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As a supply chain solution integrator, fourth party logistics (4PL) has become an important focus for improving the operational efficiency of the logistics industry in recent days. This paper addresses the mechanism design problem of the 4PL for selecting a third party logistics (3PL) provider who involves loss-averse behavior to form a longer-term strategic partnership in multi-attribute reverse auctions. Due to fluctuating costs of energy or labor and unintentional delivery failures like traffic jam or technology malfunctions, we consider two incomplete attributes, namely cost uncertainty and delivery risk. Integrating the loss-averse behavior of 3PLs, based on the prospect theory, the bid decision model is constructed to obtain 3PLs’ bidding strategies. The corresponding efficient and optimal scoring auctions that consist of cost-sharing contract and contingent penalty are developed to maximize the ex ante expected profit of the system or the 4PL depending on whether the 4PL is willing to cooperate or not. Theoretical analysis verified by numerical examples illustrates the advantage of the proposed mechanisms. Impacts of model parameters on the 4PL’s decision are also investigated and managerial insights are presented.