193 research outputs found
Generalized Second Price Auction with Probabilistic Broad Match
Generalized Second Price (GSP) auctions are widely used by search engines
today to sell their ad slots. Most search engines have supported broad match
between queries and bid keywords when executing GSP auctions, however, it has
been revealed that GSP auction with the standard broad-match mechanism they are
currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g.,
its theoretical properties are known only for the single-slot case and
full-information setting, and even in this simple setting, the corresponding
worst-case social welfare can be rather bad). To address this issue, we propose
a novel broad-match mechanism, which we call the Probabilistic Broad-Match
(PBM) mechanism. Different from SBM that puts together the ads bidding on all
the keywords matched to a given query for the GSP auction, the GSP with PBM
(denoted as PBM-GSP) randomly samples a keyword according to a predefined
probability distribution and only runs the GSP auction for the ads bidding on
this sampled keyword. We perform a comprehensive study on the theoretical
properties of the PBM-GSP. Specifically, we study its social welfare in the
worst equilibrium, in both full-information and Bayesian settings. The results
show that PBM-GSP can generate larger welfare than SBM-GSP under mild
conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in
Bayesian setting. To the best of our knowledge, this is the first work on
broad-match mechanisms for GSP that goes beyond the single-slot case and the
full-information setting
Approximating equilibrium under constrained piecewise linear concave utilities with applications to matching markets
We study the equilibrium computation problem in the Fisher market model with constrained piecewise linear concave (PLC) utilities. This general class captures many well-studied special cases, including markets with PLC utilities, markets with satiation, and matching markets. For the special case of PLC utilities, although the problem is PPAD-hard, Devanur and Kannan (FOCS 2008) gave a polynomial-time algorithm when the number of items is constant. Our main result is a fixed parameter approximation scheme for computing an approximate equilibrium, where the parameters are the number of agents and the approximation accuracy. This provides an answer to an open question by Devanur and Kannan for PLC utilities, and gives a simpler and faster algorithm for matching markets as the one by Alaei, Jalaly and Tardos (EC 2017). The main technical idea is to work with the stronger concept of thrifty equilibria, and approximating the input utility functions by ‘robust’ utilities that have favorable marginal properties. With some restrictions, the results also extend to the Arrow–Debreu exchange market model
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