A Stochastic Lake Game

In this paper we extend the deterministic model of Dechert and Brock (forthcoming) to stochastic models. First, we consider the lake game in a Brock and Mirman framework and show what happens to the Skiba point when there is uncertainty in the model. Second, we develop the model as an optimally controlled Markov process following the style of Easley and Kiefer (Econometrica 1988). In this case the lake parameters are unknown and have to be learned over time. When a Skiba point is present, learning affects the estimation problem of the parameters in that it may not be optimal to gather information about the lake when the system might be close to the (unknown) Skiba point.