Investing to get a head start in contests

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 a pure-strategy equilibrium exists in which the player with the high prize valuation invests and the opponent does not. A pure-strategy 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. An important feature of our model is that investment does not necessarily preclude fighting in the contest. We show when investment leads to active participation in the contest, and when it leads a rival to simply capitulate. This is an important distinction, especially if the overall aim is to minimize contest effort, such as in armed conflicts.