Nash Equilibria of Two-round Auctions
Abstract
In a two-round auction, a subset of bidders is selected (probabilistically), according to their bids in the first round, for the second round, where they can increase their bids. We formalize the two-round auction model, restricting the second round to a dominant strategy incentive compatible (DSIC) auction for the selected bidders. It turns out that, however, such two-round auctions are not directly DSIC, even if the probability of each bidder being selected for the second round is monotonic to its first bid, which is surprisingly counter-intuitive. We also illustrate the necessary and sufficient conditions of two-round auctions being DSIC. Besides, we characterize the Nash equilibria for untruthful two-round auctions. One can achieve better revenue performance by setting proper probability for selecting bidders for the second round compared with truthful two-round auctions.
Keywords
Cite
@article{arxiv.2312.04351,
title = {Nash Equilibria of Two-round Auctions},
author = {Chulong Zhong and Xiang Yan and Yuyi Wang and Shuangping Huang and Jin Zhong},
journal= {arXiv preprint arXiv:2312.04351},
year = {2023}
}