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- W3119498903 abstract "The theory of games in characteristic function form is well developed. However not so much work has been done on the continuity properties of the core of these games. The aim of this paper is to prove that for convex games the core behaves nicely. (We also present some counterexamples for non convex games.) In Section 1 we give some definitions and notations and prove the fundamental lemma of our paper. Section 2 lists different characterizations of convex games. In Section 3 we prove the so-called projection theorem. Roughly this theorem states that the set of core restrictions is the core of the subgame. In Section 4 we give a characterization of the extreme points of the core of a finite game; although the results of this section are already discovered in [14], we use a different method. Sections 5 and 6 contain weak and strong continuity properties of the core correspondence. Section 8 gives some information on u-continuous games. We also answer a question raised in [l 11. Section 9 is devoted to selection theorems. For an application of selection theorems to mathematical economics we refer to a forthcoming paper of Sondermann [15]. Sections 7 and 10 give some approximation theorems; the purpose of these theorems is to approximate a game with infinitely many players by a game with finitely many players. Section 11 is an attempt to describe the structure of the core of a-continuous games. We hope that our results will lead to a better understanding of the core of a game with infinitely many players. We know that for finite games our results are not general but the paper has to be seen as a paper on infinite games." @default.
- W3119498903 created "2021-01-18" @default.
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- W3119498903 date "1974-01-01" @default.
- W3119498903 modified "2023-09-27" @default.
- W3119498903 title "Convex games and extreme points" @default.
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