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

Department of Economics, Gardner Hall, University of North Carolina, Chapel Hill, NC 27599-3305
Department of Economics, University of Warwick, Coventry, CV4 7A1, United Kingdom

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 n₀ on the number of players, we obtain a bound ₀ (, n₀) so that, for any ₀(, n₀), all games in the collection with at least n₀ 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.

Key Words: Cooperative games; games without side payments (NTU games); clubs; large games; approximate cores; effective small groups; parameterized collections of games; small group effectiveness
History: Received: July 2, 1999; revision received: July 27, 2000;revision received: March 19, 2001;