This paper considers downlink spectrum allocation in a long term evolution (LTE) system macrocell which contains multiple femtocells. By incorporating cognitive capabilities into femtocell base stations, the Home evolved Node Bs (HeNBs) can be formulated as secondary base stations seeking to maximize the spectrum utility while minimizing interference to primary base stations (evolved Node-Bs). The competition amongst cognitive HeNBs for spectrum resources is formulated as a non-cooperative game-theoretic learning problem where each agent (HeNB) seeks to adapt its strategy in real time. We formulate the resource block (RB) allocation among HeNBs in the downlink of a LTE system using a game-theoretic framework, where the correlated equilibrium solutions of the formulated game are being investigated. A distributed RB access algorithm is proposed to compute the correlated equilibrium RB allocation policy..