This paper proposes an interaction strategy called the extended expectation-of-cooperation (EEoC) that is intended to spread cooperative activities in prisoner's dilemma situations over an entire agent network. Recently developed computer and communications applications run on the network and interact with each other as delegates of the owners, so they often encounter social dilemma situations. To improve social efficiency, they are required to cooperate, but one-sided cooperation is meaningless and loses some payoff due to a rip-off by defecting agents. The concept of EEoC is that when agents encounter mutual cooperation, they continue to cooperate a few times with the desire to see the emergence of cooperative behavior in their neighbors. EEoC is easy to implement in computer systems.We experimentally show that EEoC can effectively spread cooperative activities in dilemma situations in complete, Erdös-Rényi, and regular networks. We also clarify the robustness against defecting agents and the limitation of the EEoC strategy.