Equilibria Interchangeability in Cellular Games

Pavel Naumov and Margaret Protzman

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 behavior of innite 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 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. [pdf]

Conditional Interchangeability of Nash Equilibria

Pavel Naumov Margaret Protzman

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 nondeducibility relation in the information ow theory, the independence relation in probability theory, and the noninterference relation in concurrency theory.

Propositional theories of conditional nondeducibility 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. [pdf]

Strict Equilibria Interchangeability in Multi-Player Zero-Sum Games

Pavel Naumov and Italo Simonelli 

The interchangeability property of Nash equilibria in two-player zero- sum games is well-known. This paper studies possible generalizations of this property to multi-player 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. [pdf]

On Interchangeability of Nash Equilibria in Multi-Player Strategic Games

Pavel Naumov and Brittany Nicholls

The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory. [pdf]