Myopic, farsighted behaviours and conjectural learning. Application to a groundwater exploitation problem

In this paper we consider two economic agents involved in strategic interactions between them and with the environment in a repeated interplay. They face to a lack of information about the profit of the other player, make conjectures on the opponent's behavior and optimize their utility accordingly. When observing the real behavior of their opponents they adapt their conjecture following a learning model. We consider here that players have a farsighted behavior in the sense that when making the conjecture they maximize their discounted profit in infinite horizon assuming the other player behaves as prescribed by her conjecture. The main result is that the fixed points of the conjectural learning model are also the steady states of the corresponding Pareto-optimal complete-information solution for appropriately chosen Pareto weights. A similar result is obtained as a particular case when players are myopic. We apply this procedure to a groundwater management problem and perform some simulations for testing the consequences on profits and dynamics when varying some parameters of the conjecture.