Citations and Incentives in Academic Contests

There are several empirical studies of ex post analysis of citations in academia. There is no ex ante analysis of citations. I consider a game-theoretic model of a contest between scholars on the basis of two widely-used measures of citations (i.e., the ℎ-index and total citation count) and the newly-developed Euclidean index (Perry and Reny, American Economic Review, 2016). I find equilibria in which there are more and better-quality papers in the total citations contest than in the ℎ-index contest. When the marginal cost of effort is constant, the scholars are indifferent between the number of papers and the quality of papers in the total citations contest but prefer quality of papers in the Euclidean contest although the total number of citations is the same in both contests. In some cases, the total citations contest yields the same quality of papers but more papers than the Euclidean contest, a result which holds when the marginal cost of effort is increasing but is not possible when the marginal cost of effort is constant. Consistent with previous empirical results, I find that as the cost of writing a paper increases, the ℎ-index is inferior to the total citations index in both the quality and quantity of papers. This result is driven by how the cost of effort constrains the number of papers that a scholar can write and how the number of papers, in turn, constrains how the ℎ-index counts citations.