Optimal Team Incentives for Productively Heterogenous Agents

We study a contract design problem between a principal and a team of two productively heterogenous agents who can mutually monitor each other’s actions over an infinite horizon. The principal designs the explicit contract to set the stage for the agents to use implicit contracts to motivate each other—to foster cooperation while preventing collusion. Under a productive complementarity, the results are qualitatively similar to those from previous models with productively homogenous agents. In contrast, under a productive substitutability, productive heterogeneity increases the principal’s cost of creating cooperative incentives for intermediate discount factors and reduces the principal’s cost of combatting collusion for high discount factors. For intermediate discount factors, an extra constraint is needed to ensure the stage game equilibria are sufficiently rich that the less productive agent can be punished for free riding. As a result, the less productive agent’s pay is independent of the discount factor in this region. For high discount factors, collusion is a pressing concern. In this case, it is optimal to provide higher-powered collusion-proof pay (which is increasing in the discount factor) to the more productive agent and lower-powered cooperative pay (which is decreasing in the discount factor) to the less productive agent