Stackelberg Mean Field Games: convergence and existence results to the problem of Principal with multiple Agents in competition - Archive ouverte HAL
Article Dans Une Revue ArXiv e-prints Année : 2023

Stackelberg Mean Field Games: convergence and existence results to the problem of Principal with multiple Agents in competition

Résumé

In a situation of moral hazard, this paper investigates the problem of Principal with $n$ Agents when the number of Agents $n$ goes to infinity. There is competition between the Agents expressed by the fact that they optimize their utility functions through a Nash equilibrium criterion. Each Agent is offered by the Principal a contract which is divided into a Markovian part involving the state/production of the Agent and a non--Markovian part involving the states/productions of all the other Agents. The Agents are in interactions. These interactions are characterized by common noise, the empirical distribution of states/productions and controls, and the contract which is not assumed to be a map of the empirical distribution. By the help of the mean field games theory, we are able to formulate an appropriate $limit$ problem involving a Principal with a $representative$ Agent. We start by solving the problem of both the Principal and the $representative$ Agent in this $limit$ problem. Then, when $n$ goes to infinity, we show that the problem of Principal with $n$ Agents converges to the $limit$ problem of Principal with a $representative$ Agent. A notable result is that, despite allowing a general type of contracts, it is approximately optimal for the Principal to offer contracts to the $n$ Agents that are maps of the empirical distribution of states/productions and controls of the Agents.

Dates et versions

hal-04565545 , version 1 (02-05-2024)

Identifiants

Citer

Mao Fabrice Djete. Stackelberg Mean Field Games: convergence and existence results to the problem of Principal with multiple Agents in competition. ArXiv e-prints, 2023. ⟨hal-04565545⟩
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