Inefficiency of Nash equilibria
Mathematics of Operations Research
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The price of anarchy is independent of the network topology
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FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Game Theory
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SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
Approximating the pareto front of multi-criteria optimization problems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
On the quality and complexity of pareto equilibria in the job scheduling game
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
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We analyze the Pareto efficiency, or inefficiency, of solutions to routing games and load balancing games, focusing on Nash equilibria and greedy solutions to these games. For some settings, we show that the solutions are necessarily Pareto optimal. When this is not the case, we provide a measure to quantify the distance of the solution from Pareto efficiency. Using this measure, we provide upper and lower bounds on the "Pareto inefficiency" of the different solutions. The settings we consider include load balancing games on identical, uniformly-related, and unrelated machines, both using pure and mixed strategies, and nonatomic routing in general and some specific networks.