  Motivated by the lossy compression of an active-vision video stream, we
consider the problem of finding the rate-distortion function of an arbitrarily
varying source (AVS) composed of a finite number of subsources with known
distributions. Berger's paper `The Source Coding Game', \emph{IEEE Trans.
Inform. Theory}, 1971, solves this problem under the condition that the
adversary is allowed only strictly causal access to the subsource realizations.
We consider the case when the adversary has access to the subsource
realizations non-causally. Using the type-covering lemma, this new
rate-distortion function is determined to be the maximum of the IID
rate-distortion function over a set of source distributions attainable by the
adversary. We then extend the results to allow for partial or noisy
observations of subsource realizations. We further explore the model by
attempting to find the rate-distortion function when the adversary is actually
helpful.
  Finally, a bound is developed on the uniform continuity of the IID
rate-distortion function for finite-alphabet sources. The bound is used to give
a sufficient number of distributions that need to be sampled to compute the
rate-distortion function of an AVS to within a certain accuracy. The bound is
also used to give a rate of convergence for the estimate of the rate-distortion
function for an unknown IID finite-alphabet source .
