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We develop a price competition model for a new supply chain that competes in a market comprised of some rival supply chains. The new supply chain has one risk-neutral manufacturer and one risk-averse retailer in which the manufacturer is a leader and retailer is a follower. The manufacturer pays a fraction of the risk cost (caused by demand uncertainty) to the retailer. We apply this competitive model to a real-world case in a supply chain under uncertain environment and obtain the optimal wholesale and retail prices. We show that our obtained prices are better than the existing wholesale and retail prices and admit more profits for both manufacturer and retailer and generally for the entire supply chain. Also, using this case, the effects of risk sensitivity of retailer and fraction of risk cost shared by manufacturer in the total risk cost on the new supply chain’s optimal wholesale and retail prices and profits are illustrated.