Nonzero-sum risk-sensitive stochastic differential games

2016/04/05 by Mrinal K. Ghosh, Ghosh, Mrinal K., K. Suresh Kumar +3
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1604.01142

arxiv created 2016/04/05 · arxiv updated 2016/04/06

Abstract

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.

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