Elicited bid functions in (a)symmetric first-price auctions

matched within a given group. Such a design is necessary to avoid the obvious super-game
effects that would arise from the repeated interaction of the same two bidders in a series of
auctions. However, such a matching scheme also implies within-group effects: a subject’s
behavior may be contaminated by the behavior of a previous competitor, who is not
participating in the current auction. We therefore conduct most of our analysis at the group
level of aggregation, and conduct tests of individual behavior whenever the independence
criteria can be fulfilled.

3.1. Bid shading, Bid ceilings and Average revenues

3.1.1. Bid Shading

The extent by which bidders shade their bids is most relevant in the asymmetric treatments
since in equilibrium, Strong and Weak bidders are expected to bid very differently. We test
this prediction by comparing the Relative Bid Shading (henceforth, RBS) of Strong bidders to
those of Weak bidders. As bidders submit complete bid functions before receiving their
respective values, this measure of bid shading has to account for all possible values that a
bidder can receive so that we define it as

v

∑[v - bi^t(v)]

RBSi = ——=------ for t = 1,...,100 and i = S, W              (6)

∑v

v=0

Table 4 reports the average RBS in each treatment. We find no significant difference across
types in SYM, which is not surprising, since in this treatment all bidders (even though we call
some “Strong” and others “Weak”) draw their values (with replacement) from the same
distribution. In the asymmetric treatments, however, Strong bidders shade their bids

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