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

Abstract

This article is concerned with models in which an agent faces a lottery with j other agents for a prize, so that the probability of winning 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.

Keywords:

• binomial distribution
• binomial theorem
• lottery
• English auction

JEL Classification:

• D44
• C16