In this paper, we incorporate wage and effort persistence into an infinitely repeated agency problem with moral hazard. Both the principal and agent identify the stochastic production function. We showed that this model can be cast by a set of linear constraints and the quadratic utility functions. To some extent these so called linear quadratic games are analytically and numerically solvable and could avoids the intractability associated with history dependence. The principal and the agent learn about their strategies by repeatedly updating their belief on their optimal policy, taking into account the opponent’s learning behavior. This would leads to optimal time consistent strategies for both players which they would commit to it in advance. This could basically develop a framework for analyzing dynamic agency models from numerical and computational perspective.

Keywords