### Abstract

Coalition formation is an important capability of automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Recent research has revealed that traditional solution concepts, such as the Shapley value, core, least core, and nucleolus, are vulnerable to various manipulations in open anonymous environments such as the Internet. These manipulations include submitting false names, collusion, and hiding some skills. To address this, a solution concept called the anonymity-proof core, which is robust against such manipulations, was developed. However, the representation size of the outcome function in the anonymity-proof core (and similar concepts) requires space exponential in the number of agents/skills. This paper proposes a compact representation of the outcome function, given that the characteristic function is represented using a recently introduced compact language that explicitly specifies only coalitions that introduce synergy. This compact representation scheme can successfully express the outcome function in the anonymity-proof core. Furthermore, this paper develops a new solution concept, the anonymity-proof nucleolus, that is also expressible in this compact representation. We show that the anonymity-proof nucleolus always exists, is unique, and is in the anonymity-proof core (if the latter is nonempty), and assigns the same value to symmetric skills.

Original language | English |
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Title of host publication | Proceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06 |

Pages | 697-702 |

Number of pages | 6 |

Volume | 1 |

Publication status | Published - Nov 13 2006 |

Event | 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06 - Boston, MA, United States Duration: Jul 16 2006 → Jul 20 2006 |

### Other

Other | 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06 |
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Country | United States |

City | Boston, MA |

Period | 7/16/06 → 7/20/06 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Artificial Intelligence

### Cite this

*Proceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06*(Vol. 1, pp. 697-702)

**A compact representation scheme for coalitional games in open anonymous environments.** / Ohta, Naoki; Iwasaki, Atsushi; Yokoo, Makoto; Maruono, Kohki; Conitzer, Vincent; Sandholm, Tuomas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06.*vol. 1, pp. 697-702, 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06, Boston, MA, United States, 7/16/06.

}

TY - GEN

T1 - A compact representation scheme for coalitional games in open anonymous environments

AU - Ohta, Naoki

AU - Iwasaki, Atsushi

AU - Yokoo, Makoto

AU - Maruono, Kohki

AU - Conitzer, Vincent

AU - Sandholm, Tuomas

PY - 2006/11/13

Y1 - 2006/11/13

N2 - Coalition formation is an important capability of automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Recent research has revealed that traditional solution concepts, such as the Shapley value, core, least core, and nucleolus, are vulnerable to various manipulations in open anonymous environments such as the Internet. These manipulations include submitting false names, collusion, and hiding some skills. To address this, a solution concept called the anonymity-proof core, which is robust against such manipulations, was developed. However, the representation size of the outcome function in the anonymity-proof core (and similar concepts) requires space exponential in the number of agents/skills. This paper proposes a compact representation of the outcome function, given that the characteristic function is represented using a recently introduced compact language that explicitly specifies only coalitions that introduce synergy. This compact representation scheme can successfully express the outcome function in the anonymity-proof core. Furthermore, this paper develops a new solution concept, the anonymity-proof nucleolus, that is also expressible in this compact representation. We show that the anonymity-proof nucleolus always exists, is unique, and is in the anonymity-proof core (if the latter is nonempty), and assigns the same value to symmetric skills.

AB - Coalition formation is an important capability of automated negotiation among self-interested agents. In order for coalitions to be stable, a key question that must be answered is how the gains from cooperation are to be distributed. Recent research has revealed that traditional solution concepts, such as the Shapley value, core, least core, and nucleolus, are vulnerable to various manipulations in open anonymous environments such as the Internet. These manipulations include submitting false names, collusion, and hiding some skills. To address this, a solution concept called the anonymity-proof core, which is robust against such manipulations, was developed. However, the representation size of the outcome function in the anonymity-proof core (and similar concepts) requires space exponential in the number of agents/skills. This paper proposes a compact representation of the outcome function, given that the characteristic function is represented using a recently introduced compact language that explicitly specifies only coalitions that introduce synergy. This compact representation scheme can successfully express the outcome function in the anonymity-proof core. Furthermore, this paper develops a new solution concept, the anonymity-proof nucleolus, that is also expressible in this compact representation. We show that the anonymity-proof nucleolus always exists, is unique, and is in the anonymity-proof core (if the latter is nonempty), and assigns the same value to symmetric skills.

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M3 - Conference contribution

SN - 1577352815

SN - 9781577352815

VL - 1

SP - 697

EP - 702

BT - Proceedings of the 21st National Conference on Artificial Intelligence and the 18th Innovative Applications of Artificial Intelligence Conference, AAAI-06/IAAI-06

ER -