It seems that we agree that taking a game theoretic view can justify more than just 'the bare minimal extent required to protect others' as it can also include

It seems that we agree that taking a game theoretic view can justify more than just 'the bare minimal extent required to protect others' as it can also include questions of setting examples and letting justice be seen to be done that can form part of the decisions of other future potential criminals, or victims who might feel like taking the law into their own hands. So, as to 'they chose this themselves', that's begging the question a little - as we've already seen I think that believing in determinism doesn't stop you from believing that people can choose things. As to 'they deserve it', questions of what people deserve is a huge other topic, and I think it's most likely possible to define desert in terms that fit within a deterministic viewpoint. However, perhaps you're right about its effect since I do in fact think that vengeance is a thoroughly dumb rationale for treating people badly. This is to such an extent that I'd feel surprised to find anyone seriously try to justify it, which is why I didn't really engage with your apparent suggestion that it was an important justification. There are lots of ways you can try to justify criminal punishment in my view but 'vengeance' doesn't fit into any moral system I consider valuable unless it's actually being used as a code for game theoretic concerns or rehabilitation. But I don't feel so strange thinking this, since most people I know think the same, even those who don't share my views on free will and I'm pretty sure I believed it before I came to that conclusion on free will.