  The notion of interchangeability has been introduced by John Nash in one of
his original papers on equilibria. This paper studies properties of Nash
equilibria interchangeability in cellular games that model behavior of infinite
chain of homogeneous economic agents. The paper shows that there are games in
which strategy of any given player is interchangeable with strategies of
players in an arbitrary large neighborhood of the given player, but is not
interchangeable with the strategy of a remote player outside of the
neighborhood. The main technical result is a sound and complete logical system
describing universal properties of interchangeability common to all cellular
games.
