### Abstract

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

Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 19 |

Volume | 2006-113 |

Publication status | Published - 2006 |

### Publication series

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

Volume | 2006-113 |

### Keywords

- cooperative games
- simple games
- population monotonic path schemes
- coalition formation
- probabilistic values

### Cite this

*Population Monotonic Path Schemes for Simple Games*. (CentER Discussion Paper; Vol. 2006-113). Tilburg: Microeconomics.

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**Population Monotonic Path Schemes for Simple Games.** / Ciftci, B.B.; Borm, P.E.M.; Hamers, H.J.M.

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

TY - UNPB

T1 - Population Monotonic Path Schemes for Simple Games

AU - Ciftci, B.B.

AU - Borm, P.E.M.

AU - Hamers, H.J.M.

N1 - Subsequently published in Theory and Decision, 2010 Pagination: 19

PY - 2006

Y1 - 2006

N2 - A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path.A path scheme is called population monotonic if a player's payoff does not decrease as the path coalition grows.In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand.We show that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced.Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition.Extensions of these results to other probabilistic values are discussed.

AB - A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path.A path scheme is called population monotonic if a player's payoff does not decrease as the path coalition grows.In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand.We show that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced.Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition.Extensions of these results to other probabilistic values are discussed.

KW - cooperative games

KW - simple games

KW - population monotonic path schemes

KW - coalition formation

KW - probabilistic values

M3 - Discussion paper

VL - 2006-113

T3 - CentER Discussion Paper

BT - Population Monotonic Path Schemes for Simple Games

PB - Microeconomics

CY - Tilburg

ER -