In a recent paper Kinber, Smith, Velauthapillai, and Wiehagen introduced a new notion of``parallel learning.'' They call a set S of functions (m, n)-learnable if there is a learning machine which for any n-tuple of pairwise distinct functions from S learns at least m functions correctly from examples of their behavior after seeing some finite amount of input. One of the basic open questions in this area is the``inclusion problem,'' i.e., the question for which m, n, h, k, every (m, n)-learnable class is also (h, k)-learnable. In this paper we develop a general approach to solve this problem. The idea is to associate with each m, n, h, k in a uniform way a finite 2-player game such that the first player has a winning strategy in this game iff every (m, n)-learnable class is (h, k)-learnable. In this way we take the recursion theoretic disguise off the problem and isolate its combinatorial core. We also explicitly characterize the``strength'' of each particular noninclusion by the complexity of an oracle which is needed to overcome it. It turns out that there are exactly three different types of noninclusions. ] 1996 Academic Press, Inc.