Bayesian game theorists and non-Bayesian players

Bayesian game theorists claim to represent players as Bayes rational agents, maximising their expected utility given their beliefs about the choices of other players. I argue that this narrative is inconsistent with the formal structure of Bayesian game theory. This is because (i) the assumption of common belief in rationality is equivalent to equilibrium play, as in classical game theory, and (ii) the players' prior beliefs are a mere mathematical artefact and not actual beliefs held by the players. Bayesian game theory is thus a Bayesian representation of the choice of players who are committed to play equilibrium strategy profiles.