We study the situation where the members of a community have the choice to participate in the completion of a common task. The process of completing the task involves only costs and no benefits to the individuals that participate in this process. However, completing the task results in changes that significantly benefit the community and that exceed the participation efforts. A task completion social dilemma arises when the short-term participation costs dissipate any interest in the community members to contribute to the task completion process and therefore to obtain the benefits that result from completing the task. In this work, we model the task completion problem using a dynamical system that characterizes the participation dynamics in the community and the task completion process. We show how this model naturally allows for the incorporation of several mechanisms that facilitate the emergence of cooperation and that have been studied in previous research on social dilemmas, including communication across a network, and indirect reciprocity through relative reputation. We provide mathematical analyses and computer simulations to study the qualitative properties of the participation dynamics in the community for different scenarios.
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