Optimal control of quality investment in joint venture by Stackelberg game

In projects carried out as joint venture (JV), two or more legally independent firms form a strategic alliance to do a project cooperatively and to obtain the necessary credits asked by a contractor. Due to the wide scope of a joint venture project, partners are sometimes from different areas industrial fields or even different countries which might have different quality standards. Such differences in the quality standard result in the problem of quality difficulties which entails sufficient planning to avoid or decrease it. In this paper, a cost sharing coordination mechanism based on a two person Stackelberg game is proposed in which, the more qualified partner that acts as the leader invests in the quality promotion of the other partner who acts as the follower and the costs of investment are shared between the partners according to a contract. Based on the dynamic nature of the quality level and the investment programs, the problem is modeled as an optimal control problem for which the necessary and sufficient conditionsof the optimal solution arediscussed. Also, based on the Hamilton function of the optimal control problem, some alternatives for the path of investment are considered. Then the path which results in the best gain for the partners according to the leader-follower game is chosen as the solution of the problem.The results show that the optimal path of investment is parameter dependent so the sensitivity analysis is done to show how changes in the parameters affect the best path of investment.