Price of Privacy

Pavel Naumov and Jia Tao

The paper proposes a logical framework for reasoning about agents' ability to protect their privacy by hiding certain information from a privacy intruder. It is assumed that the knowledge of the intruder is derived from the observation of pieces of evidence and that there is a cost associated with the elimination of the evidence. 
The logical framework contains a modal operator labeled by a group of agents and a total budget available to this group. The key contribution of this work is the proposed incorporation of the cost factor into privacy protection reasoning within the standard modal logic framework. The main technical result are the soundness and completeness theorems for the introduced logical system with respect to a formally defined semantics. [pdf]

Marketing Impact on Diffusion in Social Networks

Pavel Naumov and Jia Tao 

The paper proposes a way to add marketing into the standard threshold model of social networks. Within this framework, the paper studies logical properties of the influence relation between sets of agents in social networks. Two different forms of this relation are considered: one for promotional marketing and the other for preventive marketing. In each case a sound and complete logical system describing properties of the influence relation is proposed. Both systems could be viewed as extensions of Armstrong's axioms of functional dependency from the database theory. [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]