Mohammad Tanvir Irfan

On influence, stable behavior, and the most influential individuals in networks: a game-theoretic approach

We introduce a new approach to the study of influence in strategic settings where the action of an individual depends on that of others in a network-structured way. We propose network influence games as a game-theoretic model of the behavior of a large but finite networked population. In particular, we study an instance we call linear-influence games that allows both positive and negative influence factors, permitting reversals in behavioral choices. We embrace pure-strategy Nash equilibrium, an important solution concept in non-cooperative game theory, to formally define the stable outcomes of a network influence game and to predict potential outcomes without explicitly considering intricate dynamics. We address an important problem in network influence, the identification of the most influential individuals, and approach it algorithmically using pure-strategy Nash-equilibria computation. Computationally, we provide (a) complexity characterizations of various problems on linear-influence games; (b) efficient algorithms for several special cases and heuristics for hard cases; and (c) approximation algorithms, with provable guarantees, for the problem of identifying the most influential individuals. Experimentally, we evaluate our approach using both synthetic network influence games and real-world settings of general interest, each corresponding to a separate branch of the U.S. Government. Mathematically, we connect linear-influence games to important models in game theory: potential and polymatrix games.

The Art Gallery Theorem for Polyominoes

We explore the art gallery problem for the special case that the domain (gallery) P is an m-polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the traditional parameter n, the number of vertices of P. In particular, we show that

Multiple visual features for the computer authentication of Jackson Pollock's drip paintings: beyond box counting and fractals

\lfloor\frac{m+1}{3} \rfloor

A game-theoretic approach to influence in networks

point guards are always sufficient and sometimes necessary to cover an m-polyomino, possibly with holes. When

Guarding polyominoes

m \leq\frac{3n}{4} - 4

Tractable Algorithms for Approximate Nash Equilibria in Generalized Graphical Games with Tree Structure.

, the sufficiency condition yields a strictly lower guard number than

FPTAS for Mixed-Strategy Nash Equilibria in Tree Graphical Games and Their Generalizations.

\lfloor\frac{n}{4}\rfloor

Causal Strategic Inference in Social and Economic Networks

, given by the art gallery theorem for orthogonal polygons.