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

encompass risk neutrality as a special case.⁴ In a symmetric setting, the expected utility
representation of such preferences is

U(v_i,b) = (v_i - b)^rF(f (b))       with r> 0                   (4)

When r = 1, (4) characterizes a risk neutral utility function whereas for r < 1, the marginal
utility of an additional unit of income decreases so that bidders’ display constant relative risk
aversion. The Risk Averse Nash Equilibrium (RANE) bidding strategy for symmetric first-
price auctions with two bidders then takes the following expression

ʌɪ

For asymmetric first-price auctions there usually are no closed-form RANE equilibrium bid
functions so that these can only be determined numerically. We derive both the RNNE and
RANE bid functions for our asymmetric framework in the next section.

2. Experimental Design and Procedure

2.1. Design

We consider two-bidder first-price auctions as described in the previous section and we study
three treatments: one that involves symmetric bidders and two that involve asymmetric
bidders (i.e., a Strong bidder and a Weak bidder). All bidders have their values drawn from
uniform distributions. In our symmetric treatment, all bidders draw their values from IS =
[0;100]. In our asymmetric treatments, the range of values of the Strong bidders is also IS but

⁴ See Holt and Davis (1995) for an outline on the use of the constant absolute and constant relative risk aversion

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