INFORMATION AND META-INFORMATION

Although notions of rationality have been extensively discussed in game theory, the epistemic conditions under which a game is played – though implicitly presumed – have seldom been explicitly analyzed and formalized. These conditions include the players' reasoning processes and capabilities, as well as their knowledge of the game situation. Some aspects of information about chance moves and other players' moves are represented by information partitions in extensive-form games. But a player's knowledge of the structure of information partitions themselves is different from his information about chance moves and other players' moves. The informational aspects captured by the extensive form have nothing to do with a player's knowledge of the structure of the game.

A common epistemic presumption is that the structure of the game is common knowledge among the players. By “common knowledge of p” is meant that p is not just known by all the players in a game, but is also known to be known, known to be known to be known, … ad infinitum. The very idea of a Nash equilibrium is grounded on the assumptions that players have common knowledge of the structure of the game and of their respective priors. These assumptions, however, are always made outside the theory of the game, in that the formal description of the game does not include them.