## Abstract

Proportional allocation is an intuitive and widely applied mechanism to allocate divisible resources. We study proportional allocation for profit sharing in coalition formation games. Here each agent has an impact or reputation value, and each coalition represents a joint project that generates a total profit. This profit is divided among the agents involved in the project based on their reputation. We study existence, computational complexity, and social welfare of core-stable states with proportional sharing. Core-stable states always exist and can be computed in time O(m log m), where m is the total number of projects. Moreover, when profits have a natural monotonicity property, there exists a reputation scheme such that the price of anarchy is 1, i.e., every core-stable state is a social optimum. However, these schemes exhibit a strong inequality in reputation of agents and thus imply a lacking fairness condition. Our main results show a tradeoff between reputation imbalance and the price of anarchy. Moreover, we show lower bounds and computational hardness results on the reputation imbalance when prices of anarchy and stability are small.

Original language | English |
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Title of host publication | Algorithmic Game Theory - 10th International Symposium, SAGT 2017, Proceedings |

Pages | 307-319 |

Number of pages | 13 |

DOIs | |

Publication status | Published - 2017 |

MoE publication type | A4 Article in a conference publication |

Event | International Symposium on Algorithmic Game Theory - L’Aquila, Italy Duration: 12 Sep 2017 → 14 Sep 2017 Conference number: 10 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10504 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Symposium on Algorithmic Game Theory |
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Abbreviated title | SAGT |

Country | Italy |

City | L’Aquila |

Period | 12/09/2017 → 14/09/2017 |