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



symmetric one, where no significant difference across bidders’ (pseudo-)types are expected or
observed;
ii) both types of bidders submit similar bid ceilings, whether the auction is
symmetric or not;
iii) the observed revenues are not significantly different from those
predicted by a Nash equilibrium model for constant relative risk averse bidders and
iv)
aggregate behavior in symmetric auctions is best explained by a Nash equilibrium model for
the constant absolute risk averse bidders and the one of asymmetric auctions is equally well
explained by a Nash model for risk neutral or homogenous constant relative risk averse
bidders.

However, when we compare the shapes of the individual bid functions to the shapes of best-
reply bid functions, then the data is much less supportive of the Nash equilibrium predictions.
In the symmetric environment, bid functions are mostly concave and they match the concave
shape of the (risk neutral) best-reply bid function in 60% of the time. Hence, although such a
behavior is neither in line with the Nash equilibrium predictions for homogenous nor for
heterogeneous bidders with constant relative risk aversion (cf. Cox
et al. 1982, 1988), it does
display clear characteristics of best-reply behavior. In the asymmetric bidding environments,
Strong bidders submit convex bid functions about half of the time but they do not “low-ball”
enough when compared to the Nash equilibrium predictions. This lack of low-balling is not
supported by best-reply behavior since the latter recommends 80% of the time bid functions
that are, on average, very similar to the risk neutral Nash equilibrium prediction. To the
contrary, Weak bidders submit concave bid functions about half of the time, which are not
supported by the Nash equilibrium. They do, however, match the characteristics of a best-
reply behavior that recommends concave functions about 75% of the time.

The outcomes of our experiment thus suggest that bidders’ behavior is more governed by
strategic considerations than by
ad hoc bidding rules. Such strategic considerations are more

28



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