This article develops a non-cooperative game with managerial quantity-setting firms in which owners choose whether to delegate output and abatement decisions to managers through a contract based on emissions (conventionally denoted as ‘green’ delegation, GD) instead of sales (sales delegation, SD), and the government levies an emissions tax to incentivise firms’ emissions-reduction actions. First, it compares the Nash equilibrium outcomes between GD and SD and then contrasts them also with profit maximisation (PM). A plethora of Nash equilibria emerges, especially in the case GD versus PM (the ‘green delegation game’), depending on the public awareness toward environmental quality, ranging from the coordination game to the ‘green’ prisoner's dilemma. Second, though the contract under GD incentivises managers for emissions, the environmental damage is lower than under SD. This is because the optimal tax more than compensates the incentive for emissions. These findings suggest that designing GD contracts paradoxically favours environmental quality.