Settling the Competition Complexity of Additive Buyers over Independent Items
arxiv(2024)
摘要
The competition complexity of an auction setting is the number of additional
bidders needed such that the simple mechanism of selling items separately (with
additional bidders) achieves greater revenue than the optimal but complex
(randomized, prior-dependent, Bayesian-truthful) optimal mechanism without the
additional bidders. Our main result settles the competition complexity of n
bidders with additive values over m < n independent items at
Θ(√(nm)). The O(√(nm)) upper bound is due to [BW19], and our
main result improves the prior lower bound of Ω(ln n) to
Ω(√(nm)).
Our main result follows from an explicit construction of a Bayesian IC
auction for n bidders with additive values over m m: SRev_n(ℰℛ^m)
= nm+O_m(ln (n)) ≤SRev_n+O_m(ln (n))(ℰℛ^m), and
therefore our result can only follow by considering all possible truncations.
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