3,218 research outputs found
Lower Bounds on Revenue of Approximately Optimal Auctions
We obtain revenue guarantees for the simple pricing mechanism of a single
posted price, in terms of a natural parameter of the distribution of buyers'
valuations. Our revenue guarantee applies to the single item n buyers setting,
with values drawn from an arbitrary joint distribution. Specifically, we show
that a single price drawn from the distribution of the maximum valuation Vmax =
max {V_1, V_2, ...,V_n} achieves a revenue of at least a 1/e fraction of the
geometric expecation of Vmax. This generic bound is a measure of how revenue
improves/degrades as a function of the concentration/spread of Vmax.
We further show that in absence of buyers' valuation distributions,
recruiting an additional set of identical bidders will yield a similar
guarantee on revenue. Finally, our bound also gives a measure of the extent to
which one can simultaneously approximate welfare and revenue in terms of the
concentration/spread of Vmax.Comment: The 8th Workshop on Internet and Network Economics (WINE
Brief Announcement: Bayesian Auctions with Efficient Queries
Generating good revenue is one of the most important problems in Bayesian auction design, and many (approximately) optimal dominant-strategy incentive compatible (DSIC) Bayesian mechanisms have been constructed for various auction settings. However, most existing studies do not consider the complexity for the seller to carry out the mechanism. It is assumed that the seller knows "each single bit" of the distributions and is able to optimize perfectly based on the entire distributions. Unfortunately this is a strong assumption and may not hold in reality: for example, when the value distributions have exponentially large supports or do not have succinct representations.
In this work we consider, for the first time, the query complexity of Bayesian mechanisms. We only allow the seller to have limited oracle accesses to the players\u27 value distributions, via quantile queries and value queries. For a large class of auction settings, we prove logarithmic lower-bounds for the query complexity for any DSIC Bayesian mechanism to be of any constant approximation to the optimal revenue. For single-item auctions and multi-item auctions with unit-demand or additive valuation functions, we prove tight upper-bounds via efficient query schemes, without requiring the distributions to be regular or have monotone hazard rate. Thus, in those auction settings the seller needs to access much less than the full distributions in order to achieve approximately optimal revenue
Sampling and Representation Complexity of Revenue Maximization
We consider (approximate) revenue maximization in auctions where the
distribution on input valuations is given via "black box" access to samples
from the distribution. We observe that the number of samples required -- the
sample complexity -- is tightly related to the representation complexity of an
approximately revenue-maximizing auction. Our main results are upper bounds and
an exponential lower bound on these complexities
The Sample Complexity of Auctions with Side Information
Traditionally, the Bayesian optimal auction design problem has been
considered either when the bidder values are i.i.d, or when each bidder is
individually identifiable via her value distribution. The latter is a
reasonable approach when the bidders can be classified into a few categories,
but there are many instances where the classification of bidders is a
continuum. For example, the classification of the bidders may be based on their
annual income, their propensity to buy an item based on past behavior, or in
the case of ad auctions, the click through rate of their ads. We introduce an
alternate model that captures this aspect, where bidders are a priori
identical, but can be distinguished based (only) on some side information the
auctioneer obtains at the time of the auction. We extend the sample complexity
approach of Dhangwatnotai et al. and Cole and Roughgarden to this model and
obtain almost matching upper and lower bounds. As an aside, we obtain a revenue
monotonicity lemma which may be of independent interest. We also show how to
use Empirical Risk Minimization techniques to improve the sample complexity
bound of Cole and Roughgarden for the non-identical but independent value
distribution case.Comment: A version of this paper appeared in STOC 201
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
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