696 research outputs found
Core-competitive Auctions
One of the major drawbacks of the celebrated VCG auction is its low (or zero)
revenue even when the agents have high value for the goods and a {\em
competitive} outcome could have generated a significant revenue. A competitive
outcome is one for which it is impossible for the seller and a subset of buyers
to `block' the auction by defecting and negotiating an outcome with higher
payoffs for themselves. This corresponds to the well-known concept of {\em
core} in cooperative game theory.
In particular, VCG revenue is known to be not competitive when the goods
being sold have complementarities. A bottleneck here is an impossibility result
showing that there is no auction that simultaneously achieves competitive
prices (a core outcome) and incentive-compatibility.
In this paper we try to overcome the above impossibility result by asking the
following natural question: is it possible to design an incentive-compatible
auction whose revenue is comparable (even if less) to a competitive outcome?
Towards this, we define a notion of {\em core-competitive} auctions. We say
that an incentive-compatible auction is -core-competitive if its
revenue is at least fraction of the minimum revenue of a
core-outcome. We study the Text-and-Image setting. In this setting, there is an
ad slot which can be filled with either a single image ad or text ads. We
design an core-competitive randomized auction and an
competitive deterministic auction for the Text-and-Image
setting. We also show that both factors are tight
On the Economic Efficiency of the Combinatorial Clock Auction
Since the 1990s spectrum auctions have been implemented world-wide. This has
provided for a practical examination of an assortment of auction mechanisms
and, amongst these, two simultaneous ascending price auctions have proved to be
extremely successful. These are the simultaneous multiround ascending auction
(SMRA) and the combinatorial clock auction (CCA). It has long been known that,
for certain classes of valuation functions, the SMRA provides good theoretical
guarantees on social welfare. However, no such guarantees were known for the
CCA.
In this paper, we show that CCA does provide strong guarantees on social
welfare provided the price increment and stopping rule are well-chosen. This is
very surprising in that the choice of price increment has been used primarily
to adjust auction duration and the stopping rule has attracted little
attention. The main result is a polylogarithmic approximation guarantee for
social welfare when the maximum number of items demanded by a
bidder is fixed. Specifically, we show that either the revenue of the CCA is at
least an -fraction of
the optimal welfare or the welfare of the CCA is at least an
-fraction of the optimal welfare, where
is the number of bidders and is the number of items. As a corollary, the
welfare ratio -- the worst case ratio between the social welfare of the optimum
allocation and the social welfare of the CCA allocation -- is at most
. We emphasize that this latter
result requires no assumption on bidders valuation functions. Finally, we prove
that such a dependence on is necessary. In particular, we show
that the welfare ratio of the CCA is at least
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
Ascending auctions: some impossibility results and their resolutions with final price discounts
When bidders are not substitutes, we show that there is no standard ascend-ing auction that implements a bidder-optimal competitive equilibrium under truthful bidding. Such an impossibility holds also in environments where the Vickrey payoff vector is a competitive equilibrium payoff and is thus stronger than de Vries, Schummer and Vohra s [On ascending Vickrey auctions for het-erogeneous objects, J. Econ. Theory, 132, 95-118] impossibility result with regards to the Vickrey payoff vector under general valuations. Similarly to Mishra and Parkes [Ascending price Vickrey auctions for general valuations, J. Econ. Theory, 132, 335-366], the impossibility can be circumvented by giving price discounts to the bidders from the final vector of prices. Nevertheless, the similarity is misleading: the solution we propose satisfies a minimality infor-mation revelation property that fails to be satisfied in any ascending auction that implements the Vickrey payoffs for general valuations. We investigate related issues when strictly positive increments have to be used under general continuous valuations.ascending auctions ; combinatorial auctions ; bidder-optimal competitive equilibrium ; non-linear pricing ; Vickrey payoffs ; increments
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