Budget constraints in homogenous multi-unit auctions

A homogenous multi-unit auction model is studied in two conditions: One is that the bidders face budget constraints and another is that the bidders do not face budget constraints. Two equilibrium bidding strategies of each bidder are presented in these two conditions. By comparing them, the authors show that the equilibrium unit price bid in the presence of budget constraints will be less than that in the absence of budget constraints. The difference between the two equilibrium bids leads to the reduced revenue of the seller. And this difference will decrease as the number of the bidders increases.