  We consider the problem of computing ratings using the results of games
played between a set of n players, and show how this problem can be reduced to
computing the positive eigenvectors corresponding to the dominant eigenvalues
of certain n by n matrices. There is a close connection with the stationary
probability distributions of certain Markov chains. In practice, if n is large,
then the matrices involved will be sparse, and the power method may be used to
solve the eigenvalue problems efficiently. We give an algorithm based on the
power method, and also derive the same algorithm by an independent method.
