Limited-Trust in Diffusion of Competing Alternatives over Social Networks

TL;DR

This paper models the diffusion of competing options in social networks considering trust behavior using limited-trust equilibrium, analyzing convergence, equilibrium states, and demonstrating improved utility with trustworthy behavior through simulations.

Contribution

It introduces a game-theoretic diffusion model incorporating limited-trust equilibrium and connects it to the linear threshold model, providing convergence analysis and simulation validation.

Findings

Trustworthy behavior increases long-term utility.

Diffusion dynamics converge to equilibrium states.

Markov chain analysis accurately predicts convergence properties.

Abstract

We consider the diffusion of two alternatives in social networks using a game-theoretic approach. Each individual plays a coordination game with its neighbors repeatedly and decides which to adopt. As products are used in conjunction with others and through repeated interactions, individuals are more interested in their long-term benefits and tend to show trust to others to maximize their long-term utility by choosing a suboptimal option with respect to instantaneous payoff. To capture such trust behavior, we deploy limited-trust equilibrium (LTE) in diffusion process. We analyze the convergence of emerging dynamics to equilibrium points using mean-field approximation and study the equilibrium state and the convergence rate of diffusion using absorption probability and expected absorption time of a reduced-size absorbing Markov chain. We also show that the diffusion model on LTE under the best-response strategy can be converted to the well-known linear threshold model. Simulation results show that when agents behave trustworthy, their long-term utility will increase significantly compared to the case when they are solely self-interested. Moreover, the Markov chain analysis provides a good estimate of convergence properties over random networks.