  A group of agents each exert effort to produce a joint output, with the
complementarities between their efforts represented by a (weighted) network.
Under equity compensation, a principal motivates the agents to work by giving
them shares of the output. We describe the optimal equity allocation. It is
characterized by a neighborhood balance condition: any two agents receiving
equity have the same (weighted) total equity assigned to their neighbors. We
also study the problem of selecting the team of agents who receive positive
equity, and show this team must form a tight-knit subset of the complementarity
network, with any pair being complementary to one another or jointly to another
team member. Finally, we give conditions under which the amount of equity used
for compensation is increasing in the strength of a team's complementarities
and discuss several other applications.
