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We consider the diffusion of two alternatives in social networks using agame-theoretic approach. Each individual plays a coordination game with itsneighbors repeatedly and decides which to adopt. As products are used inconjunction with others and through repeated interactions, individuals are moreinterested in their long-term benefits and tend to show trust to others tomaximize their long-term utility by choosing a suboptimal option with respectto instantaneous payoff. To capture such trust behavior, we deploylimited-trust equilibrium (LTE) in diffusion process. We analyze theconvergence of emerging dynamics to equilibrium points using mean-fieldapproximation and study the equilibrium state and the convergence rate ofdiffusion using absorption probability and expected absorption time of areduced-size absorbing Markov chain. We also show that the diffusion model onLTE under the best-response strategy can be converted to the well-known linearthreshold model. Simulation results show that when agents behave trustworthy,their long-term utility will increase significantly compared to the case whenthey are solely self-interested. Moreover, the Markov chain analysis provides agood estimate of convergence properties over random networks.

Limited-Trust in Diffusion of Competing Alternatives over Social Networks