### Abstract

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

Journal | Mathematical Methods of Operations Research |

Volume | 80 |

Issue number | 2 |

Pages (from-to) | 213–223 |

ISSN | 1432-2994 |

DOIs | |

Publication status | Published - 2014 |

Externally published | Yes |

### Keywords

- Core
- Core cover
- Larginal vectors
- TU-game

### Cite this

*Mathematical Methods of Operations Research*,

*80*(2), 213–223. https://doi.org/10.1007/s00186-014-0477-6

}

*Mathematical Methods of Operations Research*, vol. 80, no. 2, pp. 213–223. https://doi.org/10.1007/s00186-014-0477-6

**C-complete Sets for Compromise Stable Games.** / Platz, Trine Tornøe ; Hamers, Herbert; Quant, Marieke.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - C-complete Sets for Compromise Stable Games

AU - Platz, Trine Tornøe

AU - Hamers, Herbert

AU - Quant, Marieke

PY - 2014

Y1 - 2014

N2 - The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets. Furthermore, we discuss the number of different larginal vectors corresponding to a c-complete set of orderings.

AB - The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets. Furthermore, we discuss the number of different larginal vectors corresponding to a c-complete set of orderings.

KW - Core

KW - Core cover

KW - Larginal vectors

KW - TU-game

KW - Core

KW - Core cover

KW - Larginal vectors

KW - TU-game

UR - https://sfx-45cbs.hosted.exlibrisgroup.com/45cbs?url_ver=Z39.88-2004&url_ctx_fmt=info:ofi/fmt:kev:mtx:ctx&ctx_enc=info:ofi/enc:UTF-8&ctx_ver=Z39.88-2004&rfr_id=info:sid/sfxit.com:azlist&sfx.ignore_date_threshold=1&rft.object_id=954928623314

U2 - 10.1007/s00186-014-0477-6

DO - 10.1007/s00186-014-0477-6

M3 - Journal article

VL - 80

SP - 213

EP - 223

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 2

ER -