Diffusion, Influence and Best-Response Dynamics in Networks: An Action Model Approach

TL;DR

This paper explores how threshold models of social influence can be represented using action models, linking logical decision rules to dynamics like best-response in network games.

Contribution

It introduces a class of action models that emulate threshold-based decision-making and captures best-response dynamics in coordination and anti-coordination games.

Findings

Action models can replicate standard update mechanisms in threshold models.

Identifies a class of action models suitable for threshold decision rules.

Models include best-response dynamics in graph-based games.

Abstract

Threshold models and their dynamics may be used to model the spread of `behaviors' in social networks. Regarding such from a modal logical perspective, it is shown how standard update mechanisms may be emulated using action models -- graphs encoding agents' decision rules. A small class of action models capturing the possible sets of decision rules suitable for threshold models is identified, and shown to include models characterizing best-response dynamics of both coordination and anti-coordination games played on graphs.