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

In this note, we study a simple example of a two-stage linear-quadratic dynamic game in which the presence of simple linear state dependent constraints results in nonexistence of continuous symmetric feedback Nash equilibria and the 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.