6 problems

Impossibility claim. Given these communication constraints, there exists no distributed algorithm that can solve TP without further conditions on the sequence of communication grap…

Let the initial opinions $x_1(0),\dots,x_N(0)$ be chosen independently and uniformly from $[0,L]$, and let $q_{L,N}$ be the probability that the resulting equilibrium is stable, me…

Let $x(t)\in\mathbb{R}^n$ be a trajectory of an SBC or SBI system, and let a trajectory have pseudo-stable behavior after a time $\tau$ when the agents split into non-empty fixed a…

Let $n$ interacting agents have opinion vector $x(t)\in\mathbb{R}^n$ and bounds vector $r\in\mathbb{R}^n_{>0}$. In the synchronized bounded confidence (SBC) and synchronized bounde…

Let $r=\{r_1,\dots,r_n\}\in\mathbb{R}^n_{>0}$ be the agents' confidence bounds and let $x(t)\in\mathbb{R}^n$ evolve according to the heterogeneous Hegselmann–Krause system … where…

Let $V$ be the finite set of agents, let $X_v(t)$ be the estimator of agent $v$ at time $t$ in the model where agents retain their previous values, and let $X(\infty)$ denote the l…