This study explored whether the introduction of connected automated vehicles (CAVs) into human-driven vehicles (HVs) can mitigate the social dilemma caused by defective HVs that seek to overtake other vehicles by making frequent lane changes. In this regard, a cellular automata traffic model based on the revised S–NFS model, dealing with a mixed flow field composed of CAVs and HVs with multiple lanes, was established. We perused precise game theoretical analysis on the basis of the result obtained from traffic flow analysis through multi-agent simulation (MAS). As a result, the social efficiency deficit, quantifying the extent of the social dilemma behind such a specific traffic flow system, elucidates that the introduction of CAVs does not eliminate the social dilemma caused by defective HVs unless CAVs account for the vast majority of the mixed flow.