Budget Constraints in Combinatorial Clock Auctions

Abstract

In this chapter we analyze the Combinatorial Clock Auction (CCA) with budgetconstrained bidders. By means of illustrative examples, we highlight positive and critical aspects of bidding under a budget in the clock and in the supplementary phase. Since the supplementary phase of a CCA without constraints from the clock phase is just a VCG auction, we also relate the CCA to the VCG. In the VCG auction, bidding under a budget constraint can be strategically complicated. However, on the positive side, the information revealed in the clock can facilitate bidding since bidders can compute upper (and lower) bounds on the final VCG price. This information might allow them to bid above budget without facing the risk of having to pay more than budget, which might lead to an efficient allocation. In one example we show that the clock might actually last longer under a budget constraint. More critical is that the information provided in the clock can actually be used to bid above budget in order to raise rivals' costs. There are asymmetric equilibria that have a Hawk-Dove flavor: the most aggressive bidder gets the highest surplus. Coordination issues can arise and in the case of mis-coordination bidders have to pay more than their budget.

The Combinatorial Multi-Round Ascending Auction

“…First, the supplementary round in the CCA creates uncertainty about what the bidders will win and what they will pay. Avoiding the supplementary round can therefore help bidders discover prices more gradually and deal more easily with their budget constraints (Janssen et al, 2017). Second, submitting mutually exclusive bids in the supplementary round (in order to achieve the most preferred auction outcome) can be taxing for bidders.…”