Optimal Strategies for Second Guessers

Abstract

A 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.

Key Words:

• Guessing
• Optimal strategies
• Hierarchical linear model
• Stein estimator
• Posterior median