•We consider public procurement where quality is predetermined for each bidder.•We view a most economically advantageous tender as an asymmetric auction.•We determine the extent of competition in bidding.•We examine the influence of the quality score attributes in the competitive behavior.•We demonstrate how corruptive behavior can influence the outcome of procurement auctions. In a multidimensional procurement auction, such as a most economically advantageous tender, asymmetric opponents, with different cost structure and predetermined quality, compete for the highest score, which combines price and quality. Production inefficiency characterizes each tenderer. We derive the equilibrium equations and boundary conditions, for which closed-form solutions are not available. We compare the bidding behavior of any pair of rival tenderers and demonstrate that equilibrium prices critically depend on the comparison of the cost difference Δc with respect to the increment of score attribute s. For the same production inefficiency, a tenderer with a relatively higher Δc compared to s, stands in weak competitive position and is forced to bid more aggressively. We show how the opposing advantage of each bidder with respect to cost or score attribute induces the extent of competition. Under a different perspective, we analyze bidding by a pair of tenderers for a given maximum score, achieved when pricing is at cost. Our analysis reveals that the player with consistently higher percentage change of the probability of being more efficient than the rival, is in a disadvantageous position and receives lower score in the awarding process. Our results are useful for tenderers in assessing their competitive position. The findings enable contracting authorities to evaluate competition at the preliminary stage of design and to examine the effects of the awarding criterion on pricing.