### Abstract

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

Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 28 |

Volume | 2013-069 |

Publication status | Published - 2013 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2013-069 |

### Fingerprint

### Keywords

- matching situations
- permutation games
- assignment games

### Cite this

*A Unifying Model for Matching Situations*. (CentER Discussion Paper; Vol. 2013-069). Tilburg: Econometrics.

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**A Unifying Model for Matching Situations.** / Tejada, J.; Borm, P.E.M.; Lohmann, E.R.M.A.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - A Unifying Model for Matching Situations

AU - Tejada, J.

AU - Borm, P.E.M.

AU - Lohmann, E.R.M.A.

N1 - Pagination: 28

PY - 2013

Y1 - 2013

N2 - Abstract: We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called matching games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a matching game is always nonempty by proving that the set of matching games coincides with the set of permutation games. Then we focus on two separate problems. First, we exploit the wide range of situations comprised in our framework to investigate the relationship between matching games with different player sets but defined by the same underlying matrix. We show that the core is not only immune to the merging of a row player and a column player, but also to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general. Second, we focus on permutation games only and we analyze the set of all matrices that define permutation games with the same core. In contrast to assignment games, we show that there can be multiple matrices whose entries cannot be raised without modifying the core of the corresponding permutation game and that, for small instances, every such matrix defines an exact game.

AB - Abstract: We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called matching games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a matching game is always nonempty by proving that the set of matching games coincides with the set of permutation games. Then we focus on two separate problems. First, we exploit the wide range of situations comprised in our framework to investigate the relationship between matching games with different player sets but defined by the same underlying matrix. We show that the core is not only immune to the merging of a row player and a column player, but also to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general. Second, we focus on permutation games only and we analyze the set of all matrices that define permutation games with the same core. In contrast to assignment games, we show that there can be multiple matrices whose entries cannot be raised without modifying the core of the corresponding permutation game and that, for small instances, every such matrix defines an exact game.

KW - matching situations

KW - permutation games

KW - assignment games

M3 - Discussion paper

VL - 2013-069

T3 - CentER Discussion Paper

BT - A Unifying Model for Matching Situations

PB - Econometrics

CY - Tilburg

ER -