12 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 $\bar\Lambda^{SD}$ denote the scenario-dependent aggregation function associated with scenario-dependent systemic risk measures. Consider decompositions of $\bar\Lambda^{SD}$ i…

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…

The paper considers lane-changing interactions modeled as transferable-utility (TU) games, in which vehicles exchange right-of-way for monetary side payments and report their value…

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 the nucleolus be computed by the algorithms developed in the paper, with $T_0$ denoting the set used in the original algorithm. Extension conjecture. The algorithms developed s…

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…

Nested moat-packing conjecture. It is conjectured that

A complete simple game is a simple voting game whose desirability relation on voters is a total preorder. Voters are partitioned into types according to this preorder, and a shift-…

Core non-emptiness conjecture. The core will be non-empty, equivalently, the GC will be stable, when the channel gains $h_{m,k}$ and the powers $P_k$ are comparable for all $m$ and…