battlefields. An agent's vector of battlefield valuations is drawn from a generalized sphere in Lp-space. We identify a Bayes-Nash equilibrium in which any agent's resource allocation to a given battlefield is strictly monotone in the agent's valuation of that battlefield. In contrast to the single-unit case, however, agents never enjoy any information rent. We also outline an extension to networks of Blotto games.