I have gotten the notion that it's important for Value-Preserving Self-Modification in a potential AI agent, but I'm confused because it all sounds too much like game theory - there all all these other-agents it deals with

My impression is that, with self-modification and time, continuity of identity becomes a sticky issue. If I can become an entirely different person tomorrow, how I structure my life is not the weak game theory of "how do I bargain with another me?" but the strong game theory of "how do I bargain with someone else?"