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

shapes, Nash equilibrium predicts convex bid functions for both Strong and Weak bidders
with either type of risk preferences but this is observed about 49% of the time for Strong
bidders and about 25% of the time for Weak bidders. Further, the shapes of observed bid
functions match those of the corresponding best-reply functions about 50% of the time for
both Strong and Weak bidders. Therefore, the outcomes of our experiment suggest that
although individual behavior is usually not consistent with the Nash equilibrium predictions
for both symmetric and asymmetric first-price auctions, it still displays characteristics of best-
reply behavior and it matches the theoretical Nash equilibrium predictions in the aggregate.

The following section outlines the model of Maskin and Riley (2000a) and the theoretical
framework we use to analyze data. We determine the Risk Neutral and the Constant Relative
Risk Averse Nash Equilibrium bidding strategies for our auction games in Section 2. The
experimental procedure is described in Section 3 and we report on the outcomes in Section 4.
Section 5 concludes the paper.

1. Theoretical benchmarks

The bidding model of Maskin and Riley (2000a) extends the symmetric framework of
Vickrey (1961) to asymmetric settings and can be outlined as follows. There are two bidders,
S (Strong) and W (Weak), who draw their independent-private values from continuous
distributions FS and FW that are defined on IS = [v_s; vS ] and IW = [v_w ; v_w ], respectively. In
a first-price auction, if bidder i has value vi and obtains the item with a bid bi, she/he pays the
price bi and receives the payoff v_i -b_i . A pair of bid functions {b_S(v), b_W (v)} (with
b_i′(v_i) > 0, for i = S, W) is an equilibrium if b_i(v_i) is a best response to b_j(v_j) for all vi in Ii
and all vj in Ij, with i≠j. Let φ_i(b_i) = v_i denote the inverse function of b_i(v_i) . Bidder i’s
expected payoff then has the following expression

<<   2   3   4   5   6   7   8   >>

More intriguing information