First and second price independent values sealed bid procurement auctions: Some scalar equilibrium results

A great body of knowledge exists on the theory of auctions and competitive bidding that is of potential relevance to construction contract tendering. Most of this, however, contains assumptions - such as perfect information - that are unlikely to be tenable in practice. The aim, therefore, is to examine the effects of relaxing some of the more restrictive of these assumptions to align more closely with the construction tendering situation. In particular, the effects of additive and multiplicative (scalar) mark-ups in equilibrium are examined for first and second price auctions in situations where bidders have different, uncertain, costs. This is illustrated first by Monte Carlo simulation - by which bids are generated randomly from a normal distribution for six bidders and mark-ups applied systematically for each bidder in turn until equilibrium is reached. An extensive numerical analysis is then applied to obtain equilibrium results for both mark-up values and expected profit from the simple symmetric case through to more complex asymmetric cases for the uniform and normal distributions. In general, it is found that first price auction bidders with relatively high cv levels and a larger number of bidders involved bid higher in equilibrium but can expect little profit unless the number of bidders involved is small. Where there are asymmetries, stronger bidders (i.e. those with lower costs and less variability) bid much higher and achieve much higher profits in equilibrium. From the seller's point of view, it is cheaper, in equilibrium, to have a homogeneous group of low variability bidders. The work contributes to the body of knowledge on the economic theory of auctions by closing some of the gap between theory and practice.