Relative Performance Evaluation in Spillover Networks

Abstract

In a multi-agent contracting problem, agents are linked in performance through two ways, effort spillover for the certain part, which is governed by the spillover network, and risk correlation for the random part, which is governed by the risk structure. Assigning compensation weights on peers' performances can not only filter out common risks but also alter the agent's incentives. We study how the network structure and risk structure jointly determine the optimal linear contract. We first show that the sign of compensation sensitivity is determined by the angle between pure hedge portfolio and spillover direction. The relative weight is determined by the ratio of the dot product, between spillover vector and pure hedge portfolio, to unhedgeable risk. We then propose an index named informativeness along the spillover direction and argue that this index measures how precisely the principal can infer the agent's effort. By showing that both the implemented effort and induced welfare are increasing in the informativeness index, we argue that this informativeness index captures how central each agent is in the economy where they are linked through two channels. Finally, we show that the results regarding the relative sensitivities under the linear optimal contract can be generalized to optimal contract when compensations are bounded.

Keywords: Moral hazard in teams; Spillover network; Incentive-hedge trade-off; Centrality; Relative performance evaluation; Linear aggregation of information

JEL Classification: D70, D85, D86