In the construction industry, auctions have long been used as a method for allocating contracts. Not addressed in the literature (engineering or economics) is the fact that most, if not all, large jobs are awarded to a general contractor who in turn sub-contracts most, if not all, actual engineering services. Optimal bidding strategies in this setting require the general contractor to not only account for the optimal bidding strategies of rivals, but sub-contractors as well. Because the true cost of construction is not known until after the completion of the contract, adverse selection occurs when the winner of the contract is the one that most has under estimated the true cost. Due to the multi-stage bidding environment, adverse selection may be compounded. Therefore, not accounting for the potential for adverse selection by bidders may result in requested change orders by the general and sub-contractors or lower quality services. Either state ultimately results in an adversarial relationship between the sub-contractor and general contractor, and the client as well. This paper uses game theory to determine to what extent the multi-stage aspects of large construction contract bidding may contribute to inefficient allocation of contracts. This should better help in creating an efficient and effective contracting environment that result in less conflicts, claims and disputes for all the associated stakeholders.