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

the shape of the average concave EBR functions.¹³ To this extent, submitting a concave bid
function is more characteristic of a best-reply to the Strong bidders’ lack of low-balling than
submitting a convex bid function as predicted by the Nash equilibrium.

Such bid patterns, which remain virtually unchanged for the last 25 rounds of the experiment,
suggest that from a theoretical perspective, the Nash equilibrium predictions for Strong
bidders are more robust to the out-of-equilibrium behavior of Weak bidders than what the
predictions for Weak bidders are to the out-of-equilibrium behavior of Strong bidders. From
an empirical point of view, the observed behavior suggests that the lack of low-balling by
Strong bidders is the main reason for not observing the predicted outcomes.

3.2.3.2. Symmetric Treatment

The left-hand panel of Figure 5 reports the relative frequencies of each shape in the SYM
treatment. About 73% of all bid functions are concave and only 10% have the linear shape
predicted by RNNE and RANE. The submission of concave bid functions appears to be
consistent with best-reply bidding since this shape represents 84% of all EBR functions. The
frequencies of matched (observed and EBR) Concave shapes are also the highest in this
treatment and represent about 60% of all submitted bid functions. The plots in Figure 6
further indicate that these concave bid functions share the non-linear characteristics of best-
reply bidding. As these patterns remain unchanged for the last 25 rounds of the experiment,
the data clearly indicate that the submission of linear bid functions, as predicted by RNNE
and RANE, is not robust to the out-of-equilibrium behavior of competitors.

¹³ The plots of Weak (Strong) bidders are virtually identical to those of concave (convex) bid functions that

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