Let's say I'm interested in two player games.
I'm aware of the complexities of finding mixed Nash equilibria. To really be sure we've found all we have to enumerate all possible combinations of row and column strategies and check for indifference (ignoring other simple tricks).
Although, let's assume some pure Nash equilibria exist. Does this say anything about mixed ones?
If pure strategies do exist can my search for mixed strategies include only those that contain at least one of the strategies from the pure Nash equilibrium in their support?