3.2.2. Empirical Best Replies
A drawback of the analysis of deviations from a Nash equilibrium prediction is that it
foregoes an assessment of the subjects’ strategic behavior. Indeed, a comparison between
observed and equilibrium bid functions can be misleading because the latter are unlikely to be
best replies to the rivals’ bid functions. We therefore follow Avery and Kagel (1997) by
studying deviations from best reply bidding.11 We do so by determining for each type of
bidder in each treatment, the Empirical Best Reply (EBR) function, which is the risk neutral
best reply bid function to the distribution of the actual rivals’ bid functions.
In contrast to previous studies that compared the observed behavior in round t to an estimated
best reply from the data of all rounds, our design allows us to compare, in each round, a
bidder’s bid bit (v) to the EBR bid given the valuation that this bidder received in this
particular round. We compute a bidder’s relative error as the ratio of the difference between
the bid and the EBR bid to the bidder’s valuation, and we report the aggregate distributions
for each type and treatment in Figure 2. These distributions assume a bin range of 0.025 so
that errors in (-0.0125; +0.0125] are labeled as 0; errors in (+0.0125; +0.0375] are labeled as
0.025, etc. The plots indicate that although the distributions of both Strong and Weak bidders
usually have a modal frequency at 0, they are also skewed towards positive relative errors,
especially for Strong bidders in the LOW treatment. In this treatment, the modal frequency of
Strong bidders is at 0.5, followed by 0.4 and 0.
11 Avery and Kagel (1997) look at deviations from EBR payoffs in their ‘^-equilibrium” analysis of behavior in
second-price auction experiments with common-values and asymmetric private advantages. Fudenberg and
Levine (1997) look at deviations from EBR payoffs in their ‘^-self-confirming equilibrium” analysis of simple
extensive-form game experiments. Selten, Abbink, Buchta and Sadrieh (2002) look at deviations from EBR
payoffs in their ‘best reply ratio” analysis of 3x3 normal-form game experiments. Because we observe subjects’
complete bid-functions and because the values are drawn (with replacement) from a uniform distributions,
comparing (squared) deviations from EBR functions is analogous to comparing deviations from EBR payoffs.
18