This lecture introduces the concept of knife-edge conditions.
- 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.
- Sometimes a particular equilibrium exists only if a parameter takes on a specific value. We call this a knife-edge condition, as the parameter rests precariously on that exact number.
- Since equilibria that rely on knife-edge conditions are substantively questionable, we tend to ignore them.