Rational decisions depend on what players know, hence an appropriate epistemic analysis is an integral element of the foundations of Game Theory. We suggest a general logical approach for studying games which consists of formalizing rationality and games in epistemic logic and deriving their properties in the resulting logical system. We study a number of examples and demonstrate that our model can produce a finer-grained analysis of game-theoretical scenarios and provide a non-circular justification of Nash equilibrium strategies.

We show that within this model, in strategic-form and extensive-form games, an assumption of first-level mutual knowledge of the game and players' rationality implies Nash equilibrium and backward induction solutions. This refutes a general perception that common knowledge of rationality is needed to justify backward induction in games with perfect information.