We are interested in addressing a fundamental question: what are conditions under which an ad hoc cognitive radio MIMO (CMIMO) network can support a given rate-demand profile, defined as the set of rates requested by individual links? From an information theoretic view, a rate profile can be supported if it is within the network capacity region. However, the network capacity region of interfering MIMO networks is essentially unknown. In dynamic spectrum access, the problem is even more challenging due to the dynamics of primary/legacy users (PUs), resource constraints, and the heterogeneity of opportunistic spectrum (i.e., the set of available channels varies from one to another). Considering a non-centralized setup, we address the above question in a noncooperative game framework where each CMIMO link independently optimizes its spectrum, power allocation, and MIMO precoders to meet its rate demand. We derive sufficient conditions for the existence of a NE are derived. These conditions establish an explicit relationship between the rate-demand profile and interference from PUs, CMIMO network's interference, and CMIMO nodes' power budget. We also show that a NE, if exists, is unique. Our results help to characterize the network capacity region of CMIMO networks.