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

the RANE bidding strategies, we treat r as a “natural constant” and set it equal to .5, which is
in the mid-range of the estimates reported in the literature.⁶

Tables 2 and 3 report the nodes corresponding to the RNNE and the RANE bid functions for
our three treatments. Note that since in our experiments, bidders’ strategies are not
differentiable, the common bid ceiling requirement for continuous and differentiable bidding
strategies does no more necessarily hold.⁷ Another point worth noting is that the asymmetry
in the MIX treatment combines low-balling with the “Getty effect” so that it represents an
intermediate case between the LOW treatment in which low-balling is important and the SYM
treatment where there is no incentive at all to low-ball. Further, the equilibrium strategy for
Strong bidders in MIX is almost identical to the one of Strong bidders in the LOW treatment.
However, the equilibrium strategies for Weak bidders are very different across treatments.
This allows us to assess both the extent of low-balling by Strong bidders and the response of
Weak bidders in different bidding environments.

Table 1 - Treatment Parameters

⁶ Goeree et al. (2002) report an estimate of .48 for two-bidder auctions. Cox and Oaxaca (1996) and Chen and
Plott (1998) report estimates of .33 and .52 for auctions with 4 and 3 bidders, assuming heterogeneous risk
preferences. Pezanis-Christou and Romeu (2002) report average estimates of homogenous risk preferences that
range between .39 and 1 for auctions with 3, 4 and 5 bidders.

⁷ The RNNE best response tracing procedure for the LOW treatment converges to a cycle in which the y2
coordinates of both bidders switch between 30 and 31.

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