[1] SNE is particularly useful in areas such as the study of voting systems, in which there are typically many more players than possible outcomes, and so plain Nash equilibria are far too abundant.
[2] Nessah and Tian[3] prove that an SNE exists if the following conditions are satisfied: For example, consider a game with two players, with strategy spaces [1/3, 2] and [3/4, 2], which are clearly compact and convex.
As a result of these requirements, Strong Nash rarely exists in games interesting enough to deserve study.
Every correlated strategy supported by iterated strict dominance and on the Pareto frontier is a CPNE.
[4] Further, it is possible for a game to have a Nash equilibrium that is resilient against coalitions less than a specified size k. CPNE is related to the theory of the core.