Steele, John MZidek, James2023-05-232023-05-2319802016-09-26https://repository.upenn.edu/handle/20.500.14332/41997A model is given for a class of contests in which the participants try to guess (or estimate) unknown quantities, and the objective of each player is to come closer to the unknown quantities than an adversary. A general optimality result is proved that gives the best guessing rules for the second guesser. These rules are first calculated exactly in a certain hierarchical linear model, and then simpler approximate rules are given.This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 1980, available online: http://wwww.tandfonline.com/doi/abs/10.1080/01621459.1980.10477519Guessingoptimal strategieshierarchical linear modelstein estimatorposterior medianDynamic SystemsOther Applied MathematicsStrategic Management PolicyArticle