Interesting.

How a player would want to modify their utility function depends on how other players modify theirs. Schelling introduces "strategic moves" in games: selectively reducing your payoffs under some outcomes. (This is a formalization of unilateral commitments, e.g. burning your bridges.) A simultaneous-move game of strategic moves derived from any simple game quickly becomes a pretty tricky beast. I'll have to look at it closer; thanks for reminding.