There is another important lesson to draw from this epistemic characterization result. The widespread idea that game theory “assumes common knowledge of rationality”, perhaps in conjunction with the extensive use of equilibrium concepts in game-theoretic analysis, has lead to misconception that the Nash Equilibrium either requires common knowledge of rationality, or that common knowledge of rationality is sufficient for the players to play according to a Nash equilibrium. To be sure, game theoretic models do assume that the structure of the game is common knowledge (though, see Section 5.3). Nonetheless, the above result shows that both of these ideas are incorrect: 