Self-consistency for multi-valued solutions and reasonable outcomes

Pedro Calleja, Francesc Llerena and Peter Sudhölter

Journal of Mathematical Economics, 2025, vol. 120, issue C

Abstract: We explore the compatibility of uniform self-consistency and ordinary self-consistency, two extensions for handling multi-valued solutions within the consistency principle introduced by Hart and Mas-Colell (1989), with basic properties, such as reasonableness, which establishes bounds for payoffs based on the marginality principle. Our analysis focuses on convex games and balanced games through the study of almost positive games, a subset of convex games that plays a crucial role in the vector lattice structure of games. Further, we provide new axiomatic foundations of the core incorporating these consistency properties.

Keywords: Convex games; Shapley value; Core; Consistency; Reasonableness (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:120:y:2025:i:c:s0304406825000886

DOI: 10.1016/j.jmateco.2025.103171

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