This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon H-2/H-infinity control of time-varying stochastic systems subject to Markov jump paranieters and niultiplicative noise. It is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term. Furthermore, necessary and sufficient conditions for the finite horizon H-2/H-infinity control of stochastic Markov jump systems are presented via coupled matrix-valued equations.