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Power allocation in distributed multiple-input multiple-output radar is investigated for range-only target localisation such that the determinant of Bayesian Fisher information matrix (B-FIM) is maximised. The B-FIM is derived from a signal model that incorporates the propagation path loss, the target reflectivity, the transmitted power and target prior information. The authors model the problem as a cooperative game and exploit the solution concept of Shapley value to distribute a given power budget among all transmitting radars for localisation and integrate the algorithm with a sequential Bayesian estimator to localise target. In numerical simulations, it is shown that uniform power allocation is not in general optimal. They illustrate the impact of the radar antenna geometry and target location prior density on the allocation results and demonstrate the superior performance of the proposed optimal power allocation scheme via Monte Carlo simulations. [ABSTRACT FROM AUTHOR]