Equilibria interchangeability in cellular games

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