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This paper considers algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. Such scenarios arise, in particular, when computers or users aim to cooperate or trade over the Internet. As such participants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents' interests are best served by behaving correctly. This exposition presents a model to formally study such algorithms. This model, based on the field of mechanism design, is taken from the author's joint work with Amir Ronen, and is similar to approaches taken in the distributed AI community in recent years. Using this model, we demonstrate how some of the techniques of mechanism design can be applied towards distributed computation problems. We then exhibit some issues that arise in distributed computation which require going beyond the existing theory of mechanism design.