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This study considers the immense problem of sum rate maximisation in K-user multiple-input multiple-output interference channels (IFC). In order to address this problem, the authors propose an iterative Taylor approximation algorithm to find the optimal transmit covariance matrices, where each user maximises the sum rate function through Taylor expansion. Owing to the distributed nature of the ITA algorithm, Taylor terms can be treated as prices, where each user collects current prices from the others to perform update. This process further leads us modelling it as a more general concave n-person game to analyse the existence and uniqueness of the Nash equilibrium (NE). Then an iterative covariance-price updating (ICP) algorithm is proposed for flexible updating and establishing a convergence process to obtain the optimal solution under NE uniqueness conditions. Simulation results show that both algorithms come with similar performance and both significantly outperform the conventional iterative waterfilling algorithm.