Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
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.