  We consider a class of non-cooperative N-player non-zero-sum stochastic
differential games with singular controls, in which each player can affect a
linear stochastic differential equation in order to minimize a cost functional
which is quadratic in the state and linear in the control. We call these games
linear-quadratic-singular stochastic differential games. Under natural
assumptions, we show the existence of open-loop Nash equilibria, which are
characterized through a linear system of forward-backward stochastic
differential equations. The proof is based on an approximation via a sequence
of games in which players are restricted to play Lipschitz continuous
strategies. We then discuss an application of these results to a model of
capacity expansion in oligopoly markets.
