Convex Games and Stable Sets |
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Authors: | Ezra Einy Benyamin Shitovitz |
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Institution: | aDepartment of Economics, Ben-Gurion University of the Negev, Beer Sheva, Israel;bDepartment of Economics, University of Haifa, Haifa, Israel |
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Abstract: | It is well known that the core of a convex coalitional game with a finite set of players is the unique von Neumann–Morgenstern stable set of the game. We extend the definition of a stable set to coalitional games with an infinite set of players and give an example of a convex simple game with a countable set of players which does not have a stable set. But if a convex game with a countable set of players is continuous at the grand coalition, we prove that its core is the unique von Neumann–Morgenstern stable set. We also show that a game with a countable (possibly finite) set of players which is inner continuous is convex iff the core of each of its subgames is a stable set.Journal of Economic LiteratureClassification Numbers: C70, C71. |
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