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Truthful task scheduling mechanisms are designed to cope with the selfishness of the participating agents. They assume that the agents are selfish; each agent's goal is to maximize its own profit. However, this is not always the case; an agent may want to cause losses to the other agents besides maximizing its profit. Such an agent is said to be an antisocial agent. An antisocial agent will try to gain as much profit as possible relative to the other agents. This paper presents an antisocial strategy which can be used by the antisocial agents to inflict losses on the other agents participating in a task scheduling mechanism on related machines. This paper also studies, by simulation, the effect of different parameters, such as the degree of antisociality on the relative losses that can be inflicted on the participating agents.