I am trying to identify (and find) a science fiction story that I read probably between 35 and 50 years ago. The premise was that there was a great machine to test the skills of would-be major administrators by hooking them up to a mini-biosphere.

In the mini-biosphere a race of tiny creatures went through an entire год in the 24 hours that a human subject was hooked to the machine. Each "year" these creatures would get a new god (the latest administrative applicant) who would communicate directly with one of the creatures, who in turn would become the prophet of this new god. If the applicant/god caused too much turmoil, too many deaths, the feedback through the machine could actually kill him, but if he were too cautious he would fail the test. The main character in this story, whose own father had been killed by the machine, started off doing a dismal job, being too cautious and letting his own prophet down repeatedly (to the dismay of the audience in the gallery surrounding the machine). How he coped with his год of godhood was the essence of this story.

That's about what I remember.

Any help would be greatly appreciated!