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]

Symmetry in Information Flow

Jeffrey Kane and Pavel Naumov

The article investigates information flow properties of symmetric multi-party protocols. It gives a sound and complete axiomatic system for properties of the functional dependence predicate that are common to all protocols with the same group of symmetries. [pdf]

Rationally Functional Dependence

Pavel Naumov and Brittany Nicholls

Two different types of functional dependencies are compared: dependencies that are functional due to the laws of nature and dependencies that are functional if all involved agents behave rationally. The first type of dependencies was axiomatized by Armstrong. This article gives a formal definition of the second type of functional dependencies in terms of strategic games and describes a sound and complete axiomatization of their properties. The axiomatization is significantly different from the Armstrong’s axioms. [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]