As first noted by Borch (1960), it seems natural to consider allocations of premium among reciprocal reinsurers as a problem in cooperative game theory. In the present paper, we address this problem by defining and studying the characteristic function associated with the reinsurers’ payoffs from concluding a reciprocal treaty. First, we use the characteristic function to describe the core and bargaining set previously identified by Baton and Lemaire (1981a, 1981b). Given that the core and bargaining set may consist of more than one point, it is necessary to develop a framework for selecting a unique premium allocation. However, this effort is greatly complicated by the large number of potentially desirable mathematical properties associated with various premium-allocation methods. To address this difficulty, we consider two specific contexts for reciprocal reinsurance – within-corporate-group and between-corporate-group transactions – and provide a detailed analysis of the mathematical properties most desirable for each context. Using these properties, we are able to compare competing allocation methods to determine which is the most suitable. Our analysis shows that the Shapley value provides the most attractive allocation method for the within-group problems, whereas the nucleolus provides the most compelling outcome for the between-group case.