43 research outputs found
Representations and Parameterizations of Combinatorial Auctions
Combinatorial auctions (CAs) are an important mechanism for allocating multiple items while allowing agents to specify preferences over bundles of items. In order to communicate these preferences, agents submit bids, which consist of one or more items and a value indicating the agent’s preference for these items. The process of determining the allocation of items is known as the winner determination problem (WDP). WDP for CAs is known to be NP-complete in the general case.
We consider two distinct graph representations of a CA; the bid graph and the item graph. In a bid graph, vertices represent bids, and two vertices are adjacent if and only if the bids share items in common. In an item graph, each vertex represents a unique item, there is a vertex for each item, and any bid submitted by any agent must induce a connected subgraph of the item graph. We introduce a new definition of combinatorial
auction equivalence by declaring two CAs equivalent if and only if their bid graphs are isomorphic.
Parameterized complexity theory can be used to further distinguish between NP-hard
problems. In order to make use of parameterized complexity theory in the investigation of a problem, we aim to find one or more parameters that describe some aspect of the problem such that if we fix these parameters, then either the problem is still hard (fixed-parameter intractable), or the problem can be solved in polynomial time (fixed-parameter tractable).
We analyze WDP using bid graphs from within the formal scope of parameterized complexity theory. This approach has not previously been used to analyze WDP for CAs, although it has been used to solve set packing, which is related to WDP for CAs and is discussed in detail. We investigate a few parameterizations of WDP; some of the parameterizations are shown to be fixed-parameter intractable, while others are fixed-parameter tractable. We also analyze WDP when the graph class of a bid graph is restricted.
We also discuss relationships between item graphs and bid graphs. Although both graphs can represent the same problem, there is little previous work analyzing direct relationships between them. Our discussion on these relationships begins with a result by
Conitzer et al. [7], which focuses on the item graph representation and its treewidth, a property of a graph that measures how close the graph is to a tree. From a result by Gavril, if an item graph has treewidth one, then the bid graph must be chordal [16]. To apply the other direction of Gavril’s theorem, we use our new definition of CA equivalence. With this new definition, Gavril’s result shows that if a bid graph of a CA is chordal, then we can construct an item graph that has treewidth one for some equivalent CA
An Investigation Report on Auction Mechanism Design
Auctions are markets with strict regulations governing the information
available to traders in the market and the possible actions they can take.
Since well designed auctions achieve desirable economic outcomes, they have
been widely used in solving real-world optimization problems, and in
structuring stock or futures exchanges. Auctions also provide a very valuable
testing-ground for economic theory, and they play an important role in
computer-based control systems.
Auction mechanism design aims to manipulate the rules of an auction in order
to achieve specific goals. Economists traditionally use mathematical methods,
mainly game theory, to analyze auctions and design new auction forms. However,
due to the high complexity of auctions, the mathematical models are typically
simplified to obtain results, and this makes it difficult to apply results
derived from such models to market environments in the real world. As a result,
researchers are turning to empirical approaches.
This report aims to survey the theoretical and empirical approaches to
designing auction mechanisms and trading strategies with more weights on
empirical ones, and build the foundation for further research in the field
Generalization in portfolio-based algorithm selection
Portfolio-based algorithm selection has seen tremendous practical success
over the past two decades. This algorithm configuration procedure works by
first selecting a portfolio of diverse algorithm parameter settings, and then,
on a given problem instance, using an algorithm selector to choose a parameter
setting from the portfolio with strong predicted performance. Oftentimes, both
the portfolio and the algorithm selector are chosen using a training set of
typical problem instances from the application domain at hand. In this paper,
we provide the first provable guarantees for portfolio-based algorithm
selection. We analyze how large the training set should be to ensure that the
resulting algorithm selector's average performance over the training set is
close to its future (expected) performance. This involves analyzing three key
reasons why these two quantities may diverge: 1) the learning-theoretic
complexity of the algorithm selector, 2) the size of the portfolio, and 3) the
learning-theoretic complexity of the algorithm's performance as a function of
its parameters. We introduce an end-to-end learning-theoretic analysis of the
portfolio construction and algorithm selection together. We prove that if the
portfolio is large, overfitting is inevitable, even with an extremely simple
algorithm selector. With experiments, we illustrate a tradeoff exposed by our
theoretical analysis: as we increase the portfolio size, we can hope to include
a well-suited parameter setting for every possible problem instance, but it
becomes impossible to avoid overfitting.Comment: AAAI 202
Measuring the Efficiency of an FCC Spectrum Auction
FCC spectrum auctions sell licenses to provide mobile phone service in designated geographic territories. We propose a method to structurally estimate the deterministic component of bidder valuations and apply it to the 1995–1996 C-block auction. We base our estimation of bidder values on a pairwise stability condition, which implies that two bidders cannot exchange licenses in a way that increases total surplus. Pairwise stability holds in many theoretical models of simultaneous ascending auctions, including some models of intimidatory collusion and demand reduction. Pairwise stability is also approximately satisfied in data that we examine from economic experiments. The lack of post-auction resale also suggests pairwise stability. Using our estimates of deterministic valuations, we measure the allocative efficiency of the C-block outcome.
Truthful and Fair Resource Allocation
How should we divide a good or set of goods among a set of agents? There are various constraints that we can consider. We consider two particular constraints. The first is fairness - how can we find fair allocations? The second is truthfulness - what if we do not know agents valuations for the goods being allocated? What if these valuations need to be elicited, and agents will misreport their valuations if it is beneficial? Can we design procedures that elicit agents' true valuations while preserving the quality of the allocation? We consider truthful and fair resource allocation procedures through a computational lens. We first study fair division of a heterogeneous, divisible good, colloquially known as the cake cutting problem. We depart from the existing literature and assume that agents have restricted valuations that can be succinctly communicated. We consider the problems of welfare-maximization, expressiveness, and truthfulness in cake cutting under this model. In the second part of this dissertation we consider truthfulness in settings where payments can be used to incentivize agents to truthfully reveal their private information. A mechanism asks agents to report their private preference information and computes an allocation and payments based on these reports. The mechanism design problem is to find incentive compatible mechanisms which incentivize agents to truthfully reveal their private information and simultaneously compute allocations with desirable properties. The traditional approach to mechanism design specifies mechanisms by hand and proves that certain desirable properties are satisfied. This limits the design space to mechanisms that can be written down and analyzed. We take a computational approach, giving computational procedures that produce mechanisms with desirable properties. Our first contribution designs a procedure that modifies heuristic branch and bound search and makes it usable as the allocation algorithm in an incentive compatible mechanism. Our second contribution draws a novel connection between incentive compatible mechanisms and machine learning. We use this connection to learn payment rules to pair with provided allocation rules. Our payment rules are not exactly incentive compatibility, but they minimize a measure of how much agents can gain by misreporting.Engineering and Applied Science
Measuring the Efficiency of an FCC Spectrum Auction
FCC spectrum auctions sell licenses to provide mobile phone service in
designated geographic territories. We propose a method to structurally
estimate the deterministic component of bidder valuations and apply it
to the 1995-1996 C-block auction. We base our estimation of bidder
values on a pairwise stability condition, which implies that two bidders
cannot exchange licenses in a way that increases total surplus. Pairwise
stability holds in many theoretical models of simultaneous ascending
auctions, including some models of intimidatory collusion and demand
reduction. Pairwise stability is also approximately satisfied in data
that we examine from economic experiments. The lack of post-auction
resale also suggests pairwise stability. Using our estimates of
deterministic valuations, we measure the allocative efficiency of the
C-block outcome
Market-Based Scheduling in Distributed Computing Systems
In verteilten Rechensystemen (bspw. im Cluster und Grid Computing) kann eine Knappheit der zur Verfügung stehenden Ressourcen auftreten. Hier haben Marktmechanismen das Potenzial, Ressourcenbedarf und -angebot durch geeignete Anreizmechanismen zu koordinieren und somit die ökonomische Effizienz des Gesamtsystems zu steigern. Diese Arbeit beschäftigt sich anhand vier spezifischer Anwendungsszenarien mit der Frage, wie Marktmechanismen für verteilte Rechensysteme ausgestaltet sein sollten
Combined negotiations in E-commerce : concepts, architecture, and implementation
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal
Measuring the Efficiency of an FCC Spectrum Auction
FCC spectrum auctions sell licenses to provide mobile phone service in
designated geographic territories. We propose a method to structurally
estimate the deterministic component of bidder valuations and apply it
to the 1995-1996 C-block auction. We base our estimation of bidder
values on a pairwise stability condition, which implies that two bidders
cannot exchange licenses in a way that increases total surplus. Pairwise
stability holds in many theoretical models of simultaneous ascending
auctions, including some models of intimidatory collusion and demand
reduction. Pairwise stability is also approximately satisfied in data
that we examine from economic experiments. The lack of post-auction
resale also suggests pairwise stability. Using our estimates of
deterministic valuations, we measure the allocative efficiency of the
C-block outcome