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We investigate the existence of an optimal policy to monitor a mean fieldsystems of agents managing a risky project under moral hazard with accidentsmodeled by L\'evy processes magnified by the law of the project. We provide ageneral method to find both a mean field equilibrium for the agents and theoptimal compensation policy under general, sufficient and necessary assumptionson all the parameters. We formalize the problem as a bilevel optimization withthe probabilistic version of a mean field games which can be reduced to acontrolled McKean-Vlasov SDE with jumps. We apply our results to an optimalenergy demand-response problem with a crowd of consumers subjected to powercut/shortage when the variability of the energy consumption is too high underendogenous or exogenous strains. In this example, we get explicit solution tothe mean field game and to the McKean-Vlasov equation with jumps

Agency problem and mean field system of agents with moral hazard, synergistic effects and accidents