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Based on the assumption that in a standard eco-dumping model governments are uncertain about future product demand and allowing governments to obtain information from firms, we examine governments’ and firms’ incentives to share information. We show that when governments regulate polluting firms through emission standards, then governments and firms will reach an agreement concerning information sharing. The opposite holds when governments regulate pollution through emission taxes.

Profit shifting in international firm competition is a subject that systematically attracts economists’ interest. The possibility to improve local residents’ welfare through supporting local industries

During the last two decades World Trade Organization agreements have restricted its members from engaging in such a behavior, but the unilateral incentive to increase the market share of exporting firms remains in place. A voluminous literature referred to as “strategic environmental policy literature” examines how environmental policy instruments can be used, in the presence of environmental externalities, as second best instruments for international trade purposes when traditional trade taxes, subsidies and quotas are prohibited or restricted. Specifically, in the context of international oligopolistic competition and under complete information, among others, [

A common assumption of these studies is that governments and firms act in a complete information environment. This means that governments might perfectly foresee the future market conditions or the costs of the firms. Nonetheless, this assumption is not innocuous. As clearly indicated in the seminal study of Weitzman [

It is clear from these studies that information plays a key role. Creane and Miyagiwa (CM) using a strategic trade model under incomplete information recognized the possibility that governments and firms might share information as this is mutually beneficial [

The structure of the paper is as follows. In Section 2 the model is introduced. Then, in Sections 3 and 4 the cases of emission standards and taxes are presented and solved respectively. Finally, Section 5 provides some concluding remarks. All proofs are relegated to an

We consider a symmetric two country (home and foreign) international duopoly model, where each firm belongs to a different country and produces a homogenous good whose consumers reside in a third country. Consumers preferences can be mapped into a quasi-linear utility function which implies a linear inverse demand of the form

Both firms face the same technology which implies that a unit of production generates a unit of pollution (z). However, an exogenous abatement technology is assumed to exist and thus net pollution equals production minus abatement carried out by the firm:

The abatement cost function is assumed to be convex of the form:

Regulation of pollution by the governments takes place prior to production decisions. We examine two different ways to regulate pollution. First, we assume that governments can use an emissions standard, ^{2}, where 0 <

Before any decision takes place we assume that the government and the firm in each country may agree to share information (the governments are unable to obtain information through an alternative channel, e.g., through a study, as the demand function is determined in a third country). This is the case if and only if both participants agree. If the government or the firm is harmed by such an agreement they refuse participation. Following the assumptions above we summarize the time structure of the game in

Initially, in Stage 1, the firms decide whether they are willing to disclose information or not and at the same time the governments decide whether they will accept it or not. If they both agree, then they create an institutional structure such that information disclosure is verifiable through setting a prohibitive penalty cost for those who do not comply. We assume that the set up cost of an agreement is negligible. Then, in Stage 2 uncertainty is revealed to the firms. Given that, in Stage 3, the governments select the level of regulation (taxes or standards) in order to regulate pollution. Finally, in Stage 4, the firms choose quantities so as to maximize their profits.

In order to determine whether a government will agree with the corresponding firm to share information or not, we derive the Nash equilibria of the game for all the possible scenarios. In other words, we complete the full payoff matrices of expected welfare levels and profits for the domestic government and firm respectively, for every possible contingency, given that the rival partners share information or not.

Initially, we assume that the governments and the firms in the two countries agree to share information. Hence, the problem reduces to a simple complete information game. To derive the Subgame Perfect Nash equilibrium we solve the problem via backwards induction. When standards are used as an instrument, firms have a unique control variable (production), since abatement must be chosen such that ^{R}

From

Given equilibrium outputs, governments select the optimal level of emission standards by maximizing welfare:
_{1} = ^{2} (3 + ^{2}

Solving simultaneously Stage 4 equilibrium output (7), the domestic government’s reaction function (8) and the corresponding equations for the foreign firm and government we obtain the Subgame Perfect Nash equilibrium:
_{2} = ^{2}

In Stage 1 of the game from the governments perspective θ is unknown and thus the expected profits and welfare are:

Now, we examine the scenario where the firms and the governments do not share information. If this is the case then the governments act under incomplete information as θ is unobservable for them. Thus, the equilibrium notion that we use is Bayes Nash equilibrium. Firms’ maximizing problem follows in the lines of the previous analysis, while welfare maximization follows a slightly moderated one. Since θ is unobservable to the governments, yet they know the distribution that it follows, they maximize their expected welfare with respect to the emission standard. This results to an equivalent reaction function given in (8) after setting θ = 0.

Solving simultaneously (7) and (8) after setting θ = 0 as well as the corresponding equations for the foreign firm and government we obtain the Bayes Nash equilibrium:

The second right hand side terms of (13) and (14) indicate that expected profits and welfare depends positively on var(θ),

In order to move in Stage 1 of the game and examine whether the firms and the governments will share information or not, we need to solve for the asymmetric cases as well, where the partners in one country agree to share information, while the rival pair does not and

Before doing so we provide the optimal strategy of the domestic regulator and the firm for each possible combination of information sharing chosen by the rival pair. Lemma 1 summarizes the optimal strategy for the domestic pair (the optimal strategies for the foreign firm and government are directly implied by the ones of their correspondents in the home country).

^{cc}^{nc}^{cc}^{nc}^{cn}^{nn}^{cn}^{nn}

Proof in

Using Lemma 1, we define the Nash equilibrium of the information sharing game in the following proposition:

Proposition 1 states that as it is a dominant strategy for the governments and the firms to share information it is also a Nash equilibrium of the game. The benefits from sharing information are greater than the losses. In particular, the benefits for the firms and the governments from sharing information arise from the convexity of the profit functions with respect to the demand intercept. The losses are attributed to the convexity of the damage function of pollution with respect also to the demand intercept. When the firms decide to share their information with the governments then in exchange they get laxer regulation (higher standards) as standards depend positively on θ [see

Given this result which so far parallels the one of CM, although in a different context, it is interesting to check if the result of sharing information is socially desirable. This is true when the expected welfare level in the sharing information case is higher compared to the case where none of the two pairs share information. Proposition 2 summarizes this comparison:

^{cc}^{nn}

Proof in

This result is of major importance since it states that when emission standards are the unique policy instrument in use, information sharing occurs and this is superior in terms of expected welfare compared to the case where the two pairs do not reach an agreement. Put it differently, from the social perspective the Nash equilibrium is socially optimal. At the same time it can be shown that each firm and government prefer that the rival pair do not share information regardless of their agreement (the proof of this claim is neglected for brevity and it can be provided upon request by the authors). If the domestic players share information, then the domestic firm and government are better off if the rival pair do not reach an agreement. In this scenario, the domestic firm faces more flexible standards which in turn, when demand is high, allow the domestic firm to obtain an even larger market share, while in the opposite case the market share shrinks. The benefits attributed to the convexity of the profit function with respect to the demand intercept are now higher. If the domestic pair do not share information they prefer that the rival pair does the same. If not, then at times of high demand the rival government indirectly subsidizes the corresponding firm through laxer regulation shrinking the market share of the domestic firm and reducing so its expected profits. Contrary to that, when demand is lower then regulation is stricter benefiting the domestic pair who decided to not share information. However, the first outcome prevails to the second one. The fact that each pair prefers that the rival pair is not informed does not lead to an “informational prisoner’s dilemma” as CM claim in their model. Put it differently, when emission standards are used to subsidize exports instead of subsidies, information sharing leads to a superior outcome in terms of expected welfare. It is interesting that even if both pairs prefer that the rival one does not, indeed they do share information and this is mutually beneficial compared to the case where they do not. The benefits arising from the convexity of the profit function with respect to the demand intercept when the two pairs reach an agreement outweigh the expected welfare losses attributed to the variability of standards and, thus, the variability in the damage from pollution.

In contrast to the previous case we now assume that both governments use taxes to control pollution. Now firms have two control variables available, output and the abatement level. Solving backwards we derive the first order conditions for the domestic firm:

The output reaction function of the domestic firm is implied by

Examining the domestic government’s decision about the optimal tax we maximize welfare with respect to the emissions tax. Thus, for home we have:
_{1} = ^{2}

In order to obtain the equilibrium levels of outputs, taxes and pollution in the two countries we solve simultaneously _{2} =

Substituting the new equilibrium levels in

As in the case of standards, we the ex ante values for profits and welfare as follows:

From

In case that the governments and the firms do not reach an agreement the governments act under incomplete information. Firms’ maximizing problem remains the same as in the complete information case, while welfare maximization is moderated. Now, the two governments maximize their expected welfare with respect to the emission standard. Welfare maximization by the domestic government yields a reaction function given in (18) after setting θ = 0.

Solving simultaneously (1), (16), (17) and (18) after setting θ = 0 as well as the corresponding equations for the foreign firm and government we obtain the Bayes Nash equilibrium:

Comparing the solutions given in (22) and (19), several inferences can be drawn that play a significant role in determining the expected national welfare levels. When governments are not informed, the level of emission taxes in each country is determined at a specific level and it is not affected by θ. Contrary to the situation where the governments and the firms share information the governments do not adjust their policy to θ and, thus, when θ is positive the firm may adjust its output without being penalized by the government. This, together with the fact that now abatement does not depend on θ, creates a clear disincentive to the firms to reveal their private information.

However, this is not true for the governments. If we compare the level of pollution in equilibrium in the two polar cases we obtain that pollution is higher in the incomplete information case when θ is positive and lower if θ has the opposite sign (the difference of the two is given by:

To determine the level of expected profits and welfare for this scenario we substitute the equilibrium values given in (22) and the implied abatement level in (16), into (3) and (4) respectively. Taking expectations and after some algebraic manipulation we get:

It is clear from (23) that expected profits depend positively on var(θ). From

To complete the full payoff matrix, the asymmetric cases and the expected values of profits and welfare must be calculated (see

Proof in

Using Lemma 2, we define the Nash equilibrium of the information sharing game in the following proposition:

Proposition 3 states exactly the opposite of Proposition 1. Now, the governments and the firms do not reach an agreement since the firms are unwilling to reveal their private information about θ. That is because in the case that the firms supply their information to the governments they will adjust the tax accordingly. For example, if θ is positive, then the government raises the emissions tax further, while if θ is negative then the government cut the tax by

In order the results of this section to be comparable with those of the previous section we will see if the Nash equilibrium coincides with the optimal solution from the social perspective. Proposition 4 illustrates this comparison:

Proof in

Put it differently, Proposition 4 suggests that the Nash equilibrium with taxes is sub-optimal from the social perspective. The residents in the two countries would be better off if the firms and the governments share information, even though this does not happen in the Nash equilibrium of the game.

In this paper we examine the issue of information sharing in a strategic trade model where the exporting firms yield a pollutant as a by-product of production. Environmental policy instruments, emission standards and taxes, instead of the traditional trade instruments are implemented. Similarly to CM, we examine whether the firms and the governments will reach an agreement concerning information sharing. Contrary to CM, our results suggest that when emission taxes are used the firms are unwilling to reveal information. As a result an agreement, although socially desirable, is not achieved as a Nash equilibrium despite the fact that the firms compete in quantities. The main contribution of this study is that not only the mode of competition of the firms matters,

The suggestions of this study can be further extended. For instance, the fact that the goods may be consumed in the two exporting countries and thus consumer surplus is a determinant of welfare may affect the decisions of the governments concerning the level of regulation but not the decision to reach an agreement as long as the driving forces of the mechanism remain in place. This is true also if we allow for a higher number of firms or for pollution to be trans-boundary. If this is the case, again standards (taxes) will (not) induce the participants towards an agreement as in good times environmental policy will be laxer (tighter), while in bad times will be tighter (laxer). Therefore, the results are expected to differ only quantitatively since the damage in the case of trans-boundary pollution is expected to be higher. Another modification of the model concerns the mode of uncertainty. Firms might hold private information about their costs of abatement instead of the common demand. Put it differently, the governments do not know the exact level of abatement costs and, thus, they set up an agreement to gain the extra information. We shall expect again that, in the case of standards, contrary to that of taxes, information revelation exploits further the convexity of the profit function, enforcing a bilateral agreement. Even if the functional forms used are generalized such that an interior solution exists we expect that the basic implications of this study will be replicated, since the governments are expected to increase the variability of production through standards when the firms reveal information, while the implementation of taxes reduces the variability in production under complete information driving them to keep private their information.

The authors would like to thank the participants of IMAEF 2010 conference for their helpful comments and suggestions.

The problem is again solved by backwards induction. The reaction function of output of the domestic firm is still obtained by _{3} = ^{2} (3 +

Given the equilibrium values for outputs and standards (A1) in the two countries we determine the expected profits and welfare levels in the two countries as follows:

Using ^{cc}^{nc}^{cc}^{nc}^{cn}^{nn}^{cn}^{nn}

_{4} = ^{2}(2 + ^{4}{^{3}(1 + ^{2}[9 + 2^{2}(3 + ^{2}[27 + 2^{2} + (1 + ^{4}(3 + ^{4}^{3}}.

Using ^{cc}^{nn}

The reaction function of output of the domestic firm is given by _{3} =

Given the equilibrium values for outputs and taxes (A6) in the two countries we can determine the expected profits and welfare levels in the two countries as follows:

Using

_{4} = ^{3}{81 + 2^{2}{243 + ^{2} + (1 + ^{2} (3 + ^{2} (3 + 2^{2} ^{3}

τ_{5} = ^{2}[1134 + ^{2} [54 + 5^{2}

Using

Time Structure of the Game.