Nash Equilibria for Stochastic Games with Singular Control.

Jodi Dianetti, Universität Bielefeld

A singular stochastic control problem typically describes the situation in which
an agent has to choose optimally an irreversible strategy in order to minimize a certain cost
functional. In this talk we study a game of singular control, i.e. the problem of di erent
agents where each agent faces a singular control problem parametrized by the strategies of
her opponents. In a non-Markovian setting, we establish the existence of Nash equilibria.
Moreover, we introduce a sequence of approximating games by forcing players to choose more
regular controls, and we prove the convergence of the Nash equilibria of the approximating
games to the Nash equilibria of the original game of singular control. We nally show some
applications and we propose an algorithm to determine a Nash equilibrium for the game.
This talk is based on a joint work with Giorgio Ferrari.

Invited by Alexander Zass