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



Table 5 -Average Seller’s Revenues (and Standard Deviation)

Observed

RNNE

RANE

LOW

24.87

12.50

23.06

_______(9 obs)______

(4.47)

(.74)

(1.16)

MIX

18.51

10.61

21.15

_______(9 obs)______

(5.35)

(.33)

(.56)

SYM

42.47

33.40

44.53

_______(6 obs)______

(3.89)

(.66)

(.88)

3.2. Nash equilibrium behavior, Empirical Best Replies and shapes
of bid functions

3.2.1. Nash Equilibrium Behavior

The plots in Figure 1 show that the average bid functions are better tracked by the RANE
prediction in the symmetric treatment than in the asymmetric treatments. In the latter,
although Strong bidders bid less aggressively than Weak bidders for equal values, they
overbid mostly at low values, which is inconsistent with the risk neutral or risk averse
equilibriumpredictionsforthesetreatments.

To assess the explanatory power of these models, we compare the Relative Squared
DeviationsfromtheRNNEandRANEbidfunctions(henceforth,
RSD).WedefineRSDfor
biddertype
iinroundtas
where
bi*(v) standsfortheRNNEortheRANEbidfunctionoftypeiandthedenominatorfor

RSDit =


max<


ɪ, г           ,    2

[bit(v) - bi*(v)]
v=0


2               2 2             2

[v-bi*(v)] ,[-bi*(v)]

v=0                  v=0


fort = 1,...,100andi = S,W


themaximumpossibledeviationfromthatstrategy.

15



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