Knowledge in Communication Networks
Pavel Naumov and Jia Tao
The paper investigates epistemic properties of information flow under communication protocols with a given topological structure of the communication network. The main result is a sound and complete logical system that describes all such properties. The system consists of a variation of the multi-agent epistemic logic S5 extended by a new network-specific Gateway axiom. [pdf]
A Modal Logic for Reasoning about Economic Policies
Pavel Naumov and Jia Tao
The article introduces a modal logic for reasoning about combined effect of economic policies imposed on a group of rational agents. Modalities in this language are labeled by policies applied to the players in a strategic game. The resulting logical system allows to reason about properties that are true in all Nash equilibria of the game modified by a specific policy. The main technical result is the completeness theorem for the proposed logical system. [pdf]
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]