Abstract
| Original language | English |
|---|---|
| Place of Publication | Tilburg |
| Publisher | Microeconomics |
| Number of pages | 16 |
| Volume | 2003-19 |
| Publication status | Published - 2003 |
Publication series
| Name | CentER Discussion Paper |
|---|---|
| Volume | 2003-19 |
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Keywords
- game theory
- algorithm
- cooperative games
- kernel estimation
- peer games
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Strongly Essential Coalitions and the Nucleolus of Peer Group Games. / Brânzei, R.; Solymosi, T.; Tijs, S.H.
Tilburg : Microeconomics, 2003. (CentER Discussion Paper; Vol. 2003-19).Research output: Working paper › Discussion paper › Other research output
TY - UNPB
T1 - Strongly Essential Coalitions and the Nucleolus of Peer Group Games
AU - Brânzei, R.
AU - Solymosi, T.
AU - Tijs, S.H.
N1 - Pagination: 16
PY - 2003
Y1 - 2003
N2 - Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespeci ed collection of size polynomial in the number of players.We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore.As an application, we consider peer group games, and show that they admit at most 2n - 1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n-1. We propose an algorithm that computes the nucleolus of an n-player peer group game in O(n2) time directly from the data of the underlying peer group situation.
AB - Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespeci ed collection of size polynomial in the number of players.We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore.As an application, we consider peer group games, and show that they admit at most 2n - 1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2n-1. We propose an algorithm that computes the nucleolus of an n-player peer group game in O(n2) time directly from the data of the underlying peer group situation.
KW - game theory
KW - algorithm
KW - cooperative games
KW - kernel estimation
KW - peer games
M3 - Discussion paper
VL - 2003-19
T3 - CentER Discussion Paper
BT - Strongly Essential Coalitions and the Nucleolus of Peer Group Games
PB - Microeconomics
CY - Tilburg
ER -