An Exact Bound on Epsilon for Nonemptiness of Epsilon Cores of Games

We consider collections of games with and without side payments described by certain natural parameters. Given the parameters describing a collection of games and a lower bound n 0 on the number of players, we obtain a bound 0 ( , n 0 ) so that, for any 0 ( , n 0 ), all games in the collection with...

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Bibliographic Details
Published inMathematics of operations research Vol. 26; no. 4; pp. 654 - 678
Main Authors Kovalenkov, Alexander, Wooders, Myrna Holtz
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.11.2001
Institute for Operations Research and the Management Sciences
Subjects
approximate cores
clubs
Convexity
Cooperative games
Economic games
Economic modeling
Economic theory
effective small groups
Game theory
Games of strategy (Mathematics)
games without side payments (NTU games)
Integers
large games
Mathematical functions
Mathematical models
Mathematical vectors
Operations research
parameterized collections of games
Public economics
Real numbers
small group effectiveness
Studies
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Summary:We consider collections of games with and without side payments described by certain natural parameters. Given the parameters describing a collection of games and a lower bound n 0 on the number of players, we obtain a bound 0 ( , n 0 ) so that, for any 0 ( , n 0 ), all games in the collection with at least n 0 players have nonempty -cores. Examples are provided in which the bound on is met. For parameter values ensuring that there are many close substitutes for most players and that relatively small groups of players can realize nearly all gains to collective activities, for games with many players the bound on is small.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.26.4.654.10001