Knife-Edge Equilibria

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 specific value. We call this a knife-edge condition, as the parameter rests precariously on that exact number.
  3. Since equilibria that rely on knife-edge conditions are substantively questionable, we tend to ignore them.

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