Gordan ŽITKOVIC and I study a class of Markovian quadratic BSDE systems. We obtain the existence and uniqueness under an abstract structural condition. Easy to verify sufficient condition is provided.  We consider several applications, not only in the stochastic equilibria (as our starting motivation), but also /Gamma-martingales on manifold, and two stochastic differential games. /Gamma-martingale may related to stochastic equilibria. Even though they do not related directly, they are different applications of our framework. Therefore they can be seen related on a higher level.

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