The competition model has developed from between enterprises to between supply chains, more and more companies lay emphesis on supply chain coodination. Besides, the development of information technology make coordination and management within supply chain possible. The paper consider information sharing in two competing supply chains, each consisting of one manufactruer and one retailer. Since the way of wholesale pricing could affect the result, we take linear wholesale price to conduct the investigation. It is concluded that the higher the possibility of market demand is high, the more likely retailers do not share information. When given the market demand is high, one supply chain do not share information, the optimal strategy the other supply chainis to share demand information.