The rapid development of wind power has led to an increased demand for spinning reserve in power systems today. However, one of the most severe challenges to China's power systems is the mismatch between wind power installation capacity and the capability for supplying spinning reserve within each independently operated provincial power system. Coordinating the spinning reserve across multiple areas would providentially improve the accommodation of wind power. This paper proposes a game-theoretical model for spinning reserve trading between provincial systems that treat spinning reserve as a commodity. Based on the incomplete information, the trading price is calculated by satisfying the Bayesian Nash equilibrium, and then the trading quantity is determined. This ensures that both the buyer and the seller are able to maximize their expected profit. Case studies are performed using a 2-bus interconnected system and a 3-area IEEE RTS system. The results show that the proposed model is valid and effective.