Game theoretical analysis of incumbent platform investment and the supplier entry strategies in an e-supply chain

We investigate the interaction of platform investment strategy and a supplier entry strategy in an e-supply chain with a supplier and two e-commerce platforms. In addition to selling through the incumbent platform, the supplier may enter the entrant platform. The incumbent platform may prevent this by investing in the supplier to reduce production costs (indirect investment) or investing in its value-added service to enhance its own demand (direct investment). We analyze the incumbent platform's investment strategy with and without supplier entry to the entrant platform. Without entry, the incumbent platform prefers indirect investment only when the production cost is high and the indirect investment cost is low. With entry, however, the incumbent platform prefers indirect investment when the direct investment cost is high. We also explore the effect of the incumbent platform's investment strategy on the supplier's entry strategy. Counterintuitively, we find that direct investment by the incumbent platform increases the supplier's incentive to enter the entrant platform. Under certain conditions, the incumbent platform can effectively prevent this entrance through an indirect investment strategy. Even if the supplier enters the entrant platform, it is optimal for the incumbent platform to maintain investment. Furthermore, we further extend that the two platforms have the same commission rate to the case where the two platforms have different commission rates and show that the main results still hold. We have also expanded the situation where both platforms have investments. Interestingly, we find that when the production cost is high, the supplier's entry into the entrant platform and the entrant platform's indirect investment may benefit the incumbent platform.