This paper considers two competing supply chains that face cost uncertainty, each consisting of one supplier and one retailer. To address the uncertain cost information, we propose a decision rule based on confidence levels to measure the goals of the supply chain participants. We provide the new concept of the belief-degree cost of a supply chain that embodies the decision maker's ability to comprehensively address information uncertainty and control the risk caused by information uncertainty. We find that regardless of which of the three games it is in-integrated, hybrid, or decentralized-a chain should order more and thereby gain more profit when its cost uncertainty increases or the competing chain's cost uncertainty decreases. The chain with a low or sufficiently low belief-degree cost gains a competitive advantage on both quantity and profit. A chain's competitiveness can be enhanced by either decreasing its confidence level or increasing its rival's confidence level. Furthermore, we demonstrate that supply chain integration is the dominant strategy for given confidence levels. Nevertheless, a prisoner's dilemma occurs when the differences in the belief-degree costs of the two supply chains are not significant and the competitive intensity is high. In addition, the magnitudes of the confidence levels can be changed to avoid or cause a prisoner's dilemma. Finally, under different confidence levels, the Stackelberg model for competing hybrid or decentralized supply chains is extended to the bargaining model, and the impact of bargaining power on supply chain competition is analyzed.