## Convergence time to nash equilibria (2003)

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Venue: | In ICALP |

Citations: | 79 - 5 self |

### BibTeX

@INPROCEEDINGS{Even-dar03convergencetime,

author = {Eyal Even-dar and Alex Kesselman and Yishay Mansour},

title = {Convergence time to nash equilibria},

booktitle = {In ICALP},

year = {2003},

pages = {502--513},

publisher = {Springer-Verlag}

}

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### Abstract

Abstract. We study the number of steps required to reach a pure Nash Equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, K distinct weights and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (such as allowing the largest weight job to move first). 1

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Citation Context ...puter Science research has been focused on finding a global optimum. With the emerging interest in computational issues in game theory, the coordination ratio [17] has received considerable attention =-=[2, 7, 8, 13, 17, 25]-=-. The coordination ratio is the ratio between the worst possible Nash equilibrium (the one with maximum social cost) and the social optimum (an optimal solution with the minimal social cost). One moti... |

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Citation Context ... approximation ratio of the local optima obtained by iterative improvement appears in [5, 6, 26]. The approximation ratio of a jump (one job moves at a time) iterative improvement has been studied in =-=[10]-=-. In [6] it has been shown that for two identical machines this heuristic requires at most n 2 iterations, which immediately translates to an n 2 upper bound for two identical machines with general we... |

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Citation Context ...puter Science research has been focused on finding a global optimum. With the emerging interest in computational issues in game theory, the coordination ratio [17] has received considerable attention =-=[2, 7, 8, 13, 17, 25]-=-. The coordination ratio is the ratio between the worst possible Nash equilibrium (the one with maximum social cost) and the social optimum (an optimal solution with the minimal social cost). One moti... |

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Convergence Time To Nash Equilibria”, Technical Report, available at http://www.cs.tau.ac.il/˜evend/papers.html
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(Show Context)
Citation Context ...of unrelated, related and identical machines appears in Section 3, Section 4 and Section 5, respectively. We conclude with Section 6. Due to space limitations some proofs are omitted and can found in =-=[9]-=-. 2 Model Description In our load balancing scenario there are m parallel machines and n independent jobs. Each job selects exactly one machine. Machines Model. We consider identical, related and unre... |