The role of socially responsible firms and government subsidies in the sustainability transition: A multi-objective game

This paper develops a multi-stage game-theoretic model to examine how different institutional mechanisms influence firms’ incentives to invest in sustainability. In the base model, two competing firms decide first whether to join a sustainability initiative. Then, participating firms choose both their production quantities and levels of sustainability effort. Sustainability investments generate a green premium, reflecting consumers’ willingness to pay for environmentally responsible products, but also produce spillover effects that benefit competitors. We further analyse two contrasting scenarios. In Scenario G , a government offers subsidies to incentivize participation and align private actions with social goals. In Scenario R , firms are intrinsically motivated by corporate responsibility and pursue both profit and environmental performance. Using the ϵ -constraint method, we characterize the Pareto frontier for each scenario compare the results. Our findings reveal that well-calibrated subsidies can overcome free-rider problems and coordinate firms toward higher joint performance, while voluntary participation alone may lead to inefficient outcomes. However, at high levels of environmental ambition, both mechanisms converge in effectiveness. The results offer policy and managerial insights on how to design incentive systems that support industry-wide sustainability transitions. • Develops a multi-objective game model of firms’ sustainability investment. • Shows green premiums and spillovers jointly shape strategic firm behaviour. • Identifies conditions for full sustainability adoption by profit-maximizing firms. • Compares efficiency of self-motivated and policy-driven sustainability strategies. • Reveals policy design depends on returns from environmental investments.