the range of values for Weak bidders IW differs across treatments. Table 1 summarizes the
treatment parameters and the main characteristics of our experiments.
We use a simplified version of the design proposed by Selten and Buchta (1998) which
consists in asking each subject to submit a two-piecewise linear bid function in each round,
before receiving the private value.5 Since there is no rationale for bidding more than one’s
value in a first-price sealed-bid auction, subjects were not allowed to chose bid functions that
could generate a bid greater than the private value drawn. Also, no bid was allowed for
negative values and the submitted bid function had to span the entire range of possible
positive values. These conditions imply that the submitted bid function cannot have a non-
zero intercept and that bidder i’s task consists in choosing: i) the coordinates of an interior
node (xi1, yi1) that could represent a kink in their bid function, and ii) the bid yi2
corresponding to the highest possible value vi. With such a design, bidders could choose their
bid functions from a set of over half a million possible functions.
As the submitted bid functions are two-piecewise linear instead of differentiable, as in Maskin
and Riley (2000a), we need to determine the RNNE and the RANE bidding strategies for the
particular strategy space of our experiments. To this end, we use a numerical procedure that
traces best reply chains until a rest point is found (Harsanyi and Selten 1988). When deriving
concepts in experimental economics.
5 Selten and Buchta (1998) examine a symmetric setting which involved three bidders who had their values
drawn from a uniform distribution on [0;100] and who could submit bid functions that could have up to 10000
segments. Güth, Ivanova-Stenzel, Konigstein and Strobel (2002) use a similar design to compare treatments of
symmetric first and second price auctions to first and second price “fair division” games. In their experiments,
subjects’ private values were drawn (with replacement) from a set of 11 possible valuations {50,60,70, . ..,150}
and the submitted bids had 11 nodes.