Social norms and game theory: harmony or discord?

Recent years have witnessed an increased number of game-theoretic approaches to social norms, which apparently share some common vocabulary and methods. We describe three major approaches of this kind (due to Binmore, Bicchieri and Gintis), before comparing them systematically on five crucial themes: generality of the solution, preference transformation, punishment, epistemic conditions and type of explanation. This allows us to show that these theories are, by and large, less compatible than they seem. We then argue that those three theories struggle to account for three phenomena pertaining to social norms (namely context-dependence, conflicting norms and self-evidence), with which any complete game-theoretic account should in principle be able to deal.