Moral Hazard with Network Effects

Abstract: I study a moral hazard problem between a principal and multiple agents who experience positive peer effects represented by a (weighted) network. Under the optimal linear contract, the principal provides high-powered incentives to central agents in the network in order to exploit the larger incentive spillovers such agents create. The analysis reveals a novel measure of network centrality that captures rich channels of direct and indirect incentive spillovers and characterizes the optimal contract and its induced equilibrium efforts. The notion of centrality relevant for incentive spillovers in the model emphasizes the role of pairs of agents who link to common neighbors in the network. This characterization leads to a measure of marginal network effects and identifies the agents whom the principal targets with stronger incentives in response to the addition (or strengthening) of a link. When the principal can position agents with heterogeneous costs of effort in the network, the principal prefers to place low-cost agents in central positions. The results shed light on how firms can increase productivity through corporate culture, office layout, and social interactions.

• The paper introduces an optimal linear contract design that leverages agent centrality to mitigate moral hazard.
• It employs a network-based model with CARA preferences to quantify both direct and indirect incentive spillovers.
• Results show that targeting central agents within dense networks enhances overall productivity and principal profits.

Moral Hazard with Network Effects

Overview

This paper explores the moral hazard problem between a principal and multiple agents within a network exhibiting positive peer effects. It focuses on the optimal linear contract for incentivizing agents based on their network centrality. The research uncovers a new measure of centrality that quantifies the direct and indirect incentive spillovers across the network. This paper provides insights into optimal contract design in organizational settings and highlights how network architecture can improve productivity.

Model and Network Effects

The study adopts a multi-agent moral hazard framework where agents' interactions are captured by a directed network. Agents have CARA preferences, with their utility function reflecting the benefits of peer effects through the network structure. The principal offers linear contracts with fixed and variable components related to individual outputs affected by effort and random shocks.

Agents’ equilibrium efforts depend on performance-related compensations and network interactions. The optimal contract is derived based on a multidimensional network centrality measure which accounts for mutual influences among agents who share common neighbors.

Optimal Contracts and Incentive Spillovers

The analysis demonstrates that providing high-powered incentives to central agents amplifies the benefits of network effects due to enhanced incentive spillovers. A principal can strategically target agents to boost their efforts and those of their peers. The derivation of the optimal contract reveals compensations tied to agents’ direct and indirect network influence, highlighting the importance of agent pairs linked to common network nodes.

Comparative Statics and Network Architecture

The study conducts comparative statics to assess the impact of network changes on contracts and efforts. Increasing the weight of links or the strength of peer effects typically boosts the performance-related compensations and efforts for connected agents. The paper elucidates that dense networks enhance the principal's profits by capitalizing on network-induced productivity gains.

Application: Office Layout and Heterogeneous Costs

The practical application illustrates how network structure, like office layout, influences agent positioning and incentive provision. Given varying costs of effort, the principal prefers placing low-cost agents in central roles when network effects are significant. This design aids in leveraging peer interactions to maximize productivity efficiently.

Conclusion

This research extends network games theory by incorporating moral hazard challenges in networked organizations. It reveals the principal's preference for dense network configurations due to multifaceted incentive spillovers. Future work can explore dynamic networks and incorporate additional layers of complexity such as asymmetric information and evolving network structures. The results emphasize the strategic importance of network design in organizational settings to optimize incentive schemes and maximize output.