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In a situation of moral hazard, this paper investigates the problem ofPrincipal with $n$ Agents when the number of Agents $n$ goes to infinity. Thereis competition between the Agents expressed by the fact that they optimizetheir utility functions through a Nash equilibrium criterion. Each Agent isoffered by the Principal a contract which is divided into a Markovian partinvolving the state/production of the Agent and a non--Markovian part involvingthe states/productions of all the other Agents. The Agents are in interactions.These interactions are characterized by common noise, the empiricaldistribution of states/productions and controls, and the contract which is notassumed to be a map of the empirical distribution. By the help of the meanfield games theory, we are able to formulate an appropriate $limit$ probleminvolving a Principal with a $representative$ Agent. We start by solving theproblem of both the Principal and the $representative$ Agent in this $limit$problem. Then, when $n$ goes to infinity, we show that the problem of Principalwith $n$ Agents converges to the $limit$ problem of Principal with a$representative$ Agent. A notable result is that, despite allowing a generaltype of contracts, it is approximately optimal for the Principal to offercontracts to the $n$ Agents that are maps of the empirical distribution ofstates/productions and controls of the Agents.

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