1,355 research outputs found
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
Lottery pricing equilibria
We extend the notion of Combinatorial Walrasian Equilibrium, as defined by Feldman et al. [2013], to settings with budgets. When agents have budgets, the maximum social welfare as traditionally defined is not a suitable benchmark since it is overly optimistic. This motivated the liquid welfare of [Dobzinski and Paes Leme 2014] as an alternative. Observing that no combinatorial Walrasian equilibrium guarantees a non-zero fraction of the maximum liquid welfare in the absence of randomization, we instead work with randomized allocations and extend the notions of liquid welfare and Combinatorial Walrasian Equilibrium accordingly. Our generalization of the Combinatorial Walrasian Equilibrium prices lotteries over bundles of items rather than bundles, and we term it a lottery pricing equilibrium. Our results are two-fold. First, we exhibit an efficient algorithm which turns a randomized allocation with liquid expected welfare W into a lottery pricing equilibrium with liquid expected welfare 3-β5/2 W (β 0.3819-W). Next, given access to a demand oracle and an Ξ±-approximate oblivious rounding algorithm for the configuration linear program for the welfare maximization problem, we show how to efficiently compute a randomized allocation which is (a) supported on polynomially-many deterministic allocations and (b) obtains [nearly] an Ξ± fraction of the optimal liquid expected welfare. In the case of subadditive valuations, combining both results yields an efficient algorithm which computes a lottery pricing equilibrium obtaining a constant fraction of the optimal liquid expected welfare. Β© Copyright 2016 ACM
On Revenue Monotonicity in Combinatorial Auctions
Along with substantial progress made recently in designing near-optimal
mechanisms for multi-item auctions, interesting structural questions have also
been raised and studied. In particular, is it true that the seller can always
extract more revenue from a market where the buyers value the items higher than
another market? In this paper we obtain such a revenue monotonicity result in a
general setting. Precisely, consider the revenue-maximizing combinatorial
auction for items and buyers in the Bayesian setting, specified by a
valuation function and a set of independent item-type
distributions. Let denote the maximum revenue achievable under
by any incentive compatible mechanism. Intuitively, one would expect that
if distribution stochastically dominates .
Surprisingly, Hart and Reny (2012) showed that this is not always true even for
the simple case when is additive. A natural question arises: Are these
deviations contained within bounds? To what extent may the monotonicity
intuition still be valid? We present an {approximate monotonicity} theorem for
the class of fractionally subadditive (XOS) valuation functions , showing
that if stochastically dominates under
where is a universal constant. Previously, approximate monotonicity was
known only for the case : Babaioff et al. (2014) for the class of additive
valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation
functions.Comment: 10 page
The Economics of Lotteries: A Survey of the Literature
Lotteries represent an important source of government revenues in many states and countries, so they are of interest to public finance economists. In addition, lotteries provide researchers interested in microeconomic theory and consumer behavior with a type of experimental lab that allows economists to explore these topics. This paper surveys the existing literature on lotteries organized around these two central themes. The first section examines the microeconomic aspects of lotteries including consumer decision-making under uncertainty, price and income elasticities of demand for lottery tickets, cross-price elasticities of lottery ticket to each other and to other gambling products, consumer rationality and gambling, and the efficiency of lottery markets. The second section covers topics related to public finance and public choice including the revenue potential of lotteries, the tax efficiency and dead-weight loss of lottery games, the horizontal and vertical equity of lotteries, earmarking and the fungibility of lottery revenues, and individual state decisions to participate in participate in public lotteries.lotto, lottery, public finance, gambling
Optimal Multi-Unit Mechanisms with Private Demands
In the multi-unit pricing problem, multiple units of a single item are for
sale. A buyer's valuation for units of the item is ,
where the per unit valuation and the capacity are private information
of the buyer. We consider this problem in the Bayesian setting, where the pair
is drawn jointly from a given probability distribution. In the
\emph{unlimited supply} setting, the optimal (revenue maximizing) mechanism is
a pricing problem, i.e., it is a menu of lotteries. In this paper we show that
under a natural regularity condition on the probability distributions, which we
call \emph{decreasing marginal revenue}, the optimal pricing is in fact
\emph{deterministic}. It is a price curve, offering units of the item for a
price of , for every integer . Further, we show that the revenue as a
function of the prices is a \emph{concave} function, which implies that
the optimum price curve can be found in polynomial time. This gives a rare
example of a natural multi-parameter setting where we can show such a clean
characterization of the optimal mechanism. We also give a more detailed
characterization of the optimal prices for the case where there are only two
possible demands
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