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We analyze an agent-based model to estimate how the costs and benefits ofusers in an online social network (OSN) impact the robustness of the OSN.Benefits are measured in terms of relative reputation that users receives fromtheir followers. They can be increased by direct and indirect reciprocity infollowing each other, which leads to a core-periphery structure of the OSN.Costs relate to the effort to login, to maintain the profile, etc. and areassumed as constant for all users. The robustness of the OSN depends on theentry and exit of users over time. Intuitively, one would expect that highercosts lead to more users leaving and hence to a less robust OSN. We demonstratethat an optimal cost level exists, which maximizes both the performance of theOSN, measured by means of the long-term average benefit of its users, and therobustness of the OSN, measured by means of the life-time of the core of theOSN. Our mathematical and computational analyses unfold how changes in the costlevel impact reciprocity and subsequently the core-periphery structure of theOSN, to explain the optimal cost level.

Modeling User Reputation in Online Social Networks: The Role of Costs, Benefits, and Reciprocity