On the bang-bang type Nash equilibrium point for Markovian nonzero-sum stochastic differential game

摘要

In this paper, we study a nonzero-sum stochastic differential game inMarkovian framework. We show the existence of the Nash equilibrium point whichis discontinuous and of bang-bang type under natural conditions. The main toolis the notion of backward stochastic differential equations which, in our case,are multidimensional with discontinuous generators with respect to z component.