In reverse auctions, buyers often retain the right to bargain further concessions from the winners. The optimal form of such procurement is an English auction followed by an auctioneer's option to engage in ultimatum bargaining with the winners. We study behavior and performance in this procurement format using a laboratory experiment. Sellers closely follow the equilibrium strategy of exiting the auction at their costs and then accepting strictly profitable offers. Buyers generally exercise their option to bargain according to their equilibrium strategy, but their take-it-or-leave-it offers vary positively with auction prices when they should be invariant. We explain this deviation by modeling buyers' subjective posteriors regarding the winners' costs as distortions of the Bayesian posteriors, calculated using a formulation similar to a commonly used probability weighting function. We further test the robustness of the experimental results and the subjective posterior explanation with three additional experimental treatments.
Shachat, J., & Tan, L. (2015). An Experimental Investigation of Auctions and Bargaining in Procurement. Management Science, 61(5), 1036-1051. https://doi.org/10.1287/mnsc.2013.1880