We explore how individual equilibrium effort in tournaments varies with the number of contestants. The probability of winning a tournament depends on both effort and luck, and we show that the distribution of the luck component is critical in determining individual equilibrium effort. Our theory predicts that equilibrium effort is an increasing (decreasing) function of the number of contestants if there is considerable (little) mass on favorable draws. We test our theory using both laboratory and field experiments, and find substantial support for our theory in both settings.
- theory of tournaments