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We model situations in which a principal provides incentives to a group of agents to participate in a project (such as a social event, commercial activity or the adoption of a certain technological standartization). Agents' benefits from participation depend on the identity of other participating agents. We assume bilateral externalities and characterize the optimal incentive mechanism. Using a graph-theoretic approach we show that the optimal mechanism provides a ranking of incentives for the agents, which can be described as arising from a virtual popularity tournament among the agents (similar to ones carried out by sport associations). Rather than simply ranking agents according to their measure of popularity, the optimal mechanism makes use of more refined two-way comparison between the agents. An implication of our analysis is that higher levels of asymmetry of externalities between the agents enable a reduction of the principal's payment. In addition, contrary to intuition, an increase in the aggregate externalities, does not necessarily decrease principal's payment, nor does it change agents rewards. http://www.ma.huji.ac.il/~mseyal/documents/multiagent_October_2008B.pdf