The presence of financial constraints changes traditional auction theory predictions. In the case of multiple items, such constraints may affect revenue equivalence and efficiency of different auction formats. We consider a simple complete information setting with three financially constrained bidders and two items that have different values common to all the bidders. Using a laboratory experiment, we find that, as predicted by theory, it is more beneficial for the seller to sell the higher value item first. We then show that the first-price sealed-bid auction yields higher revenue than the English auction, with significant differences in learning of equilibrium strategies.

We explore the efficiency and revenue of proportional auctions (PA) compared to first price auction (FPA) for budget-constrained bidders. PA auctions have been used in privatization of Russian assets and in cryptocurrency sales, as they can achieve higher efficiency and revenue than FPAs when bidders face severe financial constraints. The experimental results support this in that under a tight budget constraint PA achieved higher revenue and efficiency than FPA, with these results reversed under a looser budget constraint. Detailed patterns of bidding are compared to the theoretical predictions for both PA and FPA.