NDLI: Welfare Maximization with Limited Interaction

Content Provider	IEEE Xplore Digital Library
Author	Alon, N. Nisan, N. Raz, R. Weinstein, O.
Copyright Year	2015
Description	Author affiliation: Courant Inst., New York Univ., New York, NY, USA (Weinstein, O.) \|\| Weizmann Inst. of Sci., Weizmann, Israel (Raz, R.) \|\| Tel Aviv Univ., Tel Aviv, Israel (Alon, N.) \|\| Hebrew Univ., Hebrew, Israel (Nisan, N.)
Abstract	We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model where agent's valuations are unknown to the central planner, and therefore communication is required to determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is n, then r rounds of interaction (with logarithmic bandwidth) suffice to obtain an $n^{1/(r+1)}-approximation$ to the optimal social welfare. In particular, this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size. We obtain the first multi-round lower bound for this setup. We show that even if the allowable per-round bandwidth of each agent is $n^{ε(r)},$ the approximation ratio of any r-round (randomized) protocol is no better than $Ω(n^{1/5r+1)},$ implying an Ω(log log n) lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous (r = 1) protocols [DNO14].
Starting Page	1499
Ending Page	1512
File Size	294841
Page Count	14
File Format	PDF
ISBN	9781467381918
ISSN	02725428
DOI	10.1109/FOCS.2015.95
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-10-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Protocols Approximation methods Complexity theory Upper bound Computational modeling Resource management Electronic mail Information theory Distributed matchings Multiparty Communication complexity Welfare maximization
Content Type	Text
Resource Type	Article

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