The Parable of the Fruit Sellers Or, A Game of Random Variables

Artem Hulko, Mark Whitmeyer

Published 2017-12-23Version 1

This paper analyzes a simple game with $n$ players. Fix a mean in interval $[0, 1]$ and let each player choose any random variable distributed on that interval with the given mean. The winner of the zero-sum game is the player whose random variable has the highest realization. We show that the position of the mean within the interval is crucial. Remarkably, if the given mean is above a crucial threshold then the equilibrium must contain a point mass on $1$. The cutoff is strictly decreasing in the number of players, $n$; and for fixed $\mu$, as the number of players is increased, each player places more weight on $1$ at equilibrium. We also characterize the unique symmetric equilibrium of the game when the mean is sufficiently low.