How Do I Know That I Am Not Part of Someone Else's Dream?

This question puts a peculiar twist on Descartes' story of the Evil Demon.

In the First Meditation, Descartes imagines that there is an evil demon deceiving him into thinking that he is awake, in contact with a world of physical objects around him, when in reality he is only dreaming. Yet even if an evil demon deceives me, argues Descartes, there is a "me" being deceived. Deceived about the existence of an external world or not, either way I must exist.

Yet it could be argued that there is a possibility that Descartes does not consider. He assumes that as an existing subject, in a dream world or a real world, I make judgments about my experiences, perform inferences, ask questions, consider doubts. These are actions, albeit mental actions. But what if I did not exist as a subject capable of actions, physical or mental? What if all these thoughts passing through my mind are merely experiences being fed to me? This is a scenario that should not be unfamiliar to readers of science fiction: the idea that one might exist inside the circuits of a supercomputer as a character following the script generated by a virtual reality program.