On the probability of winning a lottery with a random number of competitors

This article is concerned with models in which an agent faces a lottery with j other agents for a prize, so that the probability ofwinning the prize is 1/( j+ 1), and where j is stochastic. After describing four different situations where such a lottery is present, we construct the expected value of the probability of winning such a lottery and prove a theorem that presents the expected value in a simpler form. We then give an example of the theorem being applied to gain new insights into auction theory.