When live streamers sell products to consumers on live streaming platforms, their abilities and service efforts are private, and thus, the issues of identifying their true abilities, motivating them to use appropriate service efforts, and providing a mechanism to allocate profits remain to be resolved for live streaming platforms. Adopting a principal–agent model, we investigate the optimal contract design between a live streaming platform and live streamers. In addition, we study the impacts of the price and service competition between live streamers and the platform's corporate social responsibility on the optimal contract design. The results show that high commission rates and low signing bonuses are not always beneficial to platforms, and the optimal contract design to identify the types of live streamers can make it more profitable. In addition, the utility‐maximizing platform always sets lower commission rates and signing bonuses compared with the profit‐maximizing platform. Regardless of the platform's goal, total profits and commission rates are higher under competition compared with no competition. For the government, policies and subsidies should be provided, such as regulating commission rates by setting a limited range and increasing subsidies for the marginal costs of live streaming platforms, which can effectively motivate live streaming platforms to enhance corporate social responsibility.