Essays on Multi-unit Auctions: Theory and Experiment

This dissertation contains three essays on the topic of multi-unit auctions. In Chapter 1, I experimentally investigate implications of weak and strong budget constraints on two share auctions, the uniform price and the proportional share auction, compared to the first price auction. Under the strong budget constraint, the two share auctions raise higher revenue than the first price auction, in contrast to studies without budget constraints. More surprisingly, the proportional share auction achieves higher efficiency than the first price auction despite its inherently inefficient allocation rule. The proportional share auction performed better than the uniform price auction under the strong budget constraint, but under the weak budget constraint, the uniform price auction performed the same or better than the proportional share auction. In Chapter 2, We experimentally investigate the Generalized Second Price (GSP) auction used to sell advertising positions in online search engines. Two contrasting click through rates (CTRs) are studied, under both static complete and dynamic incomplete information settings. Subjects consistently bid above the Vikrey–Clarke–Grove’s (VCG) like equilibrium favored in the theoretical literature. However, bidding, at least qualitatively, satisfies the contrasting outcomes predicted under the two CTRs. For both CTRs, outcomes under the static complete information environment are similar to those in later rounds of the dynamic incomplete information environment. This supports the theoretical literature that uses the static complete information model as an approximation to the dynamic incomplete information under which advertising positions are allocated in field settings. Chapter 3 studies a pro-competitive effect of joint bidding in multi-unit uniform price auctions where bidders have private values and demand different quantities of units. I analyze a simple model with three identical items for sale, two small bidders each demanding a single unit, and a big bidder demanding two units. I show that joint bidding of the two small bidders, which recovers the symmetry of bidders, enhances competition among the bidders and increases efficiency and revenue of the auction.

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