Competition between Cooperative Projects

A paper needs to be good enough to be published; a grant proposal needs to be sufficiently convincing compared to the other proposals, in order to get funded. Papers and proposals are examples of cooperative projects that compete with each other and require effort from the involved agents, while often these agents need to divide their efforts across several such projects. We aim to provide advice how an agent can act optimally and how the designer of such a competition (e.g., the program chairs) can create the conditions under which a socially optimal outcome can be obtained. We therefore extend a model for dividing effort across projects with two types of competition: a quota or a success threshold. In the quota competition type, only a given number of the best projects survive, while in the second competition type, only the projects that are better than a predefined success threshold survive. For these two types of games we prove conditions for equilibrium existence and efficiency. Additionally we find that competitions using a success threshold can more often have an efficient equilibrium than those using a quota. We also show that often a socially optimal Nash equilibrium exists, but there exist inefficient equilibria as well, requiring regulation.