## Abstract

Best response (BR) dynamics is a natural method by which players proceed toward a pure Nash equilibrium via a local search method. The quality of the equilibrium reached may depend heavily on the order by which players are chosen to perform their best response moves. A deviator rule S is a method for selecting the next deviating player. We provide a measure for quantifying the performance of different deviator rules. The inefficiency of a deviator rule S with respect to an initial strategy profile p is the ratio between the social cost of the worst equilibrium reachable by S from p and the social cost of the best equilibrium reachable from p. The inefficiency of S is the maximum such ratio over all possible initial profiles. This inefficiency always lies between 1 and the price of anarchy. We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE). For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called local deviator rules. Such rules choose the next deviator as a function of a restricted set of parameters, and satisfy a natural independence condition called independence of irrelevant players. We present upper bounds on the inefficiency of some local deviator rules, and also show that for some classes of games, no local deviator rule can guarantee inefficiency lower than the price of anarchy.

Original language | English |
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Title of host publication | Algorithmic Game Theory - 10th International Symposium, SAGT 2017, Proceedings |

Editors | Vittorio Bilo, Michele Flammini |

Publisher | Springer Verlag |

Pages | 186-198 |

Number of pages | 13 |

ISBN (Print) | 9783319666990 |

DOIs | |

State | Published - 2017 |

Event | 10th International Symposium on Algorithmic Game Theory, SAGT 2017 - L’Aquila, Italy Duration: 12 Sep 2017 → 14 Sep 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10504 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 10th International Symposium on Algorithmic Game Theory, SAGT 2017 |
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Country/Territory | Italy |

City | L’Aquila |

Period | 12/09/17 → 14/09/17 |

### Funding

Funders | Funder number |
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FP7/2007 | |

Seventh Framework Programme | 337122 |

European Research Council | |

Seventh Framework Programme |

## Keywords

- Best-response dynamics
- Congestion games
- Deviator rules
- Price of anarchy