We consider the diffusion of two alternatives in social networks using a game-theoretic approach. Each individual plays a coordination game with its neighbors and decides which to adopt to maximize its payoff. 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 trustworthiness to others to maximize their long-term payoffs. To capture such trustworthy behavior, we deviate from the expected utility theory and use a new notion of rationality based on limited-trust equilibrium (LTE). By incorporating such a notion into the diffusion model, we analyze the convergence of emerging dynamics to their equilibrium points using a mean-field approximation. We study the equilibrium state and the convergence rate of the diffusion process using the absorption probability and the expected absorption time of a reduced-size absorbing Markov chain. We also show that the LTE diffusion model under the best-response strategy can be converted to the well-known linear threshold model. Simulations show that when agents behave trustworthily, their long-term payoffs will increase significantly compared to the case when they are solely self-interested. Moreover, the Markov chain analysis provides a good estimation of the convergence property over random networks.

翻译：我们采用博弈论方法研究社交网络中两种替代品的扩散过程。每个个体与邻居进行协调博弈，决定采用哪种替代品以最大化自身收益。由于产品需要与他人协同使用且存在重复交互，个体更关注长期收益，倾向于通过展现对他人的可信赖性来最大化长期回报。为刻画这种可信赖行为，我们偏离期望效用理论，采用基于有限信任均衡（LTE）的新型理性概念。通过将这一概念融入扩散模型，我们利用平均场近似分析新兴动态向其均衡点的收敛过程。基于降维吸收马尔可夫链的吸收概率与期望吸收时间，研究了扩散过程的均衡状态与收敛速率。同时证明，在最佳响应策略下，LTE扩散模型可转化为著名的线性阈值模型。模拟表明，当个体表现可信赖行为时，其长期收益相较纯粹自利情形显著提升。此外，马尔可夫链分析为随机网络上扩散过程收敛特性提供了良好估计。