Duopoly budget allocation in social networks: A nash analysis approach

In this paper, we study a strategic model of marketing and product consumption in social networks. We consider two firms in a market competing to maximize the consumption of their products. Firms have a limited budget which can be either invested on the quality of the product or spent on initial seeding in the network in order to better facilitate spread of the product. After the decision of firms, agents choose their consumptions following a myopic best response dynamics which results in a local, linear update for their consumption decision. We characterize the unique Nash equilibrium of the game between firms and study the effect of the budgets as well as the network structure on the optimal allocation. We show that at the equilibrium, firms invest more budget on quality when their budgets are close to each other. However, as the gap between budgets widens, competition in qualities becomes less effective and firms spend more of their budget on seeding. We also show that given equal budget of firms, if seeding budget is nonzero for a balanced graph, it will also be nonzero for any other graph, and if seeding budget is zero for a star graph it will be zero for any other graph.

[1]  Ali Jadbabaie,et al.  Game theoretic analysis of a strategic model of competitive contagion and product adoption in social networks , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[2]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[3]  Éva Tardos,et al.  Influential Nodes in a Diffusion Model for Social Networks , 2005, ICALP.

[4]  Ali Jadbabaie,et al.  Duopoly pricing game in networks with local coordination effects , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[5]  A. Galeotti,et al.  Influencing the influencers: a theory of strategic diffusion , 2009 .

[6]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[7]  Jeff S. Shamma,et al.  Control of preferences in social networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[8]  Ali Jadbabaie,et al.  Optimal budget allocation in social networks: Quality or seeding? , 2014, 53rd IEEE Conference on Decision and Control.

[9]  Michael Kearns,et al.  Competitive contagion in networks , 2011, STOC '12.

[10]  H. Peyton Young,et al.  Individual Strategy and Social Structure , 2020 .

[11]  Peter H. Reingen,et al.  Brand Congruence in Interpersonal Relations: A Social Network Analysis , 1984 .

[12]  Shishir Bharathi,et al.  Competitive Influence Maximization in Social Networks , 2007, WINE.

[13]  Antoni Calvó-Armengol,et al.  Centre De Referència En Economia Analítica Barcelona Economics Working Paper Series Working Paper Nº 178 Who's Who in Networks. Wanted: the Key Player Who's Who in Networks. Wanted: the Key Player Barcelona Economics Wp Nº 178 , 2022 .

[14]  J. Kleinberg.  Algorithmic Game Theory: Cascading Behavior in Networks: Algorithmic and Economic Issues , 2007 .

[15]  Linda L. Price,et al.  The market maven: A diffuser of marketplace information. , 1987 .

[16]  Andrea Montanari,et al.  The spread of innovations in social networks , 2010, Proceedings of the National Academy of Sciences.

[17]  David Godes,et al.  Using Online Conversations to Study Word-of-Mouth Communication , 2004 .

[18]  Asuman Ozdaglar,et al.  Competing over Networks , 2015 .

[19]  Glenn Ellison.  Learning, Local Interaction, and Coordination , 1993 .

[20]  Tansu Alpcan,et al.  Network Security , 2010 .

[21]  Ali Jadbabaie,et al.  Targeted marketing and seeding products with positive externality , 2012, 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[22]  H. Young,et al.  Individual Strategy and Social Structure: An Evolutionary Theory of Institutions , 1999 .

[23]  Eyton,et al.  The Diffusion of Innovations in Social Networks , 2002 .