Advances on Stackelberg open-loop and feedback strategies

In this paper, we study a familiar type of dynamic games called "common-property resource games" to establish the following results. First, the Stackelberg equilibrium may not exist in some cases, with open-loop strategies as well as with feedback strategies. Second, an explicit example is given to show that under feedback strategies, the best linear strategy on the part of the leader is inferior to a nonlinear strategy so that it is dangerous to confine our search to the Stackelberg equilibrium in the space of linear functions. Most importantly, we establish an "Implementation Lemma", which allows us to develop one methodology to obtain the Stackelberg equilibrium with feedback strategies when the equilibrium is assumed to exist.