This paper deals with price--cap regulation of a monopolistic distribution grid which sells a license to some retailer. The sale of the license is a long--term incomplete contract. Both the grid and the licensee engage in relationship--specific investments before the value and costs of the license are known. The resulting hold--up problem can be solved by the regulator by choosing a particular RPI - X regulation and forbidding renegotiation of the contract. The optimal price--cap regulation of the incomplete contract looks quite different from the usual RPI - X case which stipulates a functional relationship between a particular cost or productivity realization and a regulatory instrument X, without any dependence on further exogenous variables. In this paper, however, the Xs depend on many more exogenous variables, be it further realizations of costs and values, be it optimal probabilities of these realizations. If the regulator is only interested in efficient trade and efficient relationship--specific investments, moreover, the no--trade price, as chosen by grid and licensee, directly determines the values of the Xs.
