Allocation of the tasks in competitive market conditions at each echelon of the supply chain is an important activity in the supply chain. The task allocation problem, referred to as supply chain formation process, normally faces information asymmetry in the supply chain. The information asymmetry is caused by rational and intelligent players trying to maximize their own profit rather than opt for the supply chain profit as a whole. Thus, the process of allocating tasks in such situations becomes difficult and will result in externalities in the supply chain trades. These externalities can be internalized with present methodologies in the literature. In this paper, the major internalization methods in different contexts are considered. Lagrange relaxation and Vickery Clarke Groves (VCG) auction mechanism are explored in order to form a supply chain. This paper proposes the multi-stage auction mechanism analyzing two-way competitions, a Bertrand and Cournot competition where price per unit and quantity are the underlying two parameters in a utility analysis. To analyze the problem in real life, the industry example of Indian Railway Catering and Tourism Corporation Ltd. (IRCTC) procurement process has been taken which demonstrates the usability of the proposed framework.