Implicit Markets: Lotteries

An Equilibrium Model of Rollover Lotteries (with Giovanni Compiani and Lorenzo Magnolfi)

Abstract: In a rollover lottery, buyers pick their own numbers, and a jackpot not won rolls over to the next draw. Since they are a major source of government revenue globally, we develop an equilibrium model of this lottery to shed light on its design. Buyers care about the lottery enjoyment level and expected winnings, and the market-clearing price is not the ticket price but the expected monetary loss on a lottery ticket. The supply curve captures the relation between tickets sold and expected loss implied by the rules of the game.

We use this equilibrium model in two empirical applications. First, we test the model’s predictions on the optimal relationship between odds and population size using data from many countries, and across U.S. states. Second, we propose a structural empirical implementation of the model and nonparametrically estimate demand for U.S. national rollover lotteries by exploiting the randomness inherent in the rollover mechanism. We find that the model predicts well out of sample and show how to use it to inform lottery design.