Dynamic games applied to common resources: modeling and experimentation

We study the exploitation behavior of two symmetrical farmers using groundwater table as in Rubio & Casino (2003), where water extraction is the only input in the production process of these farmers, and the dynamic is given by the evolution of the level of the water table. In our model, strategic interaction is introduced through extraction costs which negatively depend on the level of the water table. We made the assumption that the groundwater has a flat bottom, parallel sides, and that its natural recharge is provided by a constant and positive amount of rain. Another assumption is that farmers behave non cooperatively, by maximizing their actualized utilitarian criteria. We study this model in continuous time with an infinite horizon, and consider the equilibrium paths of the four following types of behavior : myopic, feedback, open-loop and social optimum. We also studied the same model in discrete time in order to see if our results will approch those in continuous time. Unlike some articles in the literature that find different results between continuous time and discrete time, we found that the discrete time model gives results equivalent to those of the continuous time, but with the condition that discretization in time is small enough. We test the behaviors using two different protocols in the laboratory (experimental economics) for both treatments in continuous and discrete time.