I’ll note that “not being sure what utility functions are in use” is generally (in the colloquial sense) not how standard game theory works. It seems like I am not competent enough at standard game theory to clearly write down the edge cases I think might exist that could help with your understanding. This paragraph could serve as a placeholder for the case where I develop that competence.
As for non-standard game theory, you say you’re reading the 2009 book The Bounds of Reason here[1] and I wonder if you’ve heard of the newer Translucent players: Explaining cooperative behavior in social dilemmas by Valerio Capraro and J. Y. Halpern, substantially related to your topic of the process of functioning itself being part of what is considered in a way not fully instrumental (by normative procedures).
This article fails to cite chapter 7 of the older book Good and Real by Garry Drescher, published in 2006, a partially flawed discussion of similar topics. The analysis substantially by J. Y. Halpern across multiple articles is clearer in its limitations than Drescher’s, and it lets you set up new variations of sociological problems that can then be attacked by standard mathematical techniques. This is unlike the current state of a hypothetical “UDT 1.0 game theory,” itself the algorithmic similarity based subset of Drescher’s proposal[2].
Spoiler
HJPEV is bound by a magical oath that prevents this human failing in the same way it is prevented in an agent that meets tiling desiderata. This is explicit in the text. E-Book draft, 2015, chapter 113.
Admittedly this both assumes that the “time of peril” hypothesis is correct and can be handled while maintaing human freedom, and the solution only (in maximum robustness) binds until the end of this time.