7,173 research outputs found
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
Substitute Valuations: Generation and Structure
Substitute valuations (in some contexts called gross substitute valuations)
are prominent in combinatorial auction theory. An algorithm is given in this
paper for generating a substitute valuation through Monte Carlo simulation. In
addition, the geometry of the set of all substitute valuations for a fixed
number of goods K is investigated. The set consists of a union of polyhedrons,
and the maximal polyhedrons are identified for K=4. It is shown that the
maximum dimension of the maximal polyhedrons increases with K nearly as fast as
two to the power K. Consequently, under broad conditions, if a combinatorial
algorithm can present an arbitrary substitute valuation given a list of input
numbers, the list must grow nearly as fast as two to the power K.Comment: Revision includes more background and explanation
Double Auctions in Markets for Multiple Kinds of Goods
Motivated by applications such as stock exchanges and spectrum auctions,
there is a growing interest in mechanisms for arranging trade in two-sided
markets. Existing mechanisms are either not truthful, or do not guarantee an
asymptotically-optimal gain-from-trade, or rely on a prior on the traders'
valuations, or operate in limited settings such as a single kind of good. We
extend the random market-halving technique used in earlier works to markets
with multiple kinds of goods, where traders have gross-substitute valuations.
We present MIDA: a Multi Item-kind Double-Auction mechanism. It is prior-free,
truthful, strongly-budget-balanced, and guarantees near-optimal gain from trade
when market sizes of all goods grow to at a similar rate.Comment: Full version of IJCAI-18 paper, with 2 figures. Previous names:
"MIDA: A Multi Item-type Double-Auction Mechanism", "A Random-Sampling
Double-Auction Mechanism". 10 page
Auctioning Many Divisible Goods
We study the theory and practical implementation of auctioning many divisible goods. With multiple related goods, price discovery is important not only to reduce the winnerās curse, but more importantly, to simplify the bidderās decision problem and to facilitate the revelation of preferences in the bids. Simultaneous clock auctions are especially desirable formats for auctioning many divisible goods. We examine the properties of these auctions and discuss important practical considerations in applying them.Auctions, Electricity Auctions, Market Design, Clock Auctions
A Double-Sided Multiunit Combinatorial Auction for Substitutes: Theory and Algorithms
Combinatorial exchanges have existed for a long time in securities markets. In these auctions buyers and sellers can place orders on combinations, or bundles of different securities. These orders are conjunctive: they are matched only if the full bundle is available. On business-to-business (B2B) exchanges, buyers have the choice to receive the same product with different attributes; for instance the same product can be produced by different sellers. A buyer indicates his preference by submitting a disjunctive order, where he specifies how much of the product he wants, and how much he values each attribute. Only the goods with the best attributes and prices will be matched. This article considers a doubled-sided multi-unit combinatorial auction for substitutes, that is, a uniform price auction where buyers and sellers place both types of orders, conjunctive and disjunctive. We prove the existence of a linear price which is both competitive and surplus-maximizing when goods are perfectly divisible, and nearly so otherwise. We describe an algorithm to clear the market, which is particularly efficient when the number of traders is large.Combinatorial auction, economic equilibrium
Price Competition in Online Combinatorial Markets
We consider a single buyer with a combinatorial preference that would like to
purchase related products and services from different vendors, where each
vendor supplies exactly one product. We study the general case where subsets of
products can be substitutes as well as complementary and analyze the game that
is induced on the vendors, where a vendor's strategy is the price that he asks
for his product. This model generalizes both Bertrand competition (where
vendors are perfect substitutes) and Nash bargaining (where they are perfect
complements), and captures a wide variety of scenarios that can appear in
complex crowd sourcing or in automatic pricing of related products.
We study the equilibria of such games and show that a pure efficient
equilibrium always exists. In the case of submodular buyer preferences we fully
characterize the set of pure Nash equilibria, essentially showing uniqueness.
For the even more restricted "substitutes" buyer preferences we also prove
uniqueness over {\em mixed} equilibria. Finally we begin the exploration of
natural generalizations of our setting such as when services have costs, when
there are multiple buyers or uncertainty about the the buyer's valuation, and
when a single vendor supplies multiple products.Comment: accept to WWW'14 (23rd International World Wide Web Conference
PATENT LICENSING BY MEANS OF AN AUCTION: INTERNAL VS. EXTERNAL PATENTEE
An independent research laboratory owns a patented process innovation that can be licensed by means of an auction to two Cournot duopolists producing differentiated goods. For large innovations and close enough substitute goods the patentee auctions oĀ¤ only one license, preventing the full diffusion of the innovation. For this range of parameters, however, if the laboratory merged with one of the firms in the industry, full technology diffusion would be implemented as the merged entity would always license the innovation to the rival firm. This explains that, in this context, a vertical merger is both profitable and welfare improving.Patent licensing, two-part tariff contracts, vertical mergers
Ascending auctions and Walrasian equilibrium
We present a family of submodular valuation classes that generalizes gross
substitute. We show that Walrasian equilibrium always exist for one class in
this family, and there is a natural ascending auction which finds it. We prove
some new structural properties on gross-substitute auctions which, in turn,
show that the known ascending auctions for this class (Gul-Stacchetti and
Ausbel) are, in fact, identical. We generalize these two auctions, and provide
a simple proof that they terminate in a Walrasian equilibrium
Concepts and Properties of Substitute Goods
We distinguish two notions of substitutes for discrete inputs of a firm. Class substitutes are defined assuming that units of a given input have the same price while unitary substitutes treat each unit as a distinct input with its own price. Unitary substitutes is necessary and sufficient for such results as the robust existence of equilibrium, the robust inclusion of the Vickrey outcome in the core, and the law of aggregate demand, while the class substitutes condition is necessary and sufficient for robust monotonicity of certain auction/tatonnement processes. We analyze the concept of pseudo-equilibrium which extends, and in some sense approximates, the concept of equilibrium when no equilibrium exists. We characterize unitary substitutes as class substitutes plus two other properties. We extend the analysis to divisible inputs, with a particular focus on robustness of the concepts and their relation to the generalized law of aggregate demand.
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