Using game-based proofs in simulation-based proofs
One paper that deals with the issue is Games and the impossibility of Realizable Ideal Functionality by Datta et al, but it does't seem to address the issue in full generality. I am not aware of any general statement that guarantees simulation-based security of the whole protodol based on specific game-based security properties of its sub-protocols (unless of course the game-based definitions imply simulation based security, in which case the generic composition theorems by Canetti should apply). 

However, there do exist specific instances in which one can obtain simulation-based security from game based security. The most telling example in my view is a constant-round zero-knowledge (ZK) argument for NP by Feige and Shamir (see e.g. Feige's PhD), which builds on witness indistinguishabille (WI) and witness-hiding (WH) sub-protocols. Both WI and WH are (arguably) game-based definitions, and yet the entire protocol can be proved to be ZK (which is the mother of all simulation-based definitions, at least for interactive protocols).