This paper completely characterizes the set of Nash equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive...

I investigate the design of effort-maximizing mechanisms when agents have both private information and convex effort costs, and the designer has a fixed prize budget. I first demonstrate that it is always optimal for the designer to utilize a contest with as many participants as possible....