12 research outputs found
Tight Bounds for the Price of Anarchy of Simultaneous First Price Auctions
We study the Price of Anarchy of simultaneous first-price auctions for buyers
with submodular and subadditive valuations. The current best upper bounds for
the Bayesian Price of Anarchy of these auctions are e/(e-1) [Syrgkanis and
Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching
lower bounds for both cases even for the case of full information and for mixed
Nash equilibria via an explicit construction.
We present an alternative proof of the upper bound of e/(e-1) for first-price
auctions with fractionally subadditive valuations which reveals the worst-case
price distribution, that is used as a building block for the matching lower
bound construction.
We generalize our results to a general class of item bidding auctions that we
call bid-dependent auctions (including first-price auctions and all-pay
auctions) where the winner is always the highest bidder and each bidder's
payment depends only on his own bid.
Finally, we apply our techniques to discriminatory price multi-unit auctions.
We complement the results of [de Keijzer et al. 2013] for the case of
subadditive valuations, by providing a matching lower bound of 2. For the case
of submodular valuations, we provide a lower bound of 1.109. For the same class
of valuations, we were able to reproduce the upper bound of e/(e-1) using our
non-smooth approach.Comment: 37 pages, 5 figures, ACM Transactions on Economics and Computatio
On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources
We study the efficiency of the proportional allocation mechanism, that is
widely used to allocate divisible resources. Each agent submits a bid for each
divisible resource and receives a fraction proportional to her bids. We
quantify the inefficiency of Nash equilibria by studying the Price of Anarchy
(PoA) of the induced game under complete and incomplete information. When
agents' valuations are concave, we show that the Bayesian Nash equilibria can
be arbitrarily inefficient, in contrast to the well-known 4/3 bound for pure
equilibria. Next, we upper bound the PoA over Bayesian equilibria by 2 when
agents' valuations are subadditive, generalizing and strengthening previous
bounds on lattice submodular valuations. Furthermore, we show that this bound
is tight and cannot be improved by any simple or scale-free mechanism. Then we
switch to settings with budget constraints, and we show an improved upper bound
on the PoA over coarse-correlated equilibria. Finally, we prove that the PoA is
exactly 2 for pure equilibria in the polyhedral environment.Comment: To appear in SAGT 201
Smoothness for Simultaneous Composition of Mechanisms with Admission
We study social welfare of learning outcomes in mechanisms with admission. In
our repeated game there are bidders and mechanisms, and in each round
each mechanism is available for each bidder only with a certain probability.
Our scenario is an elementary case of simple mechanism design with incomplete
information, where availabilities are bidder types. It captures natural
applications in online markets with limited supply and can be used to model
access of unreliable channels in wireless networks.
If mechanisms satisfy a smoothness guarantee, existing results show that
learning outcomes recover a significant fraction of the optimal social welfare.
These approaches, however, have serious drawbacks in terms of plausibility and
computational complexity. Also, the guarantees apply only when availabilities
are stochastically independent among bidders.
In contrast, we propose an alternative approach where each bidder uses a
single no-regret learning algorithm and applies it in all rounds. This results
in what we call availability-oblivious coarse correlated equilibria. It
exponentially decreases the learning burden, simplifies implementation (e.g.,
as a method for channel access in wireless devices), and thereby addresses some
of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian
settings. Our main results are general composition theorems for smooth
mechanisms when valuation functions of bidders are lattice-submodular. They
rely on an interesting connection to the notion of correlation gap of
submodular functions over product lattices.Comment: Full version of WINE 2016 pape