Contracting theory with competitive interacting agents

TL;DR

This paper analyzes optimal contracts in a multi-agent setting with competitive agents influencing each other's projects, deriving linear contracts using advanced mathematical tools and highlighting the importance of diversifying agents' competitive appetence.

Contribution

It introduces a novel framework connecting Nash equilibria with multidimensional quadratic BSDEs to derive explicit optimal contracts in competitive multi-agent environments.

Findings

Optimal contracts are linear and involve fixed proportions of project values.

Agents with higher competitiveness receive less volatile projects and may get assistance.

Diversifying agents' competitive appetence benefits the firm's interests.

Abstract

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.