Recently, in their 2019 paper, Poyago-Theotoky and Yong consider a managerial Cournot duopoly with pollution externalities and emission taxes and propose an explicit environmental incentive in a managerial compensation contract. The authors compare several exogenous equilibria emerging in the symmetric sub-games in which the owner offers either the environmental delegation contract or the standard sales delegation contract: abatement and social welfare (resp. emission taxes) under environmental delegation are higher (resp. lower) than under sales delegation. The present work extends their model using a game-theoretic approach to analyse the asymmetric sub-games, in which only one firm adopts the environmental contract, and adds the contract decision stage. Results show that the environmental contract never emerges as the unique sub-game perfect Nash equilibrium of this non-cooperative managerial decision game. Indeed, if the green R&D technology is efficient, the sales contract emerges as the unique Pareto-inefficient Nash equilibrium. Otherwise, if the green R&D technology is inefficient, multiple Nash equilibria in pure strategies exist (coordination game). Our findings offer direct policy implications.