Article ID Journal Published Year Pages File Type
1129690 Social Networks 2006 15 Pages PDF
Abstract

We consider a firm’s profit maximization problem when the demand for the product is created by referrals between consumers connected in a small world network. We generate a small world network by applying the rewiring algorithm of Watts and Strogatz and incorporate it into the profit maximization problem. We demonstrate (i) that contrary to our anticipation, the firm’s profit smoothly (not rapidly) approaches the profit in the complete network as the rewiring probability increases, but (ii) that the per consumer profit is saturated to a finite non-zero value when the rewiring probability is near zero, implying a small world transition.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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