Contracting theory with competitive interacting Agents
Elie, Romuald; Possamaï, Dylan (2019), Contracting theory with competitive interacting Agents, SIAM Journal on Control and Optimization, 57, 2, p. 36. 10.1137/17M1121202
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Control and Optimization
SIAM - Society for Industrial and Applied Mathematics
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Abstract (EN)In a framework close to the one developed by Holmström and Milgrom , 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.
Subjects / KeywordsPrincipal multi-agents problems; relative performance; Moral hazard; competition; Nash equilibrium; Multidimensional quadratic BSDEs
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