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



and rmax as b = (n-1) /(n-1+ rmax) . The slopes of the linear part of these bid functions are
greater than the slope of the RNNE bid function (i.e., greater than
0.5). As most previous
experiments report a significant overbidding,
rmax is usually set equal to 1 so that in our case
b = 50. For bids greater than b these equilibrium strategies have to be approximated
numerically (Van Boening, Rassenti and Smith, 1998). However, an interesting property of
the CRRA model is that when valuations are drawn from a uniform distribution, then, for a
given
rmax, the linear parts of the CRRA bid functions are invariant to the distribution of risk
parameters so that we only need to specify the support of the distribution of risk parameters to
determine them. To this extent, the testing of the CRRA hypothesis would almost revert to the
testing of a
belief-free model in the sense of Chen and Plott (1998). As the CRRA model
predicts concave bid functions for
ri < 1, it could therefore provide a good fit of the observed
behavior.14 We recall that the random matching of subjects in our experiment prevents the
assessment of individual behavior so that we only check for a qualitative fit of this model
rather than estimating the individual CRRA parameters.

The data reported in the right-hand panel of Figure 5 indicates that CRRA bid functions
represent about 18% of all bid functions whereas non-CRRA concave functions represent
about 60% of them. A similar ratio of CRRA-to-concave bid functions is observed for the
EBR functions (23% vs. 61%) and the matching frequencies also show sharp differences in
favor of the submission of non-CRRA concave bid functions. To this extent, the latter would
better represent best-reply bidding than CRRA or RANE bid functions.

14 Cox et al. (1988) and Cox and Oaxaca (1996) report some non-linearity (concavity) in the estimated bid
functions, but conclude that it is generally insignificant and that the data are best explained by linear bid
functions. However, Pezanis-Christou and Romeu (2002) use structural econometric methods and show that
these non-linearities are often significant and that the observed heterogeneity in behavior usually implies a
rejection of the CRRA model of bidding. Selten and Buchta (1998) also report non-linear bid functions, many of
which displaying a concavity in their shapes.

25



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