Optimal allocation of profit across companies operating with a joint salesforce

We investigate the problem of companies that want to cooperate either by combining their salesforces or by operating a joint salesforce. Companies may have salesforce of different sizes that also differ in their effectiveness. They need an instrument to evaluate how much they gain from a cooperation, and a mechanism to allocate the profit in a fair way. In the typical case of a lack of response data we suggest to infer additional sales based on response functions for which the Dorfman–Steiner theorem is holding in the optimum. Searching for an appropriate allocation mechanism becomes diffcult because typical cooperative solutions where each company pays its own salesforce but benefits from increased sales, or where commission rates on sales are paid to a joint subsidiary, may lead to asymmetric distributions of profit contibution across companies. We suggest that companies follow the Nash-solution for cooperative games, which recommends that each company receive in advance the profit it would achieve in the case of non-cooperation, and that the remaining profit be shared equally.