Probabilistic procurement auctions

We analyse procurement auctions in which sellers are distinguished on the basis of the ratios of quality per unit of money that they offer. Sellers are privately informed on the offered quality of the technology or good. We assume that the procurer cannot perfectly identify the best offer. Thus, with positive and decreasing probability, the second, third, etc. best ratio offered is selected as the winner of the auction. We model the decision process as based on a general noisy ranking of offers. We show that, although the problem seems to be analytically intractable in general, there exists a simple symmetric, pure-strategy equilibrium in which everyone follows the simple heuristic to match the same "focal" price-quality ratio.