A Proof of Proposition 1

It is sufficient to show that no firm will deviate from the equilibrium outcome with interior solutions in choosing the prices and abatement goods at the fourth stage. In particular, we will compare Ti in the corner solutions with zero abatement goods (ai=0). Let the equilibrium outcomes with interior solutions be Ti∗=Tiai∗,aj∗,Pi∗,Pj∗ and the deviation outcomes with corner solutions with zero abatement goods be Tid=Ti0,aj∗,Pid,Pj∗. Then, we can show that Ti∗>Tid for β∈0.8,1 and i=1,2. That is, each manager can get higher payoffs under the interior solutions with positive abatement (ai>0) than deviation to zero abatement (ai=0) at the fourth stage. Therefore, when β∈0.8,1, the outcomes of interior solutions are on the equilibrium path as a subgame perfect equilibrium.

B Equilibrium without abatement goods

First, we will show the non-existence of Nash equilibrium with interior solution of abatement goods when β∈0,0.8.

Suppose that the Nash equilibrium outcomes at fourth stage have positive abatement goods, ai∗∗>0, for any given θi>0. Note that we will have ai∗∗=0 when θi=0 because purchasing abatement goods causes cost without increasing revenue in the profit function in (6). That is, it is a contradiction to have θi=0 at the supposed equilibrium path with interior solution of abatement goods. Then, with the interior solutions in the fourth stage, for any given r and θi>0, we have already obtained the equilibrium outcomes at fourth stage from (10)~(13. Hence, with the same procedures, r is determined at third stage from (16) and θ2 is determined at second stage from (20). Finally, at the first stage, the owner of firm 1 considers the reaction function of firm 2 in (20) in its profit function and decides its optimal degree of ECSR in (21), if it has interior solution, (i. e., θ1>0). However, when β∈0,0.8, it is negative in (21) and thus it will choose θ1=0. Hence, θ2=0 and ai∗∗=0. This is a contradiction with the supposed equilibrium with interior solution of positive abatement goods. Therefore, when β∈0,0.8, the outcomes of interior solutions with positive abatement goods are not on the equilibrium path as a subgame perfect equilibrium.

Second, we will now consider the outcomes without abatement goods. Then, imposing ai=0 in (9), we have the equilibrium price in the third stage, which maximizes the objective function of each manager in (5):

In the first stage, the profit of firm 2 is:

The first-order condition with respect to the degree of ECSR yields:

Then, we have θ20>0 and ∂θ2θ1∂θ1>0. This shows that θ2 is positive as far as θ1 is positive, (i. e., θ2>0 when θ1>0). In addition, ∂2θ2θ1∂θ12<0. This implies that θ1=θ2=θˉ=1−β2−1−β22d>0. Thus, we have the following relations: θ1<>θ2 when θ1<>θˉ.

At the first stage, the profit of firm 1 is:

Differentiating this profit function with respect to the degree of ECSR yields:

and

Then, we have θ1∗∗>θ2∗∗>0. Therefore, though both firms adopt ECSR sequentially, a late adopter advantage exists.

C The endogenous timing game

We endogenize the timing of the game by adopting the observable delay game, a variant of Hamilton and Slutsky (1990). In this game, firm i (i=1,2) simultaneously chooses whether to move early (ti = 1) or late (ti = 2). The ECSR decision stage is played simultaneously if both firms decide the same time, sequentially or otherwise.

First, suppose that θi>0 at the equilibrium in simultaneous choice game. Then, from the profit function of firm i in (6), both firms have the symmetric reaction functions in (19), which yields the following results of ECSR:

This is a contradiction as it implies that no firm engages in ECSR activities in a simultaneous choice game. That is, θiS=0 and aiS=0, which yields:

and

Finally, we obtain the profit rankings, which support the sequential choice game as a subgame perfect equilibrium:

and

D The market structure of eco-industry

Suppose m⩾1 eco-firms compete in producing abatement goods under a Cournot model and the two polluting firms purchase the abatement goods under ECSR. Following the analysis of Canton, Soubeyran, and Stahn (2008), we assume that the market price of eco-industry is determined by the total demand of the two polluting firms and the total supply of the productions of m eco-firms. That is, aU= aE at equilibrium where aE=∑e=1mae=∑i=12ai.

Then, assuming interior solutions of abatement goods from (11), we obtain the following inverse demand function of the abatement goods:

Using the first order condition of each eco-firm with respect to its abatement goods, ∂πe∂ae=0, and the symmetric equilibrium in the eco-industry, aU=∑e=1mae=mae,, we have:

and

Note that as m increases, ae decreases.

Finally, from the profit of polluting firm 2, we have the reaction function of firm 2:

When β>m−1m, θ2 is positive as far as θ1>0.

Then, from the first order conditions for maximizing the profits, we have

and

Note that the degree of ECSR is positive when β>β−=1+3m2+3m, where β− is increasing in m and β−=0.8 if m=1. Thus, as m approaches infinity, none of the polluitng firms purchase abatement goods from the eco-industry, even though both the polluting firms adopt ECSR. In addition, we can show that the outcomes of interior solutions are on the equilibrium path as a subgame perfect equilibrium.