Considering the sequential clearing of energy and reserves in Europe, enabling inter-area reserve exchange requires optimally allocating inter-area transmission capacities between these two markets. To achieve this, we provide a market-based allocation framework and derive payments with desirable properties. The proposed min-max least core selecting payments achieve individual rationality, budget balance, and approximate incentive compatibility and coalitional stability. The results extend the works on private discrete items to a network of continuous public choices. © 2021 The Author(s)