## Abstract

We consider a scheduling game in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to which the jobs on the machine are processed. We characterize four classes of instances in which a pure Nash equilibrium (NE) is guaranteed to exist, and show by means of an example, that none of these characterizations can be relaxed. We then bound the performance of Nash equilibria for each of these classes with respect to the makespan of the schedule and the sum of completion times. We also analyze the computational complexity of several problems arising in this model. For instance, we prove that it is NP-hard to decide whether a NE exists, and that even for instances with identical machines, for which a NE is guaranteed to exist, it is NP-hard to approximate the best NE within a factor of 2 - 1/m - epsilon for every epsilon > 0.

In addition, we study a generalized model in which players' strategies are subsets of resources, where each resource has its own priority list over the players. We show that in this general model, even unweighted symmetric games may not have a pure NE, and we bound the price of anarchy with respect to the total players' costs.

Original language | English |
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Title of host publication | Web and Internet Economics: International Conference on Web and Internet Economics (WINE 2019) |

Subtitle of host publication | 15th International Conference, WINE 2019, New York, NY, USA, December 10–12, 2019, Proceedings |

Editors | Ioannis Caragiannis, Vahab Mirrokni, Evdokia Nikolova |

Publisher | Springer, Cham |

Pages | 286-300 |

Number of pages | 15 |

ISBN (Electronic) | 978-3-030-35389-6 |

ISBN (Print) | 978-3-030-35388-9 |

DOIs | |

Publication status | Published - 3 Dec 2019 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 11920 |

ISSN | 0302-9743 |

## Keywords

- price of anarchy
- priority lists
- scheduling games
- PRICE
- Priority lists
- BOUNDS
- Scheduling games
- MECHANISMS
- Price of anarchy
- CONGESTION GAMES