A solution to a conjecture of David Schmeidler

Alain Chateauneuf, Freddy Delbaen () and Caroline Ventura ()
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Freddy Delbaen: ETH Zürich
Caroline Ventura: University of Paris 1

Economic Theory Bulletin, 2024, vol. 12, issue 2, No 5, 183-189

Abstract: Abstract The purpose of this paper is to disprove an old and interesting conjecture in the theory of cooperative games initially presented as a reasonable conjecture in the seminal work of Schmeidler (J Math Anal Appl 40:214–225, 1972): An exact capacity continuous at the empty set has a countably additive probability in its core. In this paper, we show that this conjecture is not true in general. More precisely, we give a large class of topological spaces for which the conjecture fails, even with the stronger assumption that the capacity is convex. However, on $$({\mathbb {N}},\ 2^{{\mathbb {N}}})$$ ( N , 2 N ) the conjecture holds for convex capacities, as it is easy to show. We prove that in its original form, that is for exact capacities, it fails.

Keywords: A conjecture of David Schmeidler; Core of continuous exact games; Countably additive probabilities; Convex games (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s40505-024-00271-z

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