16,510 research outputs found
On Optimal Mechanisms in the Two-Item Single-Buyer Unit-Demand Setting
We consider the problem of designing a revenue-optimal mechanism in the
two-item, single-buyer, unit-demand setting when the buyer's valuations, , are uniformly distributed in an arbitrary rectangle
in the positive quadrant. We provide a complete and
explicit solution for arbitrary nonnegative values of . We
identify five simple structures, each with at most five (possibly stochastic)
menu items, and prove that the optimal mechanism has one of the five
structures. We also characterize the optimal mechanism as a function of , and . When is low, the optimal mechanism is a posted price
mechanism with an exclusion region; when is high, it is a posted price
mechanism without an exclusion region. Our results are the first to show the
existence of optimal mechanisms with no exclusion region, to the best of our
knowledge
Pricing Ad Slots with Consecutive Multi-unit Demand
We consider the optimal pricing problem for a model of the rich media
advertisement market, as well as other related applications. In this market,
there are multiple buyers (advertisers), and items (slots) that are arranged in
a line such as a banner on a website. Each buyer desires a particular number of
{\em consecutive} slots and has a per-unit-quality value (dependent on
the ad only) while each slot has a quality (dependent on the position
only such as click-through rate in position auctions). Hence, the valuation of
the buyer for item is . We want to decide the allocations and
the prices in order to maximize the total revenue of the market maker.
A key difference from the traditional position auction is the advertiser's
requirement of a fixed number of consecutive slots. Consecutive slots may be
needed for a large size rich media ad. We study three major pricing mechanisms,
the Bayesian pricing model, the maximum revenue market equilibrium model and an
envy-free solution model. Under the Bayesian model, we design a polynomial time
computable truthful mechanism which is optimum in revenue. For the market
equilibrium paradigm, we find a polynomial time algorithm to obtain the maximum
revenue market equilibrium solution. In envy-free settings, an optimal solution
is presented when the buyers have the same demand for the number of consecutive
slots. We conduct a simulation that compares the revenues from the above
schemes and gives convincing results.Comment: 27page
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
Pricing Multi-Unit Markets
We study the power and limitations of posted prices in multi-unit markets,
where agents arrive sequentially in an arbitrary order. We prove upper and
lower bounds on the largest fraction of the optimal social welfare that can be
guaranteed with posted prices, under a range of assumptions about the
designer's information and agents' valuations. Our results provide insights
about the relative power of uniform and non-uniform prices, the relative
difficulty of different valuation classes, and the implications of different
informational assumptions. Among other results, we prove constant-factor
guarantees for agents with (symmetric) subadditive valuations, even in an
incomplete-information setting and with uniform prices
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