Three essays on contests

This dissertation studies several important issues in contest theory. The first essay reexamines the level playing field principle in contests in the context of a general contest environment where the winner and loser's payoffs depend, in part, on all players' efforts (e.g., there are rank-order spillovers). I derive a closed-form expression for the symmetric Nash equilibrium, and identify necessary and sufficient conditions for existence and uniqueness of equilibrium for this parameterized class of contests. I also examine how asymmetries among players impact efforts in a neighborhood of the symmetric equilibrium, and provide necessary and sufficient conditions for the level playing field principle to hold. In the second essay, I extend the first essay to the context of a more general environment where a player not only puts forth self-directed effort on to his own production but also expends rival-directed effort on to the production of his rival's. I also allow for spillovers of both players' productions on to the contest prize. I derive a closed-form expression for the Nash equilibrium, and identify necessary and sufficient conditions for existence and uniqueness of equilibrium for this parameterized class of contests. I show that rival-directed effort may either be positive or negative, depending on the players' abilities, marginal productions of both effort types, and the nature of spillovers. I also provide necessary and sufficient conditions for the level playing field principle to hold in this case. The third essay investigates the associative character of competition and cooperation in work environment. I consider firms in which workers form partnerships and become co-owners. Each partner not only works in his task but also help other partners in theirs. I present a multi-agent multi-task contest model to show that inefficiency always occurs. I then extend the model to multi-period and show that in partnerships in which help is important, it is more efficient to use hiring- from-outside than promoting-from-within employee policy.