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]

Functional Dependence in Strategic Games

Kristine Harjes and Pavel Naumov

The article studies properties of functional dependencies between strategies of players in Nash equilibria of multi-player strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency graph for pay-off functions. A logical system describing properties of functional dependence for any given graph is proposed and is proven to be complete. [pdf]

Cellular Games, Nash Equilibria, and Fibonacci Numbers

Kristine Harjes and Pavel Naumov

The paper introduces a notion of cellular game that is in- tended to represent rationally behaving cells of a cellular automaton. The focus is made on studying properties of functional dependence between strategies of different cells in a Nash equilibrium of such games. The main result is a sound and complete axiomatization of these properties. The construction in the proof of completeness is based on the Fibonacci numbers. [pdf]