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In this paper, we study the system-level computational resource allocation problem among multiple multimedia tasks. We consider the multimedia tasks to be autonomous, i.e., they are selfish and behave strategically. We propose a resource allocation framework based on mechanism design to prevent the tasks from behaving strategically and manipulating the available system resources. We apply two mechanisms in the framework and assess their advantages over proportional-share resource allocation algorithms, which are often used in multimedia systems. We show in the simulations that the incorporation of mechanism design for system resource allocation is a promising solution that achieves efficient, fair and robust allocation against manipulation from strategic applications.