A comment on pure-strategy Nash equilibria in competitive diffusion games

Takehara, Reiko; Hachimori, Masahiro; Shigeno, Maiko

doi:10.1016/j.ipl.2011.10.015

Cited by 28 publications

(30 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The main result of [1] claimed that any network of diameter 2 possesses a pure strategy Nash Equilibrium (N.E.). Unfortunately, as pointed out in [2], this result is not true without additional technical assumptions. In fact, even for the case of 2 competing agents on a network of diameter 2, it is possible that the game introduced in [1] does not possess a N.E.…”

Section: Introductionmentioning

confidence: 92%

“…the model of competitive information diffusion studied in [1,2] always admits a N.E. on a tree when the number of agents is 2.…”

Section: and It Is Always Possible For Player 2 To Improve Their Utmentioning

confidence: 99%

“…In the recent papers [1,2] a deterministic model for competitive information diffusion on social networks was introduced and studied. The model considers the diffusion process as a game played on the network by external agents.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nash Equilibria for competitive information diffusion on trees

Small

Mason

2013

Information Processing Letters

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 92%

“…the model of competitive information diffusion studied in [1,2] always admits a N.E. on a tree when the number of agents is 2.…”

Section: and It Is Always Possible For Player 2 To Improve Their Utmentioning

confidence: 99%

See 1 more Smart Citation

Nash Equilibria for competitive information diffusion on trees

Small

Mason

2013

Information Processing Letters

View full text Add to dashboard Cite

show abstract

“…Recently, Ito et al [4] considered the competitive diffusion game on weighted graphs, including negative weights. Concerning our model, Alon et al [1] claimed the existence of pure Nash equilibria for any number of players on graphs of diameter at most two, however, Takehara et al [11] gave a counterexample consisting of a graph with nine vertices and diameter two with no Nash equilibrium for two players.…”

Section: Related Workmentioning

confidence: 99%

Multi-player Diffusion Games on Graph Classes

Bulteau

Froese

Talmon

2015

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We study competitive diffusion games on graphs introduced by Alon et al.[1] to model the spread of influence in social networks. Extending results of Roshanbin [8] for two players, we investigate the existence of pure Nash equilibria for at least three players on different classes of graphs including paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an open question proving that there is no Nash equilibrium for three players on m × n grids with min{m, n} ≥ 5. Further, extending results of Etesami and Basar [3] for two players, we prove the existence of pure Nash equilibria for four players on every d-dimensional hypercube.

show abstract

“…Our work has been largely motivated by [1], (see also the corresponding errata [2,31]). To the best of our knowledge, this was the first article to consider such simultaneous games over networks with the players being the firms.…”

Section: Related Workmentioning

confidence: 99%

A Game-Theoretic Analysis of a Competitive Diffusion Process over Social Networks

Tzoumas

Amanatidis

Markakis

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We study a game-theoretic model for the diffusion of competing products in social networks. Particularly, we consider a simultaneous non-cooperative game between competing firms that try to target customers in a social network. This triggers a competitive diffusion process, and the goal of each firm is to maximize the eventual number of adoptions of its own product. We study issues of existence, computation and performance (social inefficiency) of pure strategy Nash equilibria in these games. We mainly focus on 2-player games, and we model the diffusion process using the known linear threshold model. Nonetheless, many of our results continue to hold under a more general framework for this process.In more detail, we first exhibit that these games do not always possess pure strategy Nash equilibria, and we prove that deciding if an equilibrium exists is co-NP-hard. We then move on to investigate conditions for the existence of equilibria. We first illustrate why we cannot hope that games over networks with special in and out-degree distributions -e.g. power law -are more stable than others, concerning for example, the form of the improvement paths, or cycles that they induce. We then study necessary and sufficient conditions for the existence of pure Nash equilibria, both for the general case but for some special cases as well. Our conditions go through the existence of generalized ordinal potential functions. We also study the existence of -generalized ordinal potentials (which yield -approximate Nash equilibria) and provide tight upper bounds on the existence of such approximations. Finally, we study the Price of Anarchy and Stability for games with an arbitrary number of players. We conclude with a discussion of the effects on the payoff of a single player (or a coalition of players) as the number of players increases.

show abstract

A comment on pure-strategy Nash equilibria in competitive diffusion games

Cited by 28 publications

References 1 publication

Nash Equilibria for competitive information diffusion on trees

Nash Equilibria for competitive information diffusion on trees

Multi-player Diffusion Games on Graph Classes

A Game-Theoretic Analysis of a Competitive Diffusion Process over Social Networks

Contact Info

Product

Resources

About