This paper develops the comparative statics properties of a contest en
countered in patent races and rent-seeking games. I show that symmetri
c equilibrium expenditure and profit per player decrease with the numb
er of competitors and the discount rate, but increase with the value o
f the prize. A fundamental lemma established in the paper shows that a
stability condition usually imposed on the model is automatically sat
isfied. I identify a class of likelihood or hazard rate functions for
which aggregate expenditure increases with the number of competitors a
nd total profits converge to zero.