Agency Problem and Mean Field System of Agents with Moral Hazard, Synergistic Effects and Accidents

Thibaut Mastrolia () and Jiacheng Zhang ()
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Thibaut Mastrolia: Department of Industrial Engineering and Operations Research
Jiacheng Zhang: The Chinese University of Hong Kong Shatin

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 3, No 6, 32 pages

Abstract: Abstract We investigate the existence of an optimal policy to monitor a mean field system of agents managing a risky project under moral hazard with accidents modeled by Lévy processes magnified by the law of the project. We provide a general method to find both a mean field equilibrium for the agents and the optimal compensation policy under general, sufficient and necessary assumptions on all the parameters. We formalize the problem as a bilevel optimization with the probabilistic version of a mean field games which can be reduced to a controlled McKean-Vlasov SDE with jumps. We apply our results to an optimal energy demand-response problem with a crowd of consumers subjected to power cut/shortage when the variability of the energy consumption is too high under endogenous or exogenous strains. In this example, we get explicit solution to the mean field game and to the McKean-Vlasov equation with jumps.

Keywords: Mean field games; Principal-multi agents problem; McKean-Vlasov SDEs; Lévy processes; Stochastic control; Energy demand-response; 91A16; 49L12; 60G55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02664-x

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