  In most conversations about explanation and AI, the recipient of the
explanation (the explainee) is suspiciously absent, despite the problem being
ultimately communicative in nature. We pose the problem `explaining AI systems'
in terms of a two-player cooperative game in which each agent seeks to maximise
our proposed measure of explanatory effectiveness. This measure serves as a
foundation for the automated assessment of explanations, in terms of the
effects that any given action in the game has on the internal state of the
explainee.
