  The authors propose a parametric model called the arena model for prediction
in paired competitions, i.e. paired comparisons with eliminations and
bifurcations. The arena model has a number of appealing advantages. First, it
predicts the results of competitions without rating many individuals. Second,
it takes full advantage of the structure of competitions. Third, the model
provides an easy method to quantify the uncertainty in competitions. Fourth,
some of our methods can be directly generalized for comparisons among three or
more individuals. Furthermore, the authors identify an invariant Bayes
estimator with regard to the prior distribution and prove the consistency of
the estimations of uncertainty. Currently, the arena model is not effective in
tracking the change of strengths of individuals, but its basic framework
provides a solid foundation for future study of such cases.
