11 research outputs found
On the Complexity of Dynamic Mechanism Design
We introduce a dynamic mechanism design problem in which the designer wants
to offer for sale an item to an agent, and another item to the same agent at
some point in the future. The agent's joint distribution of valuations for the
two items is known, and the agent knows the valuation for the current item (but
not for the one in the future). The designer seeks to maximize expected
revenue, and the auction must be deterministic, truthful, and ex post
individually rational. The optimum mechanism involves a protocol whereby the
seller elicits the buyer's current valuation, and based on the bid makes two
take-it-or-leave-it offers, one for now and one for the future. We show that
finding the optimum deterministic mechanism in this situation - arguably the
simplest meaningful dynamic mechanism design problem imaginable - is NP-hard.
We also prove several positive results, among them a polynomial linear
programming-based algorithm for the optimum randomized auction (even for many
bidders and periods), and we show strong separations in revenue between
non-adaptive, adaptive, and randomized auctions, even when the valuations in
the two periods are uncorrelated. Finally, for the same problem in an
environment in which contracts cannot be enforced, and thus perfection of
equilibrium is necessary, we show that the optimum randomized mechanism
requires multiple rounds of cheap talk-like interactions
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 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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Algorithmic Mechanism Design in Dynamic Environments
Over the past few decades, a new field has emerged from the interaction between Computer Science and Game Theory: Algorithmic Mechanism Design. The field has seen tremendous growth and has been extremely successful in tackling a wide variety of problems. Despite all this progress, the vast majority of the literature to date focuses on static, one-time decisions. In many situations of interest, however, this simplification is too far from reality. For example, a search engine must choose how to allocate its advertising inventory in the face of changing search queries and advertiser budgets. In a cloud computing center resources need to be dynamically reallocated in response to the arrival of new computational tasks of varying priority. This thesis explores the interplay of incentives and the dynamic nature of decision-making in the design of efficient mechanisms.In the first part of this thesis we study Dynamic Auction Design. We introduce a novel class of dynamic auction problems in which a monopolist is selling items in consecutive stages to buyers. We study these problem from several different perspectives: {\em Computational Complexity}, i.e. how hard is it to compute the optimal auction, {\em Competition Complexity}, i.e. how much additional competition is necessary for a standard Vickrey (second-price) auction at every stage to extract more revenue than the optimal auction, {\em Power of Adaptivity}, i.e. what is the revenue gap between adaptive and non-adaptive auctions,{\em Power of Commitment}, i.e. what happens if the seller cannot commit to her future behavior.In the second part of this thesis we study Dynamic Fair Division. We introduce a novel class of resource allocation problems in which resources are shared between agents dynamically arriving and departing over time. For a single resource, when agents are present, there is only one truly ``fair'' allocation: each agent receives of the resource. Implementing this static solution over time is notoriously impractical. There are too many disruptions to existing allocations: for a new agent to get her fair share, all other agents must give up a small piece. What if, at every arrivals we could only reclaim resources from a fixed number of agents ? We provide non-wasteful such algorithms that are almost optimal with respect to fairness, even for multiple, heterogeneous resources
Fair and Efficient Memory Sharing: Confronting Free Riders
A cache memory unit needs to be shared among n strategic agents. Each agent has different preferences over the files to be brought into memory. The goal is to design a mechanism that elicits these preferences in a truthful manner and outputs a fair and efficient memory allocation. A trivially truthful and fair solution would isolate each agent to a 1/n fraction of the memory. However, this could be very inefficient if the agents have similar preferences and, thus, there is room for cooperation. On the other hand, if the agents are not isolated, unless the mechanism is carefully designed, they have incentives to misreport their preferences and free ride on the files that others bring into memory. In this paper we explore the power and limitations of truthful mechanisms in this setting. We demonstrate that mechanisms blocking agents from accessing parts of the memory can achieve improved efficiency guarantees, despite the inherent inefficiencies of blocking