4,582 research outputs found
On the Efficiency of All-Pay Mechanisms
We study the inefficiency of mixed equilibria, expressed as the price of
anarchy, of all-pay auctions in three different environments: combinatorial,
multi-unit and single-item auctions. First, we consider item-bidding
combinatorial auctions where m all-pay auctions run in parallel, one for each
good. For fractionally subadditive valuations, we strengthen the upper bound
from 2 [Syrgkanis and Tardos STOC'13] to 1.82 by proving some structural
properties that characterize the mixed Nash equilibria of the game. Next, we
design an all-pay mechanism with a randomized allocation rule for the multi-
unit auction. We show that, for bidders with submodular valuations, the
mechanism admits a unique, 75% efficient, pure Nash equilibrium. The efficiency
of this mechanism outperforms all the known bounds on the price of anarchy of
mechanisms used for multi-unit auctions. Finally, we analyze single-item
all-pay auctions motivated by their connection to contests and show tight
bounds on the price of anarchy of social welfare, revenue and maximum bid.Comment: 26 pages, 2 figures, European Symposium on Algorithms(ESA) 201
On the Efficiency of All-Pay Mechanisms.
We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m all-pay auctions run in parallel, one for each good. For fractionally subadditive valuations, we strengthen the upper bound from 2 [22] to 1.82 by proving some struc- tural properties that characterize the mixed Nash equilibria of the game. Next, we design an all-pay mechanism with a randomized allocation rule for the multi-unit auction. We show that, for bidders with submodular valuations, the mechanism admits a unique, 75% efficient, pure Nash equilibrium. The efficiency of this mechanism outperforms all the known bounds on the price of anarchy of mechanisms used for multi-unit auc- tions. Finally, we analyze single-item all-pay auctions motivated by their connection to contests and show tight bounds on the price of anarchy of social welfare, revenue and maximum bid
Ad auctions and cascade model: GSP inefficiency and algorithms
The design of the best economic mechanism for Sponsored Search Auctions
(SSAs) is a central task in computational mechanism design/game theory. Two
open questions concern the adoption of user models more accurate than that one
currently used and the choice between Generalized Second Price auction (GSP)
and Vickrey-Clark-Groves mechanism (VCG). In this paper, we provide some
contributions to answer these questions. We study Price of Anarchy (PoA) and
Price of Stability (PoS) over social welfare and auctioneer's revenue of GSP
w.r.t. the VCG when the users follow the famous cascade model. Furthermore, we
provide exact, randomized, and approximate algorithms, showing that in
real-world settings (Yahoo! Webscope A3 dataset, 10 available slots) optimal
allocations can be found in less than 1s with up to 1000 ads, and can be
approximated in less than 20ms even with more than 1000 ads with an average
accuracy greater than 99%.Comment: AAAI16, to appea
Draft Auctions
We introduce draft auctions, which is a sequential auction format where at
each iteration players bid for the right to buy items at a fixed price. We show
that draft auctions offer an exponential improvement in social welfare at
equilibrium over sequential item auctions where predetermined items are
auctioned at each time step. Specifically, we show that for any subadditive
valuation the social welfare at equilibrium is an -approximation
to the optimal social welfare, where is the number of items. We also
provide tighter approximation results for several subclasses. Our welfare
guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes,
via the smooth-mechanism framework. Of independent interest, our techniques
show that in a combinatorial auction setting, efficiency guarantees of a
mechanism via smoothness for a very restricted class of cardinality valuations,
extend with a small degradation, to subadditive valuations, the largest
complement-free class of valuations. Variants of draft auctions have been used
in practice and have been experimentally shown to outperform other auctions.
Our results provide a theoretical justification
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