The main purpose of this paper is to analyze a development of a scenario suggested by Baston and Garnaev (2005) for modelling the situation where two departments in a large organization are each seeking to make an appointment within the same area of expertise, for instance, a computer science specialist. The departments are interested in three skills of the candidate (say, writing code, communication and in algorithms). In our scenario Department 1 wants to employ a candidate with excellent skills in writing code and communication. Department 2 is looking for a candidate with excellent skills in developing algorithms and communication. So, the departments have a joint interest, as well as their own interest. The scenario is modelled by a multistage non-zero sum game. Nash equilibrium and Stackelberg strategies are derived.