Conditional interchangeability of Nash equilibria

The notion of interchangeability was introduced by Nash in one of his original papers on equilibria in strategic games. It has been recently shown that propositional theory of this relation is the same as propositional theories of the non-deducibility relation in the information flow theory, the independence relation in probability theory, and the non-interference relation in concurrency theory. Propositional theories of conditional non-deducibility and conditional independence have been studied before. This article introduces a notion of conditional interchangeability and gives complete axiomatization of this relation with conditioning by a single player.</p