The main CSFs used in the literature are reviewed and their basic properties are explored. Different CSFs yield different games and outcomes, so it is essential to understand the differences between what is embedded in each CSF. In some cases, a little extra effort wins the field, as in racing, while in others, no matter the expense, all contestants receive a positive probability of getting a positive share, as in voting with captive voters. In others, like soccer and some armed conflicts, the probability of winning is proportional to the relative expenses. This chapter also begins an analysis of the existence and properties of a Nash equilibrium in contest games, either with identical contestants or, in the context of a couple of CSFs, with two contestants.

The concept of a contest is introduced, with examples such as political competition, litigation, wars, lobbying, awarding a prize or contract, sports, and patent races. These examples show the wide range of applications of contests, and prepare the reader for the consideration of contests as a field of study in their own right. Additionally, the main game theoretical concepts and the primary tool of this field, the Contest Success Function (CSF), are presented. The CSF, given the expenses/efforts/investments of the contestants, yields the probabilities that the contestants will win the contest or, in the case of a shared prize, the shares of the prize.