### Abstract

Original language | English |
---|---|

Pages (from-to) | 53-72 |

Number of pages | 20 |

Journal | Theory of Computing Systems |

Volume | 53 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 |

### Cite this

*Theory of Computing Systems*,

*53*(1), 53-72. https://doi.org/10.1007/s00224-013-9459-y

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*Theory of Computing Systems*, vol. 53, no. 1, pp. 53-72. https://doi.org/10.1007/s00224-013-9459-y

**The Price of Anarchy in Network Creation Games Is (Mostly) Constant.** / Mihalák, Matús; Schlegel, Jan Christoph.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - The Price of Anarchy in Network Creation Games Is (Mostly) Constant

AU - Mihalák, Matús

AU - Schlegel, Jan Christoph

PY - 2013

Y1 - 2013

N2 - We study the price of anarchy and the structure of equilibria in network creation games. A network creation game is played by n players {1,2,…,n}, each identified with a vertex of a graph (network), where the strategy of player i, i=1,…,n, is to build some edges adjacent to i. The cost of building an edge is a>0, a fixed parameter of the game. The goal of every player is to minimize its creation cost plus its usage cost. The creation cost of player i is a times the number of built edges. In the sumgame variant, the usage cost of player i is the sum of distances from i to every node of the resulting graph. In the maxgame variant, the usage cost is the eccentricity of i in the resulting graph of the game. In this paper we improve previously known bounds on the price of anarchy of the game (of both variants) for various ranges of a, and give new insights into the structure of equilibria for various values of a. The two main results of the paper show that for a>273·n all equilibria in sumgame are trees and thus the price of anarchy is constant, and that for a>129 all equilibria in maxgame are trees and the price of anarchy is constant. For sumgame this answers (almost completely) one of the fundamental open problems in the field—is price of anarchy of the network creation game constant for all values of a?—in an affirmative way, up to a tiny range of a.

AB - We study the price of anarchy and the structure of equilibria in network creation games. A network creation game is played by n players {1,2,…,n}, each identified with a vertex of a graph (network), where the strategy of player i, i=1,…,n, is to build some edges adjacent to i. The cost of building an edge is a>0, a fixed parameter of the game. The goal of every player is to minimize its creation cost plus its usage cost. The creation cost of player i is a times the number of built edges. In the sumgame variant, the usage cost of player i is the sum of distances from i to every node of the resulting graph. In the maxgame variant, the usage cost is the eccentricity of i in the resulting graph of the game. In this paper we improve previously known bounds on the price of anarchy of the game (of both variants) for various ranges of a, and give new insights into the structure of equilibria for various values of a. The two main results of the paper show that for a>273·n all equilibria in sumgame are trees and thus the price of anarchy is constant, and that for a>129 all equilibria in maxgame are trees and the price of anarchy is constant. For sumgame this answers (almost completely) one of the fundamental open problems in the field—is price of anarchy of the network creation game constant for all values of a?—in an affirmative way, up to a tiny range of a.

U2 - 10.1007/s00224-013-9459-y

DO - 10.1007/s00224-013-9459-y

M3 - Article

VL - 53

SP - 53

EP - 72

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 1

ER -