Abstract
We study a game based on a model for the spread of influence through social networks. In game theory, a Nash-equilibrium is a strategy profile in which each player’s strategy is optimized with respect to her opponents’ strategies. Here we focus on a specific two player case of the game. We show that there always exists a Nash-equilibrium for paths, cycles, trees, and Cartesian grids. We use the centroid of trees to find a Nash-equilibrium for a tree with a novel approach, which is simpler compared to previous works. We also explore the existence of Nash-equilibriums for uni-cyclic graphs, and offer some open problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: A note on competitive diffusion through social networks. Information Processing Letters 110, 221–225 (2010)
Barron, E.N.: Game Theory, An Introduction, 2nd edn. Wiley-Inter science, John Wiley and Sons, Hoboken, NJ (2008)
Bhagat, S., Goyal, A., Lakshmanan, L.V.S.: Maximizing Product Adoption in Social Networks. In: Proceedings of the Fifth ACM International Conference on Web Search and Data Mining, pp. 603–612 (2012)
Dürr, C., Thang, N.K.: Nash equilibria in Voronoi games on graphs. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 17–28. Springer, Heidelberg (2007)
Immorlica, N., Kleinberg, J.M., Mahdian, M., Wexler, T.: The role of compatibility in the diffusion of technologies through social networks. In: Proceedings of the 8th ACM Conference on Electronic Commerce, pp. 75–83 (2007)
Kempe, D., Kleinberg, J.M., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the 9th International Conference on Knowledge Discovery and Data Mining (KDD), pp. 137–146 (2003)
Mavronicolas, M., Monien, B., Papadopoulou, V.G., Schoppmann, F.: Voronoi games on cycle graphs. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 503–514. Springer, Heidelberg (2008)
Small, L., Mason, O.: Nash Equilibria for Competitive Information Diffusion on Trees. Information Processing Letters 113, 217–219 (2013)
Small, L., Mason, O.: Information diffusion on the iterated local transitivity model of online social networks. Discrete Applied Mathematics 161, 1338–1344 (2013)
Takehara, R., Hachimori, M., Shigeno, M.: A comment on pure-strategy Nash equilibria in competitive diffusion games. Information Processing Letters 112, 59–60 (2012)
West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall Inc., Upper Saddle River (2001)
Wilf, H.S.: The uniform selection of free trees. Journal of Algorithms 2, 204–207 (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Roshanbin, E. (2014). The Competitive Diffusion Game in Classes of Graphs. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-07956-1_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07955-4
Online ISBN: 978-3-319-07956-1
eBook Packages: Computer ScienceComputer Science (R0)