arXiv:2611.16207 · v1

Core nonemptiness for $2/3$-convex games

首次提交 2026-11-12 10:59

版本更新 2026-11-12 10:59

雷达观测 2026-11-13 14:16

摘要

We study the core of $2/3$-convex games, a class of transferable-utility (TU) games that generalizes convex games, which requires at least two of any three distinct coalitions satisfy the supermodular inequality. We show that every $2/3$-convex game admits a marginal worth vector in the core, and hence has a nonempty core. Our proof is constructive and yields a linear-time algorithm for finding such a core allocation. We also show that $2/3$-convexity does not imply permutational convexity in general, while the implication holds under an additional superadditivity condition on pairs of singletons. As an application, we introduce a TU model motivated by the OSCE's consensus-minus-two procedure and show that the resulting game is $2/3$-convex but need not be convex.