This paper studies the role that known bounds on message transmission times in a computer network play on the evolution of the epistemic state over time. A connection to cones of causal influence analogous to, and more general than, light cones is presented. Focusing on lower bounds on message transmission times, an analysis is presented of how knowledge about when others are guaranteed to be ignorant about an event of interest (“knowing that they don’t know”) can arise. This has implications in competitive settings, in which knowing about another’s ignorance can provide an advantage. © 2018, Springer International Publishing AG.