### Abstract

We introduce (super) polynomial bottleneck games, where the utility costs of the players are (super) polynomial functions of the congestion of the resources that they use, and the social cost is determined by the worst congestion of any resource. In particular, the delay function for any resource r is ofbut the degree is bounded the form C_{r}^{Mr}, where C_{r} is the congestion measured as the number of players that use r, and the degree of the delay function is bounded as 1 ≤ M_{r} ≤ log C_{r}. The utility cost of a player is the sum of the individual delays of the resources that it uses. The social cost of the game is the worst bottleneck resource congestion: max_{rεR} C_{r}, where R is the set of resources. We show that for super-polynomial bottleneck games with M_{r} = log C_{r}, the price of anarchy is o(√|R|), specifically O(2^{√log|R|}). We also consider general polynomial bottleneck games where each resource can have a distinct monomial latency function but the degree is bounded i.e M_{r} = O(1) with constants α ≤ M_{r} ≤ β and derive the price of anarchy as min (|R|, max(2β/C*(2|R|)^{1/α+1} ·,(2β/ C*)^{α/α+1} · (2β) ^{β-α/α+1})), where C* is the bottleneck congestion in the socially optimal state. We then demonstrate matching lower bounds for both games showing that this price of anarchy is tight.

Original language | English (US) |
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Title of host publication | Game Theory for Networks - Second International ICST Conference, GAMENETS 2011, Revised Selected Papers |

Pages | 308-320 |

Number of pages | 13 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

Event | 2nd International ICST Conference on Game Theory in Networks, GAMENETS 2011 - Shanghai, China Duration: Apr 16 2011 → Apr 18 2011 |

### Publication series

Name | Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering |
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Volume | 75 LNICST |

ISSN (Print) | 1867-8211 |

### Conference

Conference | 2nd International ICST Conference on Game Theory in Networks, GAMENETS 2011 |
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Country | China |

City | Shanghai |

Period | 4/16/11 → 4/18/11 |

### ASJC Scopus subject areas

- Computer Networks and Communications

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## Cite this

*Game Theory for Networks - Second International ICST Conference, GAMENETS 2011, Revised Selected Papers*(pp. 308-320). (Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering; Vol. 75 LNICST). https://doi.org/10.1007/978-3-642-30373-9_22