| Summary: | Correctly responding to the arrival of unexpected innovative events can help members of the franchise system rationally formulate their operational strategies and cooperative alliance modes to improve performance, while the exact time of product innovation realization is often unknown. Based on this, the strategic interactions in the business innovation system when foreseeing innovations are considered: the choice of operation strategies and cooperation modes. Using Bellman’s continuum dynamic programming theory to find the optimal strategies and system profits under the three modes of horizontal, non-cooperative and vertical cooperation within the system, the strategic interactions in the franchise system under different cooperation modes are analyzed. It is found that the prediction of innovation events will make the decision makers more active in increasing the input of current strategies, thus maximizing the initiative before the realization of innovations, and the R&D and innovation efforts of franchisors and the local service level of franchisors will increase with the increase of the innovation realization rate and the improvement rate, and the goodwill of franchisors will be improved as a result. Both horizontal and vertical cooperation models can effectively realize the Pareto improvement of the total profit of the franchise system. And the innovation realization rate and upliftment rate positively affect this improvement effect. It is worth noting that the vertical cooperation model is more effective in improving the total system profit and is better in the case of high realization rate-high uplift rate.
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