This study considers a duopoly model in which a socially responsible (SR) firm competes with a private firm by incorporating environmental externality and clean technology. We analyze the endogenous market structure where both firms strategically, sequentially, or simultaneously decide quantities, which also affect abatement activities. We reveal that depending on the relative concerns on environment and consumer surplus, the SR firm can be less or more aggressive in production and abatement, and it may earn high profits. Thus,not only the significance of externality but also the instrumental conflict of social concerns are crucial factors in determining the equilibrium of endogenous timing game. Finally, we indicate that unless the concern for externality is high, the simultaneous and sequential move game with SR firm leadership are socially desirable.