The concept of cognitive radio has recently received great attention from the researcherspsila community as a promising paradigm to achieve efficient use of the frequency resource by allowing the co-existence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper we propose and analyze a totally decentralized approach, based on game theory, to design cognitive MIMO transceivers. We consider underlay/interweave networks, where primary users establish proper null and/or soft shaping constraints on the transmit covariance matrix of secondary users, so that the interference generated by secondary users be confined within the interference-temperature limits. We formulate the resource allocation problem among secondary users as a strategic noncooperative game, where each transmit/receive pair competes against the others to maximize the information rate over its own MIMO channel, under transmit power and/or null/soft shaping constraints. We first characterize the Nash equilibria of the proposed game, showing that they can be equivalently rewritten as the solutions of a MIMO waterfilling nonlinear fixed-point equation. Based on this result, we then design low-complex asynchronous distributed algorithms that converge to the Nash equilibria of the games.