3,068 research outputs found
Optimal Auctions vs. Anonymous Pricing
For selling a single item to agents with independent but non-identically
distributed values, the revenue optimal auction is complex. With respect to it,
Hartline and Roughgarden (2009) showed that the approximation factor of the
second-price auction with an anonymous reserve is between two and four. We
consider the more demanding problem of approximating the revenue of the ex ante
relaxation of the auction problem by posting an anonymous price (while supplies
last) and prove that their worst-case ratio is e. As a corollary, the
upper-bound of anonymous pricing or anonymous reserves versus the optimal
auction improves from four to . We conclude that, up to an factor,
discrimination and simultaneity are unimportant for driving revenue in
single-item auctions.Comment: 19 pages, 6 figures, To appear in 56th Annual IEEE Symposium on
Foundations of Computer Science (FOCS 2015
Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility
The revenue optimal mechanism for selling a single item to agents with
independent but non-identically distributed values is complex for agents with
linear utility (Myerson,1981) and has no closed-form characterization for
agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for
linear utility agents satisfying a natural regularity property, Alaei et al.
(2018) showed that simply posting an anonymous price is an e-approximation. We
give a parameterization of the regularity property that extends to agents with
non-linear utility and show that the approximation bound of anonymous pricing
for regular agents approximately extends to agents that satisfy this
approximate regularity property. We apply this approximation framework to prove
that anonymous pricing is a constant approximation to the revenue optimal
single-item auction for agents with public-budget utility, private-budget
utility, and (a special case of) risk-averse utility.Comment: Appeared at EC 201
Simple Pricing Schemes for the Cloud
The problem of pricing the cloud has attracted much recent attention due to
the widespread use of cloud computing and cloud services. From a theoretical
perspective, several mechanisms that provide strong efficiency or fairness
guarantees and desirable incentive properties have been designed. However,
these mechanisms often rely on a rigid model, with several parameters needing
to be precisely known in order for the guarantees to hold. In this paper, we
consider a stochastic model and show that it is possible to obtain good welfare
and revenue guarantees with simple mechanisms that do not make use of the
information on some of these parameters. In particular, we prove that a
mechanism that sets the same price per time step for jobs of any length
achieves at least 50% of the welfare and revenue obtained by a mechanism that
can set different prices for jobs of different lengths, and the ratio can be
improved if we have more specific knowledge of some parameters. Similarly, a
mechanism that sets the same price for all servers even though the servers may
receive different kinds of jobs can provide a reasonable welfare and revenue
approximation compared to a mechanism that is allowed to set different prices
for different servers.Comment: To appear in the 13th Conference on Web and Internet Economics
(WINE), 2017. A preliminary version was presented at the 12th Workshop on the
Economics of Networks, Systems and Computation (NetEcon), 201
The Value of Knowing Your Enemy
Many auction settings implicitly or explicitly require that bidders are
treated equally ex-ante. This may be because discrimination is philosophically
or legally impermissible, or because it is practically difficult to implement
or impossible to enforce. We study so-called {\em anonymous} auctions to
understand the revenue tradeoffs and to develop simple anonymous auctions that
are approximately optimal.
We consider digital goods settings and show that the optimal anonymous,
dominant strategy incentive compatible auction has an intuitive structure ---
imagine that bidders are randomly permuted before the auction, then infer a
posterior belief about bidder i's valuation from the values of other bidders
and set a posted price that maximizes revenue given this posterior.
We prove that no anonymous mechanism can guarantee an approximation better
than O(n) to the optimal revenue in the worst case (or O(log n) for regular
distributions) and that even posted price mechanisms match those guarantees.
Understanding that the real power of anonymous mechanisms comes when the
auctioneer can infer the bidder identities accurately, we show a tight O(k)
approximation guarantee when each bidder can be confused with at most k "higher
types". Moreover, we introduce a simple mechanism based on n target prices that
is asymptotically optimal and build on this mechanism to extend our results to
m-unit auctions and sponsored search
Pricing for Online Resource Allocation: Intervals and Paths
We present pricing mechanisms for several online resource allocation problems
which obtain tight or nearly tight approximations to social welfare. In our
settings, buyers arrive online and purchase bundles of items; buyers' values
for the bundles are drawn from known distributions. This problem is closely
related to the so-called prophet-inequality of Krengel and Sucheston and its
extensions in recent literature. Motivated by applications to cloud economics,
we consider two kinds of buyer preferences. In the first, items correspond to
different units of time at which a resource is available; the items are
arranged in a total order and buyers desire intervals of items. The second
corresponds to bandwidth allocation over a tree network; the items are edges in
the network and buyers desire paths.
Because buyers' preferences have complementarities in the settings we
consider, recent constant-factor approximations via item prices do not apply,
and indeed strong negative results are known. We develop static, anonymous
bundle pricing mechanisms.
For the interval preferences setting, we show that static, anonymous bundle
pricings achieve a sublogarithmic competitive ratio, which is optimal (within
constant factors) over the class of all online allocation algorithms, truthful
or not. For the path preferences setting, we obtain a nearly-tight logarithmic
competitive ratio. Both of these results exhibit an exponential improvement
over item pricings for these settings. Our results extend to settings where the
seller has multiple copies of each item, with the competitive ratio decreasing
linearly with supply. Such a gradual tradeoff between supply and the
competitive ratio for welfare was previously known only for the single item
prophet inequality
Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
We study equilibria of markets with heterogeneous indivisible goods and
consumers with combinatorial preferences. It is well known that a
competitive equilibrium is not guaranteed to exist when valuations are not
gross substitutes. Given the widespread use of bundling in real-life markets,
we study its role as a stabilizing and coordinating device by considering the
notion of \emph{competitive bundling equilibrium}: a competitive equilibrium
over the market induced by partitioning the goods for sale into fixed bundles.
Compared to other equilibrium concepts involving bundles, this notion has the
advantage of simulatneous succinctness ( prices) and market clearance.
Our first set of results concern welfare guarantees. We show that in markets
where consumers care only about the number of goods they receive (known as
multi-unit or homogeneous markets), even in the presence of complementarities,
there always exists a competitive bundling equilibrium that guarantees a
logarithmic fraction of the optimal welfare, and this guarantee is tight. We
also establish non-trivial welfare guarantees for general markets, two-consumer
markets, and markets where the consumer valuations are additive up to a fixed
budget (budget-additive).
Our second set of results concern revenue guarantees. Motivated by the fact
that the revenue extracted in a standard competitive equilibrium may be zero
(even with simple unit-demand consumers), we show that for natural subclasses
of gross substitutes valuations, there always exists a competitive bundling
equilibrium that extracts a logarithmic fraction of the optimal welfare, and
this guarantee is tight. The notion of competitive bundling equilibrium can
thus be useful even in markets which possess a standard competitive
equilibrium
Designing cost-sharing methods for Bayesian games
We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players
- …