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In this article, contestants play with a certain probability in Contest A and with the complementary probability in Contest B. This situation is called contest uncertainty. In both contests, effort is additively distorted by a contest noise parameter which affects the sensitivity of the contest success function (CSF). In Contest A (B), this parameter is linearly added to (subtracted from) effort. We analyze the interaction of contest uncertainty and contest noise on contestant behavior and profit. For symmetric contestants, contest noise has an ambiguous effect on effort and profit. We show that more contest uncertainty can imply greater effort. Furthermore, an introduction of an infinitesimal degree of contest uncertainty can have a large impact on effort and profit. Based on the analysis, this article presents the contest organizer's incentive to manipulate the degree of uncertainty in the contest. For profit or effort maximization, the contest organizer should always eliminate any uncertainty. If contestants are asymmetric, more contest noise increases effort as well as competitive balance if both Contests A and B have the same probability of occurrence. [Copyright Elsevier B.V.]

Contest success functions, which show how probabilities of winning depend on resources devoted to a conflict, have been widely used in the literature addressing appropriative activities (economics), international and civil wars (political science), and group conflict and selection (evolutionary biology). Two well-known forms of contest success functions predict contest outcomes from the difference between the resources of each side and from the ratio of resources. The analytical properties of a given conflict model, such as the existence of equilibrium, can be drastically changed simply by altering the form of the contest success function. Despite this problem, there is no consensus about which form is analytically better or empirically more plausible. In this paper we propose an integrated form of contest success functions, which has the ratio form and the difference form as limiting cases, and study the analytical properties of this function. We also estimate different contest success functions to see which form is more empirically probable, using data from battles fought in seventeenth-century Europe and during World War II.

In this article, I analyze a class of contest success functions (CSFs) that satisfy Luce's Choice Axiom. I show that the functional forms of these CSFs can be fully identified if they are characterized by a partial differential equation (PDE), which has several intuitive economic interpretations. This PDE approach provides foundations for popular CSFs and their generalizations.

We analyze how a contest organizer chooses the winner when the contestants.efforts are already exerted and commitment to the use of a given contest success function is not possible. We define the notion of rationalizability in mixed-strategies to capture such a situation. Our approach allows to derive different contest success functions depending on the aims and attitudes of the decider. We derive contest success functions which are closely related to commonly used functions providing new support for them. By taking into account social welfare considerations our approach bridges the contest literature and the recent literature on political economy.