Physics (Internal)

Strategy of Competition between Two Groups based on an Inflexible Contrarian Opinion Model

This event is part of the Preliminary Oral Exam.

Examining Committee: H. E. Stanley, William Klein, Kevin Smith, Robert Carey We introduce an inflexible contrarian opinion (ICO) model in which a fraction of inflexible contrarians within a group holds a strong opinion opposite to the opinion held by the rest of the group. At the initial stage, stable clusters of two opinions, and exist. Then we introduce inflexible contrarians which hold a strong opinion into the opinion group. Through their interactions, the inflexible contrarians are able to decrease the size of the largest opinion cluster, and even destory it. We see this kind of method in operation, when companies send free new products to potential customers in order to convince them to adopt their product and influence others to buy it. We study the ICO model, using two different strategies, on both Erd ̈os-R ́enyi and scale-free networks. In strategy I, the inflexible contrarians are positioned at random. In strategy II, the inflexible contrarians are chosen to be the highest degrees nodes. We find that for both strategies the size of the largest cluster decreases to zero as increases as in a phase transition. At a critical threshold value the system undergoes a second-order phase transition that belongs to the same universality class of mean field percolation. We find that even for an Erd ̈os-R ́enyi type model, where the degrees of the nodes are not so distinct, strategy II is significantly more effctive in reducing the size of the largest opinion cluster and, at very small values of the largest opinion cluster is destroyed.