Indirect competition emerged from the complex organization of human societies, and knowledge of the existing network topology may aid in developing effective strategies for success. Here, we propose an agent-based model of competition with systems co-existing in a `small-world social network. We show that within the range of parameter values obtained from the model and empirical data, the network evolution is highly dependent on $k$, the local parameter describing the density of neighbors in the network. The model applied to language death and competition of telecommunication companies show strong correspondence with empirical data.
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