We study a strategic model of marketing in social networks in which two firms compete for the spread of their products. Firms initially determine the production cost of their product, which results in the payoff of the product for consumers, and the number and the location of the consumers in a network who receive the product as a free offer. Consumers play a local coordination game over a fixed network which determines the dynamics of the spreading of products. Assuming myopic best response dynamics, consumers 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 derive a lower and an upper bound on the proportion of product adoptions which not only depend on the number of initial seeds but also incorporate their locations as well. Using these bounds, we then study which consumers should be chosen initially in a network in order to maximize product adoptions for firms. We show consumers should be seeded based on their eigenvector centrality in the network. We then consider a game between two firms aiming to optimize their products adoptions while considering their fixed budgets. We describe the Nash equilibrium of the game between firms in star and k-regular networks and compare the equilibrium with our previous results.
Date of this Version
Game Theory, Social Networks, Viral Marketing, Stochastic Process, Optimization
Date Posted: 23 January 2013