This lecture introduces the concept of knife-edge conditions.

Takeaway points:

1. Games in general form can have multiple types of equilibria depending on the values of the exogenous parameters. When one parameter is large, a mixed strategy Nash equilibrium might exist; but when it is small, it might disappear.
2. Sometimes a particular equilibrium exists only if a parameter takes on a very specific value. We call this a "knife-edge" condition, as that value rest precariously on that specific value.
3. Since equilibria that rely on knife-edge conditions are substantively questionable, we tend to ignore them.