## Abstract

We introduce a new model of congestion games that captures several extensions of the classical congestion game introduced by Rosenthal in 1973. The idea here is to parameterize both the perceived cost of each player and the social cost function of the system designer. Intuitively, each player perceives the load induced by the other players by an extent of ρ≥0, while the system designer estimates that each player perceives the load of all others by an extent of σ≥0. For specific choices of ρ and σ we obtain extensions such as altruistic player behavior, risk sensitive players and the imposition of taxes on the resources. We derive tight bounds on the price of anarchy and the price of stability for a large range of parameters. Our bounds provide a complete picture of the inefficiency of equilibria for these games. As a result, we obtain tight bounds on the price of anarchy and the price of stability for the above mentioned extensions. Our results also reveal how one should “design” the cost functions of the players in order to reduce the price of anarchy. Somewhat counterintuitively, if each player cares about all other players to the extent of ρ=0.625 (instead of 1 in the standard setting) the price of anarchy reduces from 2.5 to 2.155 and this is best possible.

Original language | English |
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Pages (from-to) | 65-87 |

Number of pages | 23 |

Journal | Theoretical Computer Science |

Volume | 754 |

DOIs | |

Publication status | Published - 6 Jan 2019 |

### Funding

Pieter Kleer is supported by the NWO Gravitation Project NETWORKS, Grant Number 024.002.003.

Funders | Funder number |
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Nederlandse Organisatie voor Wetenschappelijk Onderzoek | 024.002.003 |

## Keywords

- Altruistic games
- Congestion games
- Inefficiency of equilibria
- Price of anarchy
- Price of stability
- Risk-averse players
- Universal taxes