In this paper, we investigate stable matching in structured networks. Consider case of matching in social networks where candidates are not fully connected. A candidate on one side of the market gets acquaintance with which one on the heterogeneous side depends on the structured network. We explore four well-used structures of networks and define the social circle by the distance between each candidate. When matching within social circle, we have equilibrium distinguishes from each other since each social networks topology differs. Equilibrium changes with the change on topology of each network and it always converges to the same stable outcome as complete information algorithm if there is no block to reach anyone in agents social circle.
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