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



significantly more than Weak bidders (at α = .01, one-tailed), which is in line with
Proposition 3.5 of Maskin and Riley (2000a). These predictions hold when we compare the
(distributions of) linear slope estimates of the observed bid functions: Strong bidders tend to
submit significantly less steep bid functions than Weak bidders in the asymmetric treatments,
but not in the symmetric treatment where no significant difference could be diagnosed.

We also checked whether the bid distributions of Strong bidders are stochastically greater
than those of Weak bidders as implied by Proposition 3.3 of Maskin and Riley (2000a).9 We
tested this hypothesis by comparing the distributions of
actual bids (i.e., using the realized
valuations) across bidders’ types and found that bids of Strong bidders are indeed
stochastically greater than those of Weak bidders in LOW and in MIX, and that they are
equivalent in SYM.

3.1.2. Bid Ceilings

Table 4 reports the average relative deviations from the RNNE and RANE bid ceilings for
each type of bidder, which are computed as (
yit2 - yi*2)/ yi*2 , with i = 1,...,100 and i = S,W . A
comparison of these deviations reveals no significant difference across types in any treatment.
For the asymmetric settings, this indicates that the bid ceilings are somehow coordinated
despite the asymmetry in subjects’ preferences and the lack of communication. When
compared to the RNNE bid ceilings, the observed bid ceilings are significantly greater than
those predicted for the LOW and SYM treatments but we find no significant difference
between observed and predicted ceilings for the MIX treatment. When compared to the

9 This proposition actually predicts first-order stochastic dominance, which in this case is best approximated
with non-parametric statistics that check whether one sample is
stochastically greater than another or not.

13



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