We formally model a Cournot duopoly market in which a corporate socially responsible (CSR) firm interacts with a profit-maximizing firm and where the market is regulated with an emission tax. We consider three different kinds of CSR firm behaviors: (i) consumer-friendly; (ii) environmentally-friendly; and (iii) consumer-environmentally friendly . Unlike most theoretical works within this literature, which typically use specific functional forms, we use general structures for the inverse demand function, the cost function, and for emission levels and damage functions. In terms of modeling strategy, we use two game-theoretic approaches: (i) a simultaneous game and (ii) a sequential three-stage ex-post game , in which decisions are time consistent. We found that the optimal emissions taxation rule is modified when considering different CSR motivations. We show that depending upon the CSR motivation and the price elasticity of demand in some cases we can obtain optimal emission tax rates higher, lower, or equal to marginal external emission. Finally, we also found that firms adopting consumer-friendly CSR behavior are more effective in improving the environment compared to environmentally friendly firms.