A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the complexity of equilibria
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Efficiency Loss in a Network Resource Allocation Game
Mathematics of Operations Research
A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Market equilibrium via the excess demand function
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A price-anticipating resource allocation mechanism for distributed shared clusters
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On the polynomial time computation of equilibria for certain exchange economies
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A path to the Arrow–Debreu competitive market equilibrium
Mathematical Programming: Series A and B
Market equilibrium for CES exchange economies: existence, multiplicity, and computation
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Bittorrent is an auction: analyzing and improving bittorrent's incentives
Proceedings of the ACM SIGCOMM 2008 conference on Data communication
Mathematical modeling of incentive policies in p2p systems
Proceedings of the 3rd international workshop on Economics of networked systems
Price Variation in a Bipartite Exchange Network
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
A Comparison of Bilateral and Multilateral Exchanges for Peer-Assisted Content Distribution
Network Control and Optimization
Peer-assisted content distribution with prices
CoNEXT '08 Proceedings of the 2008 ACM CoNEXT Conference
Proportional Response Dynamics in the Fisher Market
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
FairTorrent: bringing fairness to peer-to-peer systems
Proceedings of the 5th international conference on Emerging networking experiments and technologies
Cooperation via contracts: stability and algorithms
INFOCOM'10 Proceedings of the 29th conference on Information communications
Proportional response dynamics in the Fisher market
Theoretical Computer Science
Distributed algorithms via gradient descent for fisher markets
Proceedings of the 12th ACM conference on Electronic commerce
Bilateral and multilateral exchanges for peer-assisted content distribution
IEEE/ACM Transactions on Networking (TON)
Price differentiation all-pay auction-based incentives in bittorrent
GPC'10 Proceedings of the 5th international conference on Advances in Grid and Pervasive Computing
A mathematical framework for analyzing adaptive incentive protocols in P2P networks
IEEE/ACM Transactions on Networking (TON)
International Journal of Communication Networks and Distributed Systems
An open content delivery infrastructure using data lockers
Proceedings of the second edition of the ICN workshop on Information-centric networking
FairTorrent: a deficit-based distributed algorithm to ensure fairness in peer-to-peer systems
IEEE/ACM Transactions on Networking (TON)
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One of the main reasons of the recent success of peer to peer (P2P)file sharing systems such as BitTorrent is their built-in tit-for-tat mechanism. In this paper, we model the bandwidth allocation in a P2P system as an exchange economy and study a tit-for-tat dynamics, namely the proportional response dynamics, in this economy. In aproportional response dynamics each player distributes its good to its neighbors proportional to the utility it received from them in thelast period. We show that this dynamics not only converges but converges to a market equilibrium, a standard economic characterization of efficient exchanges in a competitive market. In addition, for some classes of utility functions we consider, it converges much faster than the classical tat process and any existingalgorithms for computing market equilibria. As a part of our proof we study the double normalization of a matrix, an operation that linearly scales the rows of a matrix sothat each row sums to a prescribed positive number, followed by a similar scaling of the columns. We show that the iterative double normalization process of any non-negative matrix always converges. This complements the previous studies in matrix scaling that has focused on the convergence condition of the process when the row and column normalizations are considered as separate steps.