1,462 research outputs found
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
On Simultaneous Two-player Combinatorial Auctions
We consider the following communication problem: Alice and Bob each have some
valuation functions and over subsets of items,
and their goal is to partition the items into in a way that
maximizes the welfare, . We study both the allocation
problem, which asks for a welfare-maximizing partition and the decision
problem, which asks whether or not there exists a partition guaranteeing
certain welfare, for binary XOS valuations. For interactive protocols with
communication, a tight 3/4-approximation is known for both
[Fei06,DS06].
For interactive protocols, the allocation problem is provably harder than the
decision problem: any solution to the allocation problem implies a solution to
the decision problem with one additional round and additional bits of
communication via a trivial reduction. Surprisingly, the allocation problem is
provably easier for simultaneous protocols. Specifically, we show:
1) There exists a simultaneous, randomized protocol with polynomial
communication that selects a partition whose expected welfare is at least
of the optimum. This matches the guarantee of the best interactive, randomized
protocol with polynomial communication.
2) For all , any simultaneous, randomized protocol that
decides whether the welfare of the optimal partition is or correctly with probability requires
exponential communication. This provides a separation between the attainable
approximation guarantees via interactive () versus simultaneous () protocols with polynomial communication.
In other words, this trivial reduction from decision to allocation problems
provably requires the extra round of communication
Auctions with Severely Bounded Communication
We study auctions with severe bounds on the communication allowed: each
bidder may only transmit t bits of information to the auctioneer. We consider
both welfare- and profit-maximizing auctions under this communication
restriction. For both measures, we determine the optimal auction and show that
the loss incurred relative to unconstrained auctions is mild. We prove
non-surprising properties of these kinds of auctions, e.g., that in optimal
mechanisms bidders simply report the interval in which their valuation lies in,
as well as some surprising properties, e.g., that asymmetric auctions are
better than symmetric ones and that multi-round auctions reduce the
communication complexity only by a linear factor
On the Complexity of Computing an Equilibrium in Combinatorial Auctions
We study combinatorial auctions where each item is sold separately but
simultaneously via a second price auction. We ask whether it is possible to
efficiently compute in this game a pure Nash equilibrium with social welfare
close to the optimal one.
We show that when the valuations of the bidders are submodular, in many
interesting settings (e.g., constant number of bidders, budget additive
bidders) computing an equilibrium with good welfare is essentially as easy as
computing, completely ignoring incentives issues, an allocation with good
welfare. On the other hand, for subadditive valuations, we show that computing
an equilibrium requires exponential communication. Finally, for XOS (a.k.a.
fractionally subadditive) valuations, we show that if there exists an efficient
algorithm that finds an equilibrium, it must use techniques that are very
different from our current ones
Public projects, Boolean functions and the borders of Border's theorem
Border's theorem gives an intuitive linear characterization of the feasible
interim allocation rules of a Bayesian single-item environment, and it has
several applications in economic and algorithmic mechanism design. All known
generalizations of Border's theorem either restrict attention to relatively
simple settings, or resort to approximation. This paper identifies a
complexity-theoretic barrier that indicates, assuming standard complexity class
separations, that Border's theorem cannot be extended significantly beyond the
state-of-the-art. We also identify a surprisingly tight connection between
Myerson's optimal auction theory, when applied to public project settings, and
some fundamental results in the analysis of Boolean functions.Comment: Accepted to ACM EC 201
Coordination of Purchasing and Bidding Activities Across Markets
In both consumer purchasing and industrial procurement, combinatorial interdependencies among the items to be purchased are commonplace. E-commerce compounds the problem by providing more opportunities for switching suppliers at low costs, but also potentially eases the problem by enabling automated market decision-making systems, commonly referred to as trading agents, to make purchasing decisions in an integrated manner across markets. Most of the existing research related to trading agents assumes that there exists a combinatorial market mechanism in which buyers (or sellers) can bid (or sell) service or merchant bundles. Todayâ??s prevailing e-commerce practice, however, does not support this assumption in general and thus limits the practical applicability of these approaches. We are investigating a new approach to deal with the combinatorial interdependency challenges for online markets. This approach relies on existing commercial online market institutions such as posted-price markets and various online auctions that sell single items. It uses trading agents to coordinate a buyerâ??s purchasing and bidding activities across multiple online markets simultaneously to achieve the best overall procurement effectiveness. This paper presents two sets of models related to this approach. The first set of models formalizes optimal purchasing decisions across posted-price markets with fixed transaction costs. Flat shipping costs, a common e-tailing practice, are captured in these models. We observe that making optimal purchasing decisions in this context is NP-hard in the strong sense and suggest several efficient computational methods based on discrete location theory. The second set of models is concerned with the coordination of bidding activities across multiple online auctions. We study the underlying coordination problem for a collection of first or second-price sealed-bid auctions and derive the optimal coordination and bidding policies.
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