Strict equilibria interchangeability in multi-player zero-sum games

Abstract

The interchangeability property of Nash equilibria in two-player zerosum games is well-known. This paper studies possible generalizations of this property to multi-party zero-sum games. A form of interchangeability property for strict Nash equilibria in such games is established. It is also shown, by proving a completeness theorem, that strict Nash equilibria do not satisfy any other non-trivial properties.