  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.
