  In a framework close to the one developed by Holmstr\"om and Milgrom [44], we
study the optimal contracting scheme between a Principal and several Agents.
Each hired Agent is in charge of one project, and can make efforts towards
managing his own project, as well as impact (positively or negatively) the
projects of the other Agents. Considering economic Agents in competition with
relative performance concerns, we derive the optimal contracts in both first
best and moral hazard settings. The enhanced resolution methodology relies
heavily on the connection between Nash equilibria and multidimensional
quadratic BSDEs. The optimal contracts are linear and each agent is paid a
fixed proportion of the terminal value of all the projects of the firm.
Besides, each Agent receives his reservation utility, and those with high
competitive appetence are assigned less volatile projects, and shall even
receive help from the other Agents. From the principal point of view, it is in
the firm interest in our model to strongly diversify the competitive appetence
of the Agents.
