Discontinuous Nash Equilibria in a Two Stage Linear-Quadratic Dynamic Game with Linear Constraints

In this paper, we study a simple example of a two-stage linear-quadratic dynamic game in which pres- ence of simple linear state dependent constraints results in non-existence of continuous symmetric feedback Nash equilibria and existence of continuum of discontinuous symmetric feedback Nash equilibria. The example is not an abstract model — it has obvious applications in economics of resource extraction.