I study the properties of optimal long-term contracts in an environment in which the agent.s type evolves stochastically over time. The model stylizes a buyer-seller relationship but the results apply quite naturally to many contractual situations including regulation and optimal...

We show that local potential maximizer (\cite{morris+05}) with constant weights is stochastically stable in the log-linear dynamics provided that the payoff function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of...