Multi-Player Diffusion Games on Graph Classes

TL;DR

This paper investigates the existence of pure Nash equilibria in multi-player diffusion games on various graph classes, revealing non-existence on certain grids and existence on hypercubes, thus advancing understanding of strategic influence spread.

Contribution

It extends prior work by analyzing multi-player scenarios, proving non-existence of equilibria on large grids and existence on hypercubes, answering open questions in the field.

Findings

No Nash equilibrium for three players on (m x n) grids with min(m, n) >= 5

Pure Nash equilibria exist for four players on every d-dimensional hypercube

Extends previous results from two-player to multi-player diffusion games

Abstract

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 x 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.