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arXiv · 2312.04351

Nash Equilibria of Two-round Auctions

Chulong Zhong·Xiang Yan·Yuyi Wang·Shuangping Huang·Jin Zhong
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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.

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Chulong Zhong, Xiang Yan, Yuyi Wang, Shuangping Huang, Jin Zhong. 2023-12-07. Nash Equilibria of Two-round Auctions. https://doi.org/10.1145/3627676.3627682

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