Investing to get ahead (start) in contests

Abstract

In a contest, rivals compete for a prize by making irretrievable outlays. Commonly, researchers assume that contestants spontaneously start to compete at some designated time. In practice, however, preparation is an important part of the actual contest, where rivals may undertake actions in order to improve their chance of winning the prize. We model this as a two-player all-pay auction under complete information in which rivals can make an investment to try to get a head start before the contest is played. We provide conditions under which an equilibrium exists in which the player with the high prize valuation invests and the opponent does not. Importantly, an equilibrium can also exist in which it is the player with the low prize valuation that makes the investment. The investment opportunity allows the rivals to move some of the competition to the investment stage, reducing the intensity of fighting in the contest. Indeed, the investment can be so large in the first period that there is no fighting at all in the contest. This is important information if the aim is to minimize contest effort, such as in armed conflicts.

Keywords: all-pay auction, pre-contest investment, endogenous head start