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Setting equilibrium prices, approximately

Brendan Lucier
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]

Shahar Dobzinski, Michal Feldman, Inbal Talgam-Cohen, Omri Weinstein
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

Xiaotie Deng, Christos Papadimitriou, Shmuel Safra
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]

Shahar Dobzinski, Michal Feldman, Inbal Talgam-Cohen, Omri Weinstein
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]

Kamal Jain, Mohammad Mahdian, Amin Saberi
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]

Bundit Laekhanukit, Guyslain Naves, Adrian Vetta
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]

Spyros Angelopoulos, Atish Das Sarma, Avner Magen, Anastasios Viglas
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

Jasper de Jong, Marc Uetz
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

Huw Dixon
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]

Sayan Bhattacharya, Janardhan Kulkarni, Kamesh Munagala, Xiaoming Xu
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]

Sham M. Kakade, Michael Kearns, Luis E. Ortiz
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]

Nikhil R. Devanur, Vijay V. Vazirani
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]

B. Lucier, A. Borodin
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

Aaron Bodoh-Creed
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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