A Differential Game Theory Approach to Improving Supply Chain Management in Small and Medium Enterprises

In this research, a mathematical model based on game theory, utilizing differential games, is presented with the aim of enhancing supply chain management in SMEs. This study is applied in terms of its objective and exploratory in terms of data collection methods. The necessary data were gathered through standardized questionnaires and interviews with ۵۰ SMEs and analyzed using descriptive statistics and Python software.The model's findings demonstrate the decisive superiority of the perfect subgame strategy across all key performance indicators. This strategy leads to higher levels of fixed capital in the long term and, while achieving greater profitability, also optimizes investment management. Both instantaneous profit and sustainable profit indicators are significantly higher in this strategy compared to the open-loop strategy. This superiority stems from the flexibility and adaptability of decisions to dynamic market conditions in the perfect subgame approach, which enables firms to provide optimal responses based on the current state of capital. Additionally, the model's sensitivity analysis shows that the advantage of the perfect subgame strategy remains stable against changes in discount rates and depreciation rates. Therefore, the model proves that feedback and state-dependent strategies, as manifested in perfect subgame equilibrium, not only increase short-term efficiency but also ensure long-term financial stability and sustainability for the supply chains of SMEs.In conclusion, SMEs can improve supply chain coordination, reduce operational risks, and create sustainable competitive advantages by intelligently selecting between the lower-cost open-loop strategy in stable environments and the more dynamic perfect subgame strategy in volatile conditions.

کلیدواژه ها:

Supply chain ، Small and Medium-Sized Enterprises ، Game Theory ، Differential Games ، Perfect Subgame ، Open Loop