We analyze the impact of the retailer's overconfidence on the supply chain performance. We consider a duopolistic market with uncertain demand where one overconfident retailer and one rational retailer compete in selling the same product. We identify two cases in terms of the rational retailer's overconfidence awareness: (1) the rational retailer is aware of the other retailer's overconfidence; (2) the rational retailer is not aware of the other retailer's overconfidence. We first analyze the two retailers’ decision processes in a Nash game and derive their optimal decisions, and further discuss a Stackelberg-like game for an extension. We conduct a numerical analysis to examine the impact of overconfidence on the optimal pricing, ordering decisions and expected profits. We find that the higher the overconfident level is, the higher selling price that the overconfident retailer charges. Together, the results stress that the overconfidence does not necessarily damage the supply chain performance.