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Not sure about envy specifically, but I had a prof in grad school, her name was Rachel Kranton, and she was a theorist specializing in offbeat utility functions, such as utility functions that depend on your own perceptions of what you are "supposed" to have, which sounds a little like envy.
Definitely would love to dive into that stuff more now.
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Someone’s probably done this, but I’ve never seen it, what happens if you put envy into a utility function in a similar way that altruism is sometimes incorporated?