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Setting equilibrium prices, approximately
2013
ACM SIGecom Exchanges
We outline recent results, positive and negative, on 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. ...
doi:10.1145/2509013.2509017
fatcat:mnlqfizrlfgqtkpp6bue4nhoy4
Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
[chapter]
2015
Lecture Notes in Computer Science
Competitive 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). ...
doi:10.1007/978-3-662-48995-6_22
fatcat:jzqzmax4bnap5muhrfp424vsfq
2 A SAM as a Walrasian Equilibrium Framework
[chapter]
2019
Non-Extensive Entropy Econometrics for Low Frequency Series
Thus, such a statistical equilibrium approximates, but does not achieve, Pareto-efficiency. ...
The observed equilibrium price system is a (locally) stable equilibrium of trial-and-error price adjustment. ...
doi:10.1515/9783110605914-010
fatcat:bqyzv3azprgl7ecm7xfkrihr6u
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 à by looking at all these equivalence classes. ...
doi:10.1016/s0022-0000(03)00011-4
fatcat:zpmweftxz5fqhdzsunj4qxzxbm
Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
[article]
2014
arXiv
pre-print
Compared to other 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. ...
arXiv:1406.0576v1
fatcat:5oybgrza5rdm5pu4wcxiuutusq
Approximating Market Equilibria
[chapter]
2003
Lecture Notes in Computer Science
Using this notion, we present the first fully polynomial-time 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. ...
doi:10.1007/978-3-540-45198-3_9
fatcat:hzmninu2xrc6zg7x6iho772ky4
Non-redistributive Second Welfare Theorems
[chapter]
2012
Lecture Notes in Computer Science
As ε → 0, the limit of these 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 εapproximate 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. ...
doi:10.1007/978-3-642-35311-6_17
fatcat:2ukhjfvjozaqplrueds2vlrjei
On-Line Algorithms for Market Equilibria
[chapter]
2005
Lecture Notes in Computer Science
Since exact equilibria will not be found in such a 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. ...
doi:10.1007/11533719_61
fatcat:f6t4s26otjebnkjq6f7i4zvij4
The quality of equilibria for set packing and throughput scheduling games
2019
International Journal of Game Theory
Under the assumption that players are allowed to play suboptimally and achieve an α-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 αapproximate subgame perfect equilibrium of any sequential version of the set packing game, are an α-approximate Nash equilibrium ...
doi:10.1007/s00182-019-00693-1
fatcat:6gdh3glxbjcpzantgrbg5ni55e
Approximate Bertrand Equilibria in a Replicated Industry
1987
The Review of Economic Studies
This paper considers the existence and properties of 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. ...
doi:10.2307/2297445
fatcat:athkepikpzdf7ekfmoo6ur6ksm
On Allocations with Negative Externalities
[chapter]
2011
Lecture Notes in Computer Science
Finally, for the maximum revenue Nash 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. ...
doi:10.1007/978-3-642-25510-6_3
fatcat:h5t6ywgiwjcrnckka2olivoi3i
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 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 ...
doi:10.1007/978-3-540-27819-1_2
fatcat:ujju73dy6naifnnhxawufmmusm
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 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. ...
doi:10.1007/978-3-540-24597-1_13
fatcat:wb7ulnol7rhxvhs56qk63e3kba
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 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. ...
doi:10.1137/1.9781611973075.46
dblp:conf/soda/LucierB10
fatcat:ql3mupttffgszarfhzjlc7uy4a
Efficiency and information aggregation in large uniform-price auctions
2013
Journal of Economic Theory
We show that the uniform-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. ...
doi:10.1016/j.jet.2013.09.012
fatcat:lzpg2gt4qzavhaztx5iriuwvjy
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