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

■ Obs □EBR □ Matched

■ Obs □EBR □ Matched

Figure 5: Distribution of bid function shapes in SYM

For each bidder, we count the number of rounds in which she/he submitted a CRRA bid
function, assuming b = 50 (i.e., r_max = 1 ). A bid functions qualifies as a “CRRA bid
function” if it is linear with s1 ≥ .5, s2 ≥ 0 and y2 ≥ 50 or concave with s1 ≥ .5, 0 ≤ s2 < s1,
b = 50, y₁ ≥ b and y₂ ≥ b . It appears that for 28 out of 36 subjects who ever submitted
CRRA bid functions, the average rate of submission of such bid functions is 22%. We test the
null hypothesis that the probability for a bidder to submit a CRRA bid function is equal to 0.5
against the alternative that it is smaller than 0.5. According to the Binomial test, we cannot
reject this hypothesis for only 6 subjects (at α=.05 one-tailed). When the test is conducted
over the last 25 rounds, we cannot reject the null of CRRA bidding for one more bidder and
the modal frequency is still on Concave (i.e., about 70% of all bid functions). Therefore, as, 6
or 7 CRRA bidders out of 36 do not represent a significant rate of success according to the
Binomial test, we infer that subjects are not likely to submit CRRA bid functions. We also
tested a softer version of the CRRA model which assumes y1 > 40 so that we allow for a non-
linearity at b > 40 instead of the critical b = 50 . In this case the mode of the distribution of
shapes remains on Concave (57%, followed by CRRA: 31%) and we cannot reject the null of

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