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Setting equilibrium prices, approximately

2013
*
ACM SIGecom Exchanges
*

We outline recent results, positive and negative, on

doi:10.1145/2509013.2509017
fatcat:mnlqfizrlfgqtkpp6bue4nhoy4
*pricing*indivisible goods to*approximately*maximize social welfare. ... We describe a relaxation of standard*pricing*problems in which a seller can bundle goods together prior to sale. ... We will review some well-known impossibility results, then turn to*approximation*methods as a way to circumvent them. First, we must establish what it means to*set*"appropriate"*prices*. ...##
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Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
[chapter]

2015
*
Lecture Notes in Computer Science
*

Competitive

doi:10.1007/978-3-662-48995-6_22
fatcat:jzqzmax4bnap5muhrfp424vsfq
*equilibrium*, the central*equilibrium*notion in markets with indivisible goods, is based on*pricing*each good such that the demand for goods equals their supply and the market clears. ... of*pricing*bundles rather than individual goods. ...*Set*the*price*of every such bundle to p B = v − for some small = (v). ...##
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2 A SAM as a Walrasian Equilibrium Framework
[chapter]

2019
*
Non-Extensive Entropy Econometrics for Low Frequency Series
*

Thus, such a statistical

doi:10.1515/9783110605914-010
fatcat:bqyzv3azprgl7ecm7xfkrihr6u
*equilibrium**approximates*, but does not achieve, Pareto-efficiency. ... The observed*equilibrium**price*system is a (locally) stable*equilibrium*of trial-and-error*price*adjustment. ...##
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On the complexity of price equilibria

2003
*
Journal of computer and system sciences (Print)
*

*approximates*the market

*equilibrium*arbitrarily close when the number of goods is bounded and the utilities linear. ... We prove complexity,

*approximability*, and inapproximability results for the problem of finding an exchange

*equilibrium*in markets with indivisible (integer) goods, most notably a polynomial algorithm that ... We shall guess (an

*approximation*to) the

*equilibrium*

*prices*p Ã by looking at all these equivalence classes. ...

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Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
[article]

2014
*
arXiv
*
pre-print

Compared to other

arXiv:1406.0576v1
fatcat:5oybgrza5rdm5pu4wcxiuutusq
*equilibrium*concepts involving bundles, this notion has the advantage of simulatneous succinctness (O(m)*prices*) and market clearance. ... Our first*set*of results concern welfare guarantees. ...*set*under these*prices*. ...##
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Approximating Market Equilibria
[chapter]

2003
*
Lecture Notes in Computer Science
*

Using this notion, we present the first fully polynomial-time

doi:10.1007/978-3-540-45198-3_9
fatcat:hzmninu2xrc6zg7x6iho772ky4
*approximation*scheme for finding a market*equilibrium**price*vector. ... A notion of*approximate*market*equilibrium*was proposed by Deng, Papadimitriou and Safra [5] . ... Therefore, the*price*vector p * together with the allocation x is an ε-*approximate*market*equilibrium*. Proof. ...##
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Non-redistributive Second Welfare Theorems
[chapter]

2012
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Lecture Notes in Computer Science
*

As ε → 0, the limit of these

doi:10.1007/978-3-642-35311-6_17
fatcat:2ukhjfvjozaqplrueds2vlrjei
*approximate*equilibria need not be an*equilibrium*but we show, using a more general*price*mechanism than the reals, that it is a "generalized*equilibrium*". ... Such an economy always has a market clearing ε*approximate**equilibrium*. ... The allocation x may not be supported by a*set*of real*prices*. For example, there is obviously no*set*of*prices*supportingx when the market does not have an exact*equilibrium*. ...##
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On-Line Algorithms for Market Equilibria
[chapter]

2005
*
Lecture Notes in Computer Science
*

Since exact equilibria will not be found in such a

doi:10.1007/11533719_61
fatcat:f6t4s26otjebnkjq6f7i4zvij4
*setting*, we appeal to the concept of*approximate**equilibrium*defined in previous studies of the problem, to characterize the quality of our solutions. ... We consider a variation of the classical problem of finding*prices*which guarantee*equilibrium*in linear markets consisting of divisible goods and agents with money. ... As we mentioned, in our*setting*the algorithm assigns*prices*trying to*approximate*the*price**equilibrium*that we would get in an offline*setting*. ...##
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The quality of equilibria for set packing and throughput scheduling games

2019
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International Journal of Game Theory
*

Under the assumption that players are allowed to play suboptimally and achieve an α-

doi:10.1007/s00182-019-00693-1
fatcat:6gdh3glxbjcpzantgrbg5ni55e
*approximate**equilibrium*, our tight*price*of anarchy bounds are α + 1 for Nash and subgame perfect equilibria, but less ... We introduce*set*packing games as an abstraction of situations in which n selfish players select disjoint subsets of a finite*set*of indivisible items, and analyze the quality of several equilibria for ... Theorem 6 For*set*packing games and any α ≥ 1, the actions played in an α*approximate*subgame perfect*equilibrium*of any sequential version of the*set*packing game, are an α-*approximate*Nash*equilibrium*...##
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Approximate Bertrand Equilibria in a Replicated Industry

1987
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The Review of Economic Studies
*

This paper considers the existence and properties of

doi:10.2307/2297445
fatcat:athkepikpzdf7ekfmoo6ur6ksm
*approximate*Bertrand equilibria in a replicated industry.*Price**setting*firms produce a homogeneous product with weakly convex costs. ... Rather, we employ the solution concept of an epsilon-*equilibrium*or "*approximate**equilibrium*". An ? ... Since*price*-*setting*is not irreversible, the no regret property of pure-strategy equilibria is particularly attractive. 2. ...##
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On Allocations with Negative Externalities
[chapter]

2011
*
Lecture Notes in Computer Science
*

Finally, for the maximum revenue Nash

doi:10.1007/978-3-642-25510-6_3
fatcat:h5t6ywgiwjcrnckka2olivoi3i
*equilibrium*, we show a 2-*approximation*for bipartite graphs (without*price*relaxation), and complement this result by showing that the problem is NP-Hard even on trees ... In this model, any fixed*setting*of the*price*induces a sub-game on the buyers. We show that it is an exact potential game which admits multiple pure Nash Equilibria. ...*Approximation*Algorithm for the Pessimistic Nash*Equilibrium*(PNE) problem with relaxed*prices*. ...##
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Graphical Economics
[chapter]

2004
*
Lecture Notes in Computer Science
*

classical Arrow-Debreu economics, in which an undirected graph specifies which consumers or economies are permitted to engage in direct trade, and the graph topology may give rise to local variations in the

doi:10.1007/978-3-540-27819-1_2
fatcat:ujju73dy6naifnnhxawufmmusm
*prices*... (non-graphical) economies, which generalizes the algorithm of Deng et al. [2002] to non-linear utility functions; (3) an algorithm for computing equilibria in the graphical*setting*, which runs in time ... It turns out that any ε-*approximate**equilibrium*in our*setting*with monotonically increasing utility functions can be transformed into an*approximate**equilibrium*in which the market exactly clears while ...##
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An Improved Approximation Scheme for Computing Arrow-Debreu Prices for the Linear Case
[chapter]

2003
*
Lecture Notes in Computer Science
*

Recently, Jain, Mahdian and Saberi [5] had given a FPTAS for the problem of computing a market

doi:10.1007/978-3-540-24597-1_13
fatcat:wb7ulnol7rhxvhs56qk63e3kba
*equilibrium*in the Arrow-Debreu*setting*, when the utilities are linear functions. ... In this paper, we give a strongly polynomial time*approximation*scheme for this problem. Our algorithm builds upon the main ideas behind the algorithm in [3] . ... In the AD*setting*, the*equilibrium**prices*are not unique. So we start with arbitrary*prices*and compute the buyers' budgets from their initial endowments. ...##
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Price of Anarchy for Greedy Auctions
[chapter]

2010
*
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
*

We focus on the problem of designing mechanisms that

doi:10.1137/1.9781611973075.46
dblp:conf/soda/LucierB10
fatcat:ql3mupttffgszarfhzjlc7uy4a
*approximately*optimize social welfare at every Bayes-Nash*equilibrium*(BNE), which is the standard notion of*equilibrium*in*settings*of incomplete information ... This solution concept is closely related to the well-studied*price*of anarchy. ...*price*mechanism that achieves a (c + 1)*approximation*at every Bayesian Nash*equilibrium*. ...##
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Efficiency and information aggregation in large uniform-price auctions

2013
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Journal of Economic Theory
*

We show that the uniform-

doi:10.1016/j.jet.2013.09.012
fatcat:lzpg2gt4qzavhaztx5iriuwvjy
*price*auction is*approximately*efficient with a large number of participants and asymptotically aggregates idiosyncratic bidder information into the market*price*. ... We prove that the equilibria of a large interdependent-value, uniform-*price*auction model where bidders have arbitrary preferences for multiple units can be*approximated*by a nonatomic exchange economy ... A*Approximation*Framework We develop our*approximation*tools in a general framework so that the results can be applied outside of the uniform-*price*auction*setting*we study. ...
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