Forecasting and rank-order contests

Forecasting is modeled as a rank-order contest with privately informed players. Rankorder contests are shown to be natural generalizations of Hotelling’s classic location game. Positioning at the posterior mean is shown to be a Nash equilibrium in a perfectly symmetric setting with no prior information. In the presence of prior information the equilibrium is no longer at the posterior mean. Pure-strategy equilibria are shown to exist when the state space is discrete and the signal space continuous. A differential equation characterization of the symmetric equilibrium is provided for the winner-takes-all contest, in which only the forecaster with the lowest forecast error is rewarded. According to numerical simulations, in a winner-takes-all contest the amount of differentiation increases in the number of forecasters. If instead the forecaster with the highest forecast error is the only one to be punished, the amount of differentiation decreases in the number of players, and extreme conservatism results in the limit with an infinite number of forecasters. The more convex is the prize structure, the greater the incentive to differentiate.