Variant of the Decisional Bilinear Diffie Hellman problem
Your problem is stronger than the DBDH problem because any oracle that responds to your query can also respond to DBDH. I think that you must try to reduce this problem to DDH. This means an input $(e(g,g),P=e(g,g)^x,R=e(g,g)^y,Q)$ and the decision whether $Q=e(g,g)^{xy}$.