# Principal's beliefs in a repeated moral hazard problem

I have a question about models of repeated principal-agent models.

There is this famous piece by Bengt Holmstrom: Moral hazard and observability, 1979, The Bell Journal of Economics. It presents the classical principal-agent model with moral hazard. Papers by Rogerson (ECTA 1985) or Spear and Srivastava (REStud 1987) extend his model to a repeated game.

The principal must choose an incentive-compatible contract. The agent has to choose an action $a$. The agent produces a random quantity $x$ from the distribution $f(x,a)$. The principal does not observe $a$ but it observes $x$.

My question is the following. In these models (and many other papers in this literature), the distribution $f$ is publicly known. Do there exist some results/articles assuming that $f$ is unobserved by the principal (or the agent). Instead, the principal may have a prior belief and update it over time as the game is repeated for instance.

• This is the case in the recent literature on contracts for experimenting agents ; you can look at the papers by Johannes Hörner, Marina Halac etc. – Oliv Mar 7 '17 at 16:21