Second-Price Ad Auctions with Binary Bids and markets with good competition

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Abstract

Given a bipartite graph G=(U,V,E) with U={1,,n}, and a positive budget Bv for each v in V, a B-matching M in G is a second-price B-matching if, for every edge uv in M, there is an edge uw in E so that less than Bw edges uw with u<u belong to M. The Second-Price Ad Auction with Binary Bids (B2PAA) consists of, given G and B as above, finding a second-price B-matching in G as large as possible. The particular case of this problem where Bv=1 for all v, called Second-Price Matching (2PM), is known to be APX-hard and there is a 2-approximation for it. We present a way to use this approximation and similar ones to approximate B2PAA. Also, we formalize the idea of a competitive market, present an improved approximation for 2PM on competitive markets, extend the inapproximability result for competitive markets and analyze the performance of an algorithm of Azar, Birnbaum, Karlin, and Nguyen for the online 2PM on competitive markets. Our improved approximation can also be used for B2PAA.

Keywords

Approximation algorithms
Combinatorial auctions
Matchings

Cited by (0)

1

Partially supported by CNPq 309657/2009-1, 475064/2010-0, and Project MaCLinC of NUMEC/USP.

2

Supported by grant 2009/00387-7, São Paulo Research Foundation (FAPESP) and Project MaCLinC of NUMEC/USP.