In the context of the platform economy, considering a third-party logistics (3PL) company providing logistics services, a three-stage game-theoretic model is constructed to examine the financing strategies of competing retailers, incorporating an e-commerce platform, a third-party logistics (3PL) provider, and two capital-constrained retailers. Based on retailers’ financing decisions, we analyze four modes: both retailers choose platform financing (PP), retailer 1 chooses platform financing while retailer 2 chooses 3PL financing (PL), retailer 1 chooses 3PL financing while retailer 2 chooses platform financing (LP), and both retailers choose 3PL financing (LL). By comparing the equilibrium strategies of capital-constrained retailers under these four financing modes, the following conclusions are drawn: (1) When considering logistics service effort, the 3PL firm is more willing to provide financing than the platform. (2) When the procurement cost is low, financing competition between the platform and the 3PL leads to lower interest rates, with PL/LP modes resulting in lower rates. (3) The equilibrium strategy of the retailers is influenced by the procurement cost and the commission rate, and when the PP mode is an equilibrium, the two retailers may fall into a Prisoner’s Dilemma. (4) When the procurement cost is high and the commission rate is low, the LL mode can achieve mutual benefits for the platform, 3PL, and retailers.