ON THE COMPLEXITY OF EQUILIBRIUM COMPUTATION IN FIRST-PRICE AUCTIONS

被引：1

作者：

Filos-Ratsikas, Aris ^{[1
]}

Giannakopoulos, Yiannis ^{[2
]}

Hollender, Alexandros ^{[3
]}

Lazos, Philip ^{[4
]}

Pocas, Diogo ^{[5
]}

机构：

[1] Univ Edinburgh, Sch Informat, Informat Forum, Edinburgh EH8 9AB, Midlothian, Scotland

[2] Friedrich Alexander Univ Erlangen Nurnberg, Dept Data Sci, D-91058 Erlangen, Germany

[3] Univ Oxford, Dept Comp Sci, Oxford OX1 3QD, England

[4] IOHK, 4 Battery Rd, Singapore, Singapore

[5] Univ Lisbon, Fac Ciencias, LASIGE, P-1749016 Lisbon, Portugal

来源：

SIAM JOURNAL ON COMPUTING | 2023年 / 52卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

first-price auctions; Bayes--Nash equilibria; approximate equilibria; subjective pri-ors; PPAD; FIXP; NASH-EQUILIBRIA; EXISTENCE; PRICE; GAMES; UNIQUENESS;

D O I：

10.1137/21M1435823

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider the problem of computing a (pure) Bayes--Nash equilibrium in the first price auction with continuous value distributions and discrete bidding space. We prove that when bidders have independent subjective prior beliefs about the value distributions of the other bidders, computing an \varepsilon-equilibrium of the auction is PPAD-complete, and computing an exact equilibrium is FIXP-complete. We also provide an efficient algorithm for solving a special case of the problem for a fixed number of bidders and available bids.

引用

页码：80 / 131

页数：52

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