5,118 research outputs found
Market Equilibrium with Transaction Costs
Identical products being sold at different prices in different locations is a
common phenomenon. Price differences might occur due to various reasons such as
shipping costs, trade restrictions and price discrimination. To model such
scenarios, we supplement the classical Fisher model of a market by introducing
{\em transaction costs}. For every buyer and every good , there is a
transaction cost of \cij; if the price of good is , then the cost to
the buyer {\em per unit} of is p_j + \cij. This allows the same good
to be sold at different (effective) prices to different buyers.
We provide a combinatorial algorithm that computes -approximate
equilibrium prices and allocations in
operations -
where is the number goods, is the number of buyers and is the sum
of the budgets of all the buyers
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
Geometry Helps to Compare Persistence Diagrams
Exploiting geometric structure to improve the asymptotic complexity of
discrete assignment problems is a well-studied subject. In contrast, the
practical advantages of using geometry for such problems have not been
explored. We implement geometric variants of the Hopcroft--Karp algorithm for
bottleneck matching (based on previous work by Efrat el al.) and of the auction
algorithm by Bertsekas for Wasserstein distance computation. Both
implementations use k-d trees to replace a linear scan with a geometric
proximity query. Our interest in this problem stems from the desire to compute
distances between persistence diagrams, a problem that comes up frequently in
topological data analysis. We show that our geometric matching algorithms lead
to a substantial performance gain, both in running time and in memory
consumption, over their purely combinatorial counterparts. Moreover, our
implementation significantly outperforms the only other implementation
available for comparing persistence diagrams.Comment: 20 pages, 10 figures; extended version of paper published in ALENEX
201
Converging an Overlay Network to a Gradient Topology
In this paper, we investigate the topology convergence problem for the
gossip-based Gradient overlay network. In an overlay network where each node
has a local utility value, a Gradient overlay network is characterized by the
properties that each node has a set of neighbors with the same utility value (a
similar view) and a set of neighbors containing higher utility values (gradient
neighbor set), such that paths of increasing utilities emerge in the network
topology. The Gradient overlay network is built using gossiping and a
preference function that samples from nodes using a uniform random peer
sampling service. We analyze it using tools from matrix analysis, and we prove
both the necessary and sufficient conditions for convergence to a complete
gradient structure, as well as estimating the convergence time and providing
bounds on worst-case convergence time. Finally, we show in simulations the
potential of the Gradient overlay, by building a more efficient live-streaming
peer-to-peer (P2P) system than one built using uniform random peer sampling.Comment: Submitted to 50th IEEE Conference on Decision and Control (CDC 2011
Clustering Algorithms for Scale-free Networks and Applications to Cloud Resource Management
In this paper we introduce algorithms for the construction of scale-free
networks and for clustering around the nerve centers, nodes with a high
connectivity in a scale-free networks. We argue that such overlay networks
could support self-organization in a complex system like a cloud computing
infrastructure and allow the implementation of optimal resource management
policies.Comment: 14 pages, 8 Figurs, Journa
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