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]

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]

Epistemic Logic for Communication Chains

Jeffrey Kane and Pavel Naumov

The paper considers epistemic properties of linear communication chains. It describes a sound and complete logical system that, in addition to the standard axioms of S5 in a multi-modal language, contains two non-trivial axioms that capture the linear structure of communication chains. [pdf]