Game Theoretic Analysis of a Strategic Model of Competitive Contagion and Product Adoption in Social Networks

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General Robotics, Automation, Sensing and Perception Laboratory
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Game Theory
Social Networks
Viral Marketing
Stochastic Process
Controls and Control Theory
Dynamic Systems
Other Applied Mathematics
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Fazeli, Arastoo

In this paper we propose and study a strategic model of marketing and product adoption in social networks. Two firms compete for the spread of their products in a social network. Considering their fixed budgets, they initially determine the payoff of their products and the number of their initial seeds in a network. Afterwards, neighboring agents play a local coordination game over a fixed network which determines the dynamics of the spreading. Assuming myopic best response dynamics, agents choose a product based on the payoff received by actions of their neighbors. This local update dynamics results in a game-theoretic diffusion process in the network. Utilizing earlier results in the literature, we find a lower and an upper bound on the proportion of product adoptions. We derive an explicit characterization of these bounds based on the payoff of products offered by firms, the initial number of adoptions and the underlying structure of the network. We then consider a case in which after switching to the new product, agents might later switch back to the old product with some fixed rate. We show that depending on the rate of switching back to the old product, the new product might always die out in the network eventually. Finally, we consider a game between two firms aiming to optimize their products adoptions while considering their fixed budgets. We describe the Nash equilibrium of this game and show how the optimal payoffs offered by firms and the initial number of seeds depend on the relative budgets of firms.

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Fazeli, A. & Jadbabaie, A. (2012). Duopoly Pricing Game in Networks With Local Coordination Effects. Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, pp. 74-79. © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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