### Abstract

We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the local-average-distance version, we prove an upper bound of 2^{O}( ^{√ lg n}), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the local- diameter version, we prove a lower bound of Ω( √n), and a tight upper bound of 3 for trees. All of our upper bounds apply equally well to previously extensively studied network creation games, both in terms of the diameter metric de- scribed above and the previously studied price of anarchy (which are related by constant factors). In surprising contrast, our model has no parameter α for the link creation cost, so our results automatically apply for all values of α without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler and more general proofs that get at the heart of network creation games.

Original language | English (US) |
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Title of host publication | SPAA'10 - Proceedings of the 22nd Annual Symposium on Parallelism in Algorithms and Architectures |

Pages | 106-113 |

Number of pages | 8 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 22nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'10 - Thira, Santorini, Greece Duration: Jun 13 2010 → Jun 15 2010 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
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### Other

Other | 22nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'10 |
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Country | Greece |

City | Thira, Santorini |

Period | 6/13/10 → 6/15/10 |

### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture

### Keywords

- Nash equilibrium
- Network design
- Price of anarchy
- Routing

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## Cite this

*SPAA'10 - Proceedings of the 22nd Annual Symposium on Parallelism in Algorithms and Architectures*(pp. 106-113). (Annual ACM Symposium on Parallelism in Algorithms and Architectures). https://doi.org/10.1145/1810479.1810502