A note on the continuity of the optimal auction

- I study the continuity of the optimal auction revenue as a function of the types distribution.
- Revenue is lowersemicontinuous for convergence in distribution.
- Revenue is continuous if the limit distribution is a continuous distribution.

In the independent private values auction model I study the continuity properties of the optimal auction revenue as a function of the valuations or types distribution. I show that the optimal revenue is lowersemicontinuous for convergence in distribution. If the limit distribution is continuous, the optimal auction revenue is continuous in distribution as well.