Nonzero-sum risk-sensitive stochastic differential games
  We study two person nonzero-sum stochastic differential games with risk-sensitive discounted and ergodic cost criteria. Under certain conditions we establish a Nash equilibrium in Markov strategies for the discounted cost criterion and a Nash equilibrium in stationary strategies for the ergodic cost criterion. We achieve our results by studying the relevant systems of coupled HJB equations. 
Mrinal K. Ghosh, K. Suresh Kumar and Chandan Pal
math.OC