Strategic Seeding of Rival Opinions

TL;DR

This paper models strategic opinion seeding in social networks, analyzing the existence of equilibrium states, their computational complexity, and proposing an efficient approximation algorithm for best responses.

Contribution

It introduces a network influence game with opinion dynamics, proves conditions for equilibrium existence, and develops a greedy algorithm for approximate best responses.

Findings

Pure Nash equilibrium may not always exist.

Consensus dynamics guarantee equilibrium existence.

Greedy algorithm approximates best responses within (1 - 1/e) factor.

Abstract

We present a network influence game that models players strategically seeding the opinions of nodes embedded in a social network. A social learning dynamic, whereby nodes repeatedly update their opinions to resemble those of their neighbors, spreads the seeded opinions through the network. After a fixed period of time, the dynamic halts and each player's utility is determined by the relative strength of the opinions held by each node in the network vis-a-vis the other players. We show that the existence of a pure Nash equilibrium cannot be guaranteed in general. However, if the dynamics are allowed to progress for a sufficient amount of time so that a consensus among all of the nodes is obtained, then the existence of a pure Nash equilibrium can be guaranteed. The computational complexity of finding a pure strategy best response is shown to be NP-complete, but can be efficiently approximated to within a (1 - 1/e) factor of optimal by a simple greedy algorithm.