A Tale of a Principal and Many, Many Agents

Romuald Elie (), Thibaut Mastrolia () and Dylan Possamaï ()
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Romuald Elie: Université Paris–Est Marne–la–Vallée, Champs–sur–Marne 77454 Marne–la–Vallée CEDEX 2, France
Thibaut Mastrolia: CMAP, École Polytechnique, Université Paris Saclay, 91128 Palaiseau, France
Dylan Possamaï: Columbia University, New York, New York 10027

Mathematics of Operations Research, 2019, vol. 44, issue 2, 440-467

Abstract: In this paper, we investigate a moral hazard problem in finite time with lump-sum and continuous payments, involving infinitely many agents with mean-field type interactions, hired by one principal. By reinterpreting the mean-field game faced by each agent in terms of a mean-field forward-backward stochastic differential equation (FBSDE), we are able to rewrite the principal’s problem as a control problem of the McKean-Vlasov stochastic differential equations. We review one general approach to tackling it, introduced recently using dynamic programming and Hamilton-Jacobi-Bellman (HJB for short) equations, and mention a second one based on the stochastic Pontryagin maximum principle. We solve completely and explicitly the problem in special cases, going beyond the usual linear-quadratic framework. We finally show in our examples that the optimal contract in the N -players’ model converges to the mean-field optimal contract when the number of agents goes to +∞.

Keywords: moral hazard; mean-field games; McKean-Vlasov SDEs; mean-field FBSDEs; infinite dimensional HJB equations (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (22)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:44:y:2019:i:2:p:440-467

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