Two-Player Competitive Diffusion Game: Graph Classes and the Existence of a Nash Equilibrium

  • Naoka FukuzonoEmail author
  • Tesshu HanakaEmail author
  • Hironori KiyaEmail author
  • Hirotaka OnoEmail author
  • Ryogo Yamaguchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)


The competitive diffusion game is a game-theoretic model of information spreading on a graph proposed by Alon et al. (2010). In the model, a player chooses an initial vertex of the graph, from which information by the player spreads through the edges connected with the initial vertex. If a vertex that is not yet influenced by any information receives information by a player, it is influenced by the information and it diffuses it to adjacent vertices. A vertex that simultaneously receives two or more types of information does not diffuse any type of information from then on. The objective of a player is to maximize the number of vertices influenced by the player’s information. In this paper, we investigate the existence of a pure Nash equilibrium of the two-player competitive diffusion game on chordal and its related graphs. We show that a pure Nash equilibrium always exists on block graphs, split graphs and interval graphs, all of which are well-known subclasses of chordal graphs. On the other hand, we show that there is an instance with no pure Nash equilibrium on (strongly) chordal graphs; the boundary of the existence of a pure Nash equilibrium is found.


Nash equilibrium Competitive diffusion game Algorithmic game theory Chordal graph 


  1. 1.
    Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: A note on competitive diffusion through social networks. Inf. Process. Lett. 110(6), 221–225 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brandstadt, A., Spinrad, J.P., et al.: Graph Classes: A Survey, vol. 3. SIAM, Philadelphia (1999)CrossRefGoogle Scholar
  3. 3.
    Bulteau, L., Froese, V., Talmon, N.: Multi-player diffusion games on graph classes. Internet Math. 12(6), 363–380 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dirac, G.A.: On rigid circuit graphs. Abh. Math. Semin. Univ. Hambg 25(1), 71–76 (1961)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Etesami, S.R., Basar, T.: Complexity of equilibrium in competitive diffusion games on social networks. Automatica 68, 100–110 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Farber, M.: Characterizations of strongly chordal graphs. Discrete Math. 43(2–3), 173–189 (1983)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Harary, F.: A characterization of block-graphs. Can. Math. Bull. 6(1), 1–6 (1963)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ito, T., et al.: Competitive diffusion on weighted graphs. In: Dehne, F., Sack, J.-R., Stege, U. (eds.) WADS 2015. LNCS, vol. 9214, pp. 422–433. Springer, Cham (2015). Scholar
  9. 9.
    Lekkeikerker, C., Boland, J.: Representation of a finite graph by a set of intervals on the real line. Fundamenta Mathematicae 51(1), 45–64 (1962)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Roberts, F.S., Spencer, J.H.: A characterization of clique graphs. J. Comb. Theory Ser. B 10(2), 102–108 (1971)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Roshanbin, E.: The competitive diffusion game in classes of graphs. In: Gu, Q., Hell, P., Yang, B. (eds.) AAIM 2014. LNCS, vol. 8546, pp. 275–287. Springer, Cham (2014). Scholar
  12. 12.
    Small, L., Mason, O.: Nash equilibria for competitive information diffusion on trees. Inf. Process. Lett. 113(7), 217–219 (2013)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Sukenari, Y., Hoki, K., Takahashi, S., Muramatsu, M.: Pure Nash equilibria of competitive diffusion process on toroidal grid graphs. Discrete Appl. Math. 215, 31–40 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Takehara, R., Hachimori, M., Shigeno, M.: A comment on pure-strategy nash equilibria in competitive diffusion games. Inf. Process. Lett. 112(3), 59–60 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Graduate School of InformaticsNagoya UniversityNagoyaJapan
  2. 2.Department of Information and System EngineeringChuo UniversityTokyoJapan
  3. 3.Development Bank of JapanTokyoJapan

Personalised recommendations