Title: The Efficaciousness of Small Groups and the Approximate Core Property in Games Without Side Payments: Some First Results
Abstract: Small groups are efficacious, or, in other words, large groups are inessential, if almost all gains to group or coalition formation can be realized by groups bounded in absolute size. The approximate core property is that all sufficiently large games have nonempty approximate cores. The substitution property is that in all sufficiently large games, most players have many substitutes. In Wooders (1991) in the context of an environment satisfying the substitution property it was shown that large games satisfy inessentiality of large groups if and only if they have the approximate core property. In this paper we begin a similar study for games without sidepayments, NTU games. For such games we define two concepts of efficacy of small groups, an approximate core property, and boundedness of marginal contributions to groups. We show that both efficacy of small groups conditions imply the approximate core property. We also show that boundedness of marginal contributions implies efficacy of small groups. This paper is a preliminary investigation aimed at eventually obtaining results for games without sidepayments analogous to those of Wooders (1991).
Creation-Date: February 1991
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