Sequence prediction is a key component of intelligence. This can be extended to define a game between intelligent agents. An analog of a result of Legg shows that this game is a computational resources arms race for agents with enormous resources. Software experiments provide evidence that this is also true for agents with more modest resources. This arms race is a relevant issue for AI ethics. This paper also discusses physical limits on AGI theory. Keywords. Sequence prediction, AI ethics, physical limits on computing.