Firms and banks decide whether or not to apply a green (environmentally friendly) or brown (conventional) investment and policy, respectively. We develop an evolutionary game to show the conditions such that the economy dynamically evolves towards one state or another, i.e., green vs brown or fluctuates around them. We show that the green state is asymptotically stable if the green firms’ revenues minus their bank loans and transition costs are greater than the brown firms’ revenues and pollution costs, together with green interest rates, such that the default risk is lower for green firms. Otherwise, the economy converges to the conventional brown situation. Banking policies and productive activities characterized by indifference towards green make the economy fluctuate around these states, i.e., green and brown, and multiple equilibria can emerge. We show how equilibrium can change their stability/instability, and the economy converges to one state or another.