We investigated the required conditions in which cooperation is dominant in social media using the model of a meta-rewards game, which is a dual part of Axelrod's metanorms game. Social media such as Twitter and Facebook have rapidly been growing in recent years. However, we do not know whether or not the currently popular social media will remain in the future. A number of studies have been conducted to try to understand the conditions or mechanisms that create and keep social media thriving using a public goods game and/or meta-rewards games, in which situations where many users post articles and respond to them as reactions in social media correspond to situations where cooperation is dominant in these games. However, they assume that agent networks in social media are complete graphs that are known to be dissimilar to actual social networks. We examined the conditions required to keep agent networks thriving based on Watts and Strogatz (WS) and Barabasi-Albert (BA) models, which are more similar to actual social networks. We experimentally found similarities and differences in the conditions for cooperation-dominant situations between networks based on complete graphs and those based on WS and BA models. Our results indicated that it was easier to maintain cooperation-dominant situations in BA-model networks than in other networks.