Examination of the term "block" shows that it is counterintuitive and misleading when used in connection with the core and should be avoided or clarified whenever possible, despite its history of past usage in the literature of economics and game theory. Economists new to game theory often imagine that the core is related to the ability of coalitions to obstruct the system, but this is incorrect. The difficulty disappears if the core is described in terms of "improving" or "recontracting" rather than "blocking." The core, after all, expresses what coalitions can or cannot do for themselves, not what they can or cannot do to their opponents. It is worth noting, moreover, that in the formal theory of simple games, such as voting games, the well-established terms "block" and "blocking coalition" enjoy their common English meanings, and this usage is being extended to graph theory and other mathematical subjects where structures similar to simple games occur.
Shapley, Lloyd S., Let's Block "Block". Santa Monica, CA: RAND Corporation, 1972. https://www.rand.org/pubs/papers/P4779.html. Also available in print form.
Shapley, Lloyd S., Let's Block "Block", Santa Monica, Calif.: RAND Corporation, P-4779, 1972. As of September 08, 2021: https://www.rand.org/pubs/papers/P4779.html