By means of topological games, we will show that under certain circumstances on topological spaces X , Y and Z , every two variable set-valued function F:X times Y to 2^Z is strongly upper (resp. lower) quasi-continuous provided that F_x is upper (resp. lower) semi-continuous and F^y is lower (resp. upper) quasi-continuous. Moreover, we will prove that if F is compact-valued and Z is second countable, then for each y_0 in Y , there is a dense G_ delta subset D of X such that F is upper (resp. lower) semi-continuous at each point of D times {y_0 } .

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