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

TL;DR

This paper develops a framework for optimal monitoring and compensation policies in mean field systems of agents managing risky projects with moral hazard, accidents, and synergistic effects, applying to energy demand-response scenarios.

Contribution

It introduces a general method to find mean field equilibria and optimal policies in systems with jumps and moral hazard, including explicit solutions for specific applications.

Findings

Explicit solutions for mean field games with jumps.

Optimal policies for energy demand management.

Framework applicable to systems with accidents and synergistic effects.

Abstract

We investigate the existence of an optimal policy to monitor a mean field systems of agents managing a risky project under moral hazard with accidents modeled by L\'evy 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