6 problems

Let $P$ be the set of players and let $\mathcal{K}$ be a coalition structure, with core stability meaning that no subset $S \subseteq P$ can deviate to form a new coalition and mak…

Let $G=(V,E)$ be a graph, with the energy game assigning each coalition its graph energy and with $\boldsymbol{\varphi}$ denoting the Shapley value. Energy-game core conjecture. Fo…

Facet characterization conjecture. If $|N|\geq 3$, then the facet-defining inequalities for the cone $E(N)$ are exactly the inequalities corresponding to non-trivial irreducible mi…

Let $w_1,w_2,w_3, \ldots, w_m$ be positive weights, let $w$ be their maximum, and set … For a voting game with these weights, let $\beta_i$ denote the relative Banzhaf index of pla…

Let $\operatorname{Nak}^{\mathcal{T}}(n,t)$ denote the maximum possible Nakamura number among weighted games on $n$ players with $t$ types of players, where $t\in\mathbb{N}_{>0}$.…

Let $n\ge 2$, let $\mathfrak{W}$ denote the class of weighted games, and let $c_{\mathcal{P}}(n,\mathfrak{W})$ be the cost of local monotonicity for the power-index collection…