Social Networks and the Choices People Make

Abstract: Social marketing is becoming increasingly important in contemporary business. Central to social marketing is quantifying how consumers choose between alternatives and how they influence each other. This work considers a new but simple multinomial choice model for multiple agents connected in a recommendation network based on the explicit modeling of choice adoption behavior. Efficiently computable closed-form solutions, absent from analyses of threshold/cascade models, are obtained together with insights on how the network affects aggregate decision making. A stylized "brand ambassador" selection problem is posed to model targeting in social marketing. Therein, it is shown that a greedy selection strategy leads to solutions achieving at least $1-1/e$ of the optimal value. In an extended example of imposing exogenous controls, a pricing problem is considered wherein it is shown that the single player profit optimization problem is concave, implying the existence of pure strategy equilibria for the associated pricing game.