Unilateral actions, the case of international environmental problems

Resource and Energy Economics 26 (2004) 373–391

Unilateral actions, the case of international environmental problems Urs Steiner Brandt∗ Department of Environmental and Business Economics, University of Southern Denmark, Niels Bohrs Vej 9, 6700 Esbjerg, Denmark Received 30 September 2002; received in revised form 26 February 2004; accepted 2 March 2004

Abstract When abatement costs are uncertain but correlated, and a country becomes privately informed that costs are low, then unilateral actions can serve as a signalling device to reveal low costs and this can have the potential to trigger positive responses abroad. However, the country engaging in unilateral actions is the one with the highest expectation about the other countries’ reactions, and it might suffer from an effect similar to the winner’s curse. © 2004 Elsevier B.V. All rights reserved. JEL classification: Q28; H4; D8 Keywords: International environmental problems; Unilateral reductions; Signalling costs

1. Introduction The lack of supranational authority implies that international policy measures must rely solely on voluntary contributions. Barrett (1991, 1994) seriously questions the effectiveness of international environmental agreements, as exemplified by the troublesome process of regime building for the climate change issue. He points out that creating the right set of incentives for voluntary reductions of emissions in excess of purely non-coordinated reduction levels is not easy. Therefore, a very concerned country might initiate unilateral actions if such actions act as ‘setting a good example’. The main purpose of this paper is to re-examine the prospect of unilateral actions as a non-cooperative alternative to the cooperative actions of multinational negotiations. Although it cannot be expected that such ∗ Tel.: +45 65504184; fax: +45 65501091. E-mail address: [email protected] (U.S. Brandt).

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actions in themselves will bring about a fully cooperative solution, they nevertheless might make a difference in overcoming the first and potentially most troublesome phase in the process of building up an effective reduction regime in situations where incentives do not support cooperation. Unilateral actions appear in many areas of the international society, e.g. unilateral reductions in armaments, unilateral aid to developing countries, unilateral reductions in trade sanctions or increases of trade concessions, and in the field of transboundary pollution problems, unilateral cut backs in emissions. Seminal paper by Hoel (1991) analyses the prospect of unilateral actions with respect to international environmental problems. Using a setting with transboundary externalities, no enforcement of property rights, and where the individual actions of the countries are strategic substitutes, then under full information, unilateral actions by one country always trigger lower reductions in the other countries. Basically, given this set-up, unilateral actions will never be worthwhile undertaking. In this paper, unilateral actions are re-formulated, not as setting a good example (as in Hoel, 1991), but rather as transmitting relevant information. Hoel (1991) finds, in a deterministic framework, that “setting a good example” by a unilateral act of cutting back own emissions will imply that the overall emissions are reduced by less than this countries’ own reduction. Our analysis operates in a stochastic environment, and in this respect, does not add any new insights into the puzzle that Hoel’s result establishes. On the other hand, since informational asymmetries are more the rule than the exception, our findings are important in their own respect, in that they provide a rationale for “setting a good example” in this new framework. In order for a unilateral action to work, it must somehow transmit information that directly alters the position of the reaction functions of the other countries in a preferred direction from the initiators’ point of view.1 In this way, unilateral actions are analyzed in the framework of a signalling game approach. This is accomplished by invoking three assumptions. First, the costs are positively correlated between countries. The second is that a country can be fully (but privately) informed about the relevant cost parameter, and this incurs a fixed cost. Finally, it is assumed that no verification technologies exist, which implies that transmission of information is only possible by making a reduction effort. Given these assumptions, unilateral actions are indeed profitable if the costs of the informed country turn out to be low. The prospect or likelihood of unilateral actions depends on the finer details of the information-structure. The common-sense result that the higher the correlation, the more likely that a unilateral action is profitable is (almost always) confirmed by the analysis. The inclusion of private information is fundamental to our analysis. The effect of private information on the effectiveness of alleviating international environmental problems has been addressed by Bac (1996), who includes incomplete information about valuation of the damages in his model. In Bac (1996), the mechanism to achieve cooperation is that of a 1 Our signalling approach resembles the idea of ‘leading by example’, analysed in Hermalin (1998). Here, the leader is defined on the basis of being better informed, and has to undertake some costly effort to convince others that effort is worthwhile undertaking. The difference between the two approaches is that in our model, the countries are initially uninformed, but can choose to become informed, which is costly. Hence, the choice to become informed is determined endogenously in the model and in this respect resembles the approach of Kessler (1998). She discusses the idea of undertaking a costly information gathering activity in order to become (privately) informed.

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infinite repetition of the stage game and by applying the Folk theorem. He interprets the game as a chicken-game, whereas in most of the literature, international environmental problems are interpreted as prisoner’s dilemma games (see e.g. Barrett, 1994 and Sandler, 1997). In Bac’s model the players end up in a war-of-attrition game, where the first to deviate (e.g., by choosing a cooperate reduction strategy) is the ‘loser’. In this way, a unilateral action is an equilibrium strategy in a dynamic chicken game.2 Our approach is quite different, and focuses on how to move away from a low reduction environment without the use of the Folk theorem and without a prior assumption that the highest possible sustainable payoff is a focal point as in Bac (1996). Instead, we consider the situation where incentives resemble the incentives in a prisoner’s dilemma game, and without any assumption about an infinite time horizon. Under such circumstances, where cooperation is most difficult to achieve, we investigate whether it is possible for a country, by increasing its reduction effort, to encourage other countries to do likewise. Our approach is most relevant in cases where either no negotiation is present, due to, e.g. the lack of effective mechanisms that can generate and/or sustain cooperation, or when negotiations are stuck in a dead-lock, e.g. caused by too costly reduction obligations. Here, application of thread-based arguments, (such as those that are build on the Folk theorem), might not enable progress. Our approach shows a way out of such a dead-lock by increasing the set of possible strategies a country can undertake in order to increase the total reductions. Hence, this paper seeks to determine whether it is possible, under the worst possible circumstances, to make any progress and pave the way for future cooperation. The idea of unilateral disclosure of information is also analyzed in Kamphu (1988), in the context of regulation of a firm. He analyses whether a regulated firm will ever unilaterally disclose information. The answer is yes if the regulator, with sufficiently high probability, can detect false reports, and hence can trust in the reports and use the information contained in them even though the firm and the regulator have opposing interests.3 If the regulator is only partially informed, the firm may unilaterally provide him with additional information. In our approach, if costs are sufficiently correlated, then the informed country will make its unilateral move to disclose its information, and in the separating equilibrium, the information will be trusted, and the other countries will respond by increasing their own reduction levels. Pereau and Tazdait (2001) analyze unilateral action in a model that builds on the concept of coalition stability.4 They show a type of action denoted “precautionary unilateral commitment”. In the event of failure of international negotiations, some countries can decide to act unilaterally while others defect. The ones that act unilaterally will be the ones 2 In a chicken game two asymmetric Nash equilibria exits, both implying that only one country reduces its emission. This is interpreted by Bac (1996) as a unilateral action. The main reason for this is that there are only two countries, in which case the reduction in damage from own reductions are significant. As the number of countries increases, the prisoner’s dilemma structure will dominate. 3 This disclosure occurs in spite of the absence of rules and rewards for the firm for disclosure of its private information. These reports are made unilaterally and emerge endogenously out of the strategic interaction between the firm and the regulators. 4 A coalition is said to be stable if none of its members want to leave and none of the non-members want to join. In these types of models, one of the unexplained issues is who is to participate in the coalition, since the essential assumption is that a coalition exists. Our paper also offers an explanation for this. In the event that unilateral action is due to development of new, environmentally friendly technology, the countries that can make best use of the technology are the ones with the highest correlation, and hence are the ones that will form the coalition.

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that have the smallest belief about the other countries doing likewise. The reason for this type of unilateral action is that it is profitable to form some kind of coalition. (Therefore, a number of countries also have incentives to act unilaterally.) Compared to this, we focus on situations where it is not profitable to form coalitions and we analyze what mechanisms could trigger unilateral actions. In this case, our approach will also work in the model of Pereau and Tazdait when their model is transformed into an appropriate private information setting. Then, if a country, by making a unilateral move, shows that costs are low, and a coalition of a given size exists, the size of a stable coalition will probably increase, the reason being that the costs of joining the coalition will be smaller. In our analysis the informed country signals that costs of reductions are lower than expected and this enables progress. However, the correlation of costs can also be given another interpretation. Standard trade theory predicts that more strict national regulation implies specialization in the environmentally friendly goods. Steininger (1995) notes that such a standard approach lacks modelling of the dynamic impacts on regulation, since Rigid National Environmental Policy might trigger innovation and the country might receive a double gain: first through export revenue due to its first mover advantages in new technologies and second because of less pollution if the pollutant in question is internationally dispersed. Steininger (1995) presents the example of Austria, which, by strict environmental regulation through setting strict standards on SO2 , experienced export success due to the development of environmentally friendly technologies. Germany and the Netherlands followed Austrian regulation and Austrian exports flowed to Germany and the Netherlands in the years that followed. It is also conceivable that the Austrian development of new technology could trigger more reductions in other countries due to new and cheaper abatement technologies. This interpretation can be given to the unilateral action analyzed in this paper. Imagine that a country undertakes a unilateral action, such as strict national regulation, or subsidization of the environmental goods sector. If new technology is developed, then this will initiate more reductions abroad, as these countries now obtain access to cheaper reduction possibilities.5 The country undertaking the unilateral action must convince the others that costs are low. However, in order for the country to export its new technology, the other countries will also have to engage in more strict regulation. They will do this if they are convinced that the newly developed technology is really sufficiently cheap. To gain further insight into the cause and prospect of unilateral action, changes in the basic model are made by introducing a simple public choice model. In this model the decision about the level of environmental regulation in a country is determined by the lobbying activities of two pressure groups in that country: an industrial group lobbying for no reductions and an environmental group lobbying for high levels of reductions. The more pressure a group exerts, the more it influences the policy outcome. The observation that the political process in a country is polymorphic is also analysed in, e.g. Dijkstra (1999) who uses an influential function. Our model now yields a broader framework for understanding the reasons why a country moves first, the initial positions of the countries and how transmission of information interferes with policy choices in other countries. 5 Here, the level of correlation depends on the other countries’ ability to integrate the new technology into their polluting industries.

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Some of the results of the analysis show that unilateral action is most likely when costs are positively correlated, when a country can be fully informed at low costs and when a country can receive a perfect signal. Moreover, unilateral action is most likely when the countries are initially reluctant to engage in any significant reduction effort, which could be caused by pressure from lobby groups. Finally, an interesting result emerges regarding which country initiates unilateral actions: the problem of the country that initiates the unilateral action is that, since it is the one with the highest estimate of the response of the other countries if reduction costs are revealed as being low, this country is likely to overestimate the actual response of the other countries. This might explain why unilateral actions are initiated, but as Barrett (1998) claims, initiatives of this kind are seldom rewarded. The paper is organized as follows: in Section 2, the basic model is presented, and private information about costs is introduced in Section 3. The next section presents the formal signalling game model and shows when unilateral actions are possible. In Section 5, we relax the assumptions and this shows the robustness of our results. Finally, an alternative specification of the way environmental policy is determined is given in Section 6, while Section 7 concludes the paper.

2. Model The set of countries is I = (1, 2, . . . , N). Each country emits ei , the polluting substance, which causes environmental degradation both domestically and abroad. For simplicity, assume a uniformly mixed pollutant giving rise to a
global emission problem. Hence, every country is affected by the total emission level, e = ei . Let the emission level in the case of no environmental concern be eoi , and assume that ei ∈ (0, eoi ).6 Compared to eoi , a country might undertake some reduction efforts. Let qi = eoi − ei be the actual reduction level of country i, hence, the level of reductions is measured by how much emissions are reduced compared to eoi . We have that qi ∈
Qi = (0, eoi ). Due to the global pollutant assumption, it is the total reduction level, q = qi , that is relevant for a country’s reduced level of environmental degradation. Bi (q) measures the benefits to country i from total reductions, q. On the other hand, costs of controlling emissions only depend on own reductions, qi , and are measured by Ci (qi ). We make the standard assumptions on the functions that Bi (q) > 0 and Bi (q) < 0, while Ci (qi ) > 0 and Ci (qi ) > 0.7 Hence, the net benefit (NB) to country i from own and total reduction efforts amounts to: NBi = Bi (q) − Ci (qi ),

i = 1, 2.

(1)

Given the assumptions, the net benefit function is strictly concave in qi . If each country behaves non-cooperatively, it maximises its own net-benefit function with respect to its own reductions, qi , considering only damage in its own country but not the damage it causes in other countries, or alternatively, not considering the public good character of its own reductions. The first-order condition for a country to maximize its net benefit in a 6 7

See Brandt (2002) for a model where, for strategic reasons, emissions are increased possibly above eoi . For a more detailed discussion of these assumptions, see e.g. Finus (2001).

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non-cooperative setting is obtained by differentiating (1) with respect to own reductions, taking the other countries’ reductions q−i as given: NBi = Bi (q) − Ci (qi ) = 0. Define the best reply function, or the reaction function of country i, as the function that relates the optimal choice of country i to the reduction choices of the other countries, qi = qi (q−i ). The slope of this function is given by as (∂qi (q−i )/∂q−i ) = (Bi /Ci − Bi ).8 Since Bi (q) < 0 and Ci (qi ) > 0, we have that −1 < (∂qi (q−i )/∂q−i ) < 0. Moreover, given the assumptions on the benefit and cost functions, there exists a unique (and interior) Nash equilibrium given by qnc = (q1nc , q2nc , . . . , qnnc ) at the intersection of the reaction curves.9 Assume that in the case of no coordination, these levels will result.10

3. Cost uncertainty Next, private information about reduction costs is introduced. For all I ∈ I, let θ i be a shift parameter in the cost function of country i and let θi ∈ (L, H). Hence, we assume two possible cost types, where Ci (L, qi ) < Ci (H, qi ) for all qi ∈ Qi . Let ρj = prob(θj = L) be the (common) prior probability that the cost parameter of country j is low, with θ = (θ1 , θ2 , . . . , θn ). Let ρ = (ρ1 , ρ2 , . . . , ρn ) be the vector of common prior beliefs about the types of the n countries. Assume the following single crossing condition (SCC): for all ρ > ρ and all q1 , q2 ∈ Qi with q1 ≤ q2 : NBi (L, qi2 , ρ ) − NBi (L, qi1 , ρ ) > NBi (H, qi2 , ρ ) − NBi (H, qi1 , ρ ). The SCC says that an increase in beliefs (beliefs that costs are higher), increases the NB more for a low cost country than for a high cost country. The reaction function of country i, in the most general form, is given by qi = qi (θi , q−i (ρ), ρ), which says that the best reply function by country i is dependent on own type, θ i , expected reduction choices of the other countries, q−i (ρ), and the common prior belief vector, ρ. In a two country model, q1 = q1 (q2 (θ), θ) denotes the reaction function for country 1 under full information, while q1 = q1 (q2 (ρ), ρ) is the situation with complete uncertainty. The non-cooperative (Nash) equilibrium is given by qinc = qinc (ρ) under complete uncertainty, and qinc = qinc (θ) under full information of two countries.11 To illustrate how revelation of information influences the choices in the non-cooperative equilibrium, assume the following one-period, two-country situation: initially, there is common uncertainty about the costs. The relevant reaction function for country 1 is q1 = q1 (q2 (ρ), ρ) and for country 2, q2 = q2 (q1 (ρ), ρ) with the resulting Nash equilibrium outcome qnc (ρ). If now both countries costs are revealed to be low, then both countries reaction functions shift outwards to q1 = q1 (q2 (L), L) and q2 = q2 (q1 (L), L) as shown in Fig. 1, 8

Conditions that guarantee a unique (and interior) Nash equilibrium are given in Finus (2001, Chapter 9). nc ), which, due to the assumption of a uniformly mixed pollutant, We occasionally
use vector notation Bi (qi , q−i nc is equal to Bi (qi + j=i qj ). 10 This is a common observation; see e.g. Hoel (1997). 11 In Brandt (2003a) it is shown that ∂q /∂θ > 0, implying that the higher the other countries’ costs, the higher i j the own reduction. Since ρ is the probability of low costs, the more likely that the other country has low costs, the lower will be the own reduction. 9

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Fig. 1. Changes in the equilibrium when costs change.

which implies, an increase in both countries’ reduction levels (moving from point A to B in Fig. 1). Now look at the following set-up: if costs are fully correlated, and one country becomes fully informed that costs are low, and can report verifiable information about its cost costlessly, (or at sufficiently low cost), then it is optimal for this country to reveal its costs. However, when costs are positively correlated, a high cost has the same incentives as the low cost country to try to persuade the other country that costs are low. In order for the low cost type to be perceived as having truly low costs, it must engage in an action that distinguishes it from the shadow of the high cost country. The appropriate way to analyze this is by use of a signalling game model.

4. Incentives to signal that costs are low First, we set up a benchmark model where costs between countries are fully correlated. This case is not meant to represent a realistic situation, but it will make it easier to set up the signalling model. In Section 5, we then analyze the effect of the correlation on the profitability of unilateral actions. The timing of events in the benchmark model is as follows. Initially, the countries are at qnc . No country wants to initiate further reductions. The costs of further reductions are uncertain but most importantly, costs are fully correlated between countries. Nature draws a (common) type θ from the set (L, H), according to a probability distribution (ρ, 1−ρ) where ρ = prob(θ = L). This information structure is common knowledge to all. One country, denoted country i, makes an effort to reveal θ and this country becomes totally informed, whereas the other countries remain uninformed. If it turns out that costs are low, the country will initiate full-scale unilateral actions if such actions indisputably reveal to all

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other countries that costs are low. If it is revealed that costs are high, no further reductions will be made. Formally, the informed country chooses a reduction level qi ∈ Qi . The j = i countries observe qj , but not θ, and choose their reduction level qj ∈ Qj . The net benefit functions are still NBi = NBi (θ, qi , qj ), but now the types of the uninformed countries are determined by their posterior belief: NBj = NBj (ρ(qi ), qi , qj (qi , ρ(qi )). Formally, the following four assumptions are made regarding the information structure: Assumption A1 (correlation of costs). The cost parameter is fully correlated between countries, i.e. θi = θj , ∀i, j ∈ I. Assumption A2 (assessment of costs). Any country i can become fully (but privately) informed about θ i . The cost of doing so, is Di > 0. Assumption A3 (profitability of unilateral actions for one country). ¯ and let ρo < ρ. ¯ (a) Let q(ρ1 ) = q(ρ2 ) for all ρ1 < ρ¯ and ρ2 < ρ, (b) Let ∃i ∈ I : NBi (ρ, qi (ρ), q−i (ρ)) ≤ NBi (L, qi (L), q−i (L)) + Di and ∀j = i : NBj (ρ, qj (ρ), q−j (ρ)) > NBj (L, qj (L), q−j (L)) + Dj . Assumption A4 (Information-transmission). No verification technologies exist. The first assumption (A1) requires that the underlying cost parameter is fully positively correlated between countries. International environmental problems exist where the costs of reductions are positively correlated between countries. This could be the case in situations where, if a country takes unilateral actions, it has to implement measures that hereafter are also available to other countries. In addition to the example of Austria already discussed in Section 1, another example of this is the attempt to reduce current CO2 emissions using windmills to generate energy. If the establishment of windmills and their integration into the conventional energy-system can be shown to be cheap, it will be cheap for every country that can use wind for energy production.12 If switching from coal fired to natural gas fired power plants is revealed to be cheap, this can be used by any country that uses coal as its fuel-input. The classic example that shows a case with positively correlated costs and how their revelation enabled further reductions can be found in the efforts to control substances that deplete the ozone layer. In 1987, a breakdown in the negotiations over the Montreal Protocol seemed inevitable, but following the rapid development of acceptable (i.e. cheap) substitutes (in the US), producers had much to gain from a CFC-ban. Producers had no incentives to put up any political opposition to the Montreal Protocol, and a breakthrough in the negotiations occurred (Sandler, 1997). Although costs are not likely to be fully positively correlated, for now, this is assumed, and the analysis can be thought of as being 12 In Denmark, subsidisation of infant windmill industries, in combination with strict national environmental policies, has resulted in export success. According to Brandt and Svendsen (2003), the majority of the windmill turbine producers are Danish companies, which operate worldwide, typically exporting 70–90% of their total production. For example, the biggest firm, Danish Vestas, had an average export share of 83.4% for 1998–2000. In the case of windmills, the relative price of windmills is still above that of conventional energy production. But the introduction of off-shore windmills might pave the way for the windmills to be competitive without subsidies.

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used to answer the following question: how does correlation of costs influence the likelihood of profitable unilateral actions? How changes in the correlation affect the likelihood of unilateral actions is analyzed in Section 5. Assumption A2 says that a country becomes fully informed about costs without undertaking the actual reductions: to make our analysis tractable, it is simply (but somewhat unrealistically) assumed that a country can be fully informed. We assume that the country incurs a fixed (sunk) cost to become informed. This could range all the way from detailed reports to R&D in less-polluting technologies. We will analyse the effects of this assumption in Section 6.13 Assumption A3a means that with the current state of information, for all ρ < ρ, ¯ the reduction levels will remain unchanged. This assumption is needed in order for unilateral actions ever to be profitable, and can be justified by the fact that costs of reductions refer to further reductions. Given this Assumption, A3b says that one and only one country has an incentive to gather information. One way of thinking of this is that at a given point in time, no country has such an incentive, but as time passes, cost and damage figures change, or the cost of becoming informed changes (e.g. new scientific information reveals that damage costs are higher than expected). All in all, the effect of this is assumed to be that at some point in time it is worthwhile for one country to become informed. Section 6 offers an alternative explanation of how to identify the country that undertakes unilateral actions. Assumption A4 is probably the most critical assumption. The assumption means that although a country becomes fully informed about the common cost parameter, it cannot costlessly verify this information to the other countries. This can be justified by pointing out that, even if the country observes that costs are high, it has an incentive (now more than ever) to persuade the uninformed countries that costs are low, by misstating data, or any other possible way of misinforming. This assumption is needed in order for a country to distinguish itself from the shadow of a high cost country by use of a costly signal (the unilateral actions) that would never be profitable if it had high costs. Again, we offer a different set-up in Section 6 that, from a public choice point of view, gives a more detailed account of the mechanisms by which information is transmitted between countries. With these assumptions in place, we turn to the description of the signalling game that forms the basis for the unilateral actions. Under what conditions can a low cost country reveal its true costs and get the uninformed countries to increase their reductions accordingly? First of all, a collection of reduction levels and beliefs (ˆqH , qˆ L , ρ(q ˆ i )) forms a sequential equilibrium if the following conditions are satisfied: 13 Although we assume in A2 that a country can become fully informed, this is not realistic. Under more realistic circumstances a country can make an investigation that reveals information, but only yields an imprecise assessment estimate. Such an approach is shown in Kessler (1998), where the more a country invests in the information gathering activity (which increases the costs of investigation), the higher is the probability to becoming informed. In real life, probably the only way to be fully informed is through “learning by doing” activities. The country will then engage in unilateral actions if its estimates, both of the costs and the responses, are high enough to make unilateral actions a priori profitable. In theory, instead of undertaking unilateral actions, the government in a country could invoke a truthful revelation mechanism. It would be relevant to consider a direct mechanism as a part of an outcome of a multilateral negotiation, see e.g. Brandt (2003b). We leave such an option to further research, and stick to the idea that only a full scale unilateral action fully reveals the information to this and all other countries such that no revelation mechanism exists other than the learning by doing activity.

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(i) optimality for the country with costs θ: qˆ θ ∈ arg max NBi (θ, qi , qj (qi , ρ(qi )); (ii) beliefs are Bayes consistent: ˆ qH ) = 0 and ρ(ˆ ˆ qL ) = 1 (a) If qˆ H = qˆ L , then ρ(ˆ (b) If qˆ H = qˆ L , then ρ(ˆ ˆ qH ) = ρ(ˆ ˆ qL ) = ρo (c) If qθ = (ˆqH , qˆ L ), then ρ(qθ ) = 0. We will only focus on separating equilibria, since we are interested in the circumstances under which unilateral actions will turn out to be profitable. As shown in Brandt (2002), when the response set is continuous, all sequential pooling equilibrium will be eliminated by use of the intuitive criterion (Cho and Kreps, 1987). In our case the response set is defined by the continuous reaction function, and hence, no pooling equilibrium withstands the intuitive criterion.14 In order to fully describe the set of possible separating equilibrium outcomes, we assume that out-of-equilibrium signals are followed by the most unfavorable beliefs seen from the sender’s point of view, which implies that any out-of-equilibrium moves are followed by the worst possible beliefs from the point of view of the informed country. This now means that if qθ = qˆ L , then ρ(q ˆ θ ) = 0. If costs turn out to be low, the informed country will try to convince the uninformed country that costs are truly low. It can do so by unilaterally increasing its reductions to such an extent that only a low cost country could profit from such a move, even if beliefs are updated most favorably from the point of view of the informed country. If costs turn out to be low, the following two conditions are necessary for the low cost country to separate. NBi (L, qi , 1) ≥ NBi (L, q(L, 1), 0)

(3.a)

NBi (H, qi , 1) ≤ NBi (H, q(H, 0), 0).

(3.b)

In order to describe the set of separating equilibrium outcomes, define the following two sets: ∗ ∗ RL i = (qi ∈ Qi |NBi (L, qi , 1) ≥ NBi (L, q(L, 1), 0)) ∗ ∗ RH i = (qi ∈ Qi |NBi (H, qi , 1) ≤ NBi (H, q(H, 0), 0)).

The intersection of these two sets is given by RSC = (qi |qi ∈ RL ∩ RH ). In order for the low cost type to accomplish this, assume the following single crossing condition (SCC): for all ρ > ρ and all q1 , q2 ∈ Qi with q1 ≤ q2 : NBi (L, qi2 , ρ ) − NBi (L, qi1 , ρ ) > NBi (H, qi2 , ρ ) − NBi (H, qi1 , ρ ). The SCC says that an increase in beliefs (beliefs that costs are higher), increases the NB more for a low cost country than for a high cost country. The set of separating equilibrium outcomes is given by

14

qˆ iL ∈ RSC

(4.a)

qˆ iH = q(H, 0)

(4.b)

A nice treatment of signalling games can be found in Gibbons (1996) and Fudenberg and Tirole (1993).

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Given the assumptions stated in this paper, it will always exist: Result 1. Given the single crossing condition, there always exists a separating equilibrium given by (4.a) and (4.b).


Proof. see appendix.

H This result is reproduced in Fig. 2, where RL i and Ri are indicated by the dotted lines as defined above. The intercept indicated by the bold line shows the set of separating equilibrium outcomes, all implying an increase in reduction levels for the low cost compared to the full information situation. Since the set of separating outcomes is large, a selection among them is necessary in order to get a unique prediction. This is done by the use of equilibrium refinements. Such refinements used for signalling games are based on the notion of forward induction, which asserts that when rational players enter a game, they should, in evaluating strategies, reason from the beginning of the game-tree by using introspection, i.e. by examining who has an incentive to send possible out-of-equilibrium messages, and then revise beliefs accordingly. Given that it is common knowledge among the players that everyone engages in this introspection process, an implicit communication emerges. To see how refinements based on this idea work, imagine that a player picks a candidate equilibrium outcome and then reviews the beliefs about out-of-equilibrium information sets that sustain this outcome. The player then applies a refinement criterion that describes what constitutes a reasonable belief. If, by taking into account the reasonableness of these beliefs and believing that the other players do so too, at least one player has an incentive to deviate, hence this outcome is no longer an equilibrium in the refined game. The requirement for formation of beliefs applied in this paper says that it should be common knowledge among rational players that they never play a strategy profile that a particular player has no incentive to play. We say that a strategy q is weakly dominated by another strategy q for type θ, if, no matter what beliefs the uninformed player could possibly hold after observing the move of the informed player, the expected payoff of playing q always exceeds the expected maximum payoff of playing q for the informed player.

Fig. 2. The set of separating equilibrium outcomes.

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Definition. Weakly dominated (WD) strategy: a strategy q is WD by q for type θ, if minρ NBi (θ, q , ρ) ≥ maxρ NBi (θ, q , ρ) ⇒ NBi (θ, q , 0) ≥ NBi (θ, q , 1). The definition says that even in the case where q is followed by the worst possible circumstances from the point of view of the informed player, this reduction level is still preferred to q , even when q is followed by the best possible circumstances, then q is weakly dominated for this type. By invoking the following requirement, we want to reduce the set of separating equilibria. Requirement for belief formation. If a signal q is weakly dominated for one type θ, but not for the other type, then the uninformed player’s belief should place zero probability that θ has sent q , i.e. q must be followed by posterior ρ(θ|q ) = 0. This relatively non-controversial requirement has tremendous cutting power on the set of separating equilibria, as stated now: Result 2. There exists one undominated separating equilibrium, (ˆqiL , qˆ iH ) = (qiUA , q(H, 0)), where qiUA = suparg(qi ∈ Qi |NBi (H, qi , 1) = NBi (H, q(H, 1), 0)). Proof. see appendix.




The following proposition summarizes the main findings of this section: Proposition 1. Given A1-A4 and the SCC, when costs are fully correlated and a country can be fully informed, then qiUA > q(L, 1), qˆ iH = q(H, 0), and the response by the uninformed countries is also to increase reductions. Hence, the reduction of each country is higher, and in this case, unilateral action clearly has a potential to move the other countries’ reduction levels in the right direction (seen both from an environmental and an economic point of view). Note that the reason for unilateral action is the inability of a low cost country to verify its costs unless it engages in costly activity that convinces the other countries about its true type. Hence, unilateral actions are a consequence of an adverse selection problem and the incentives (for a high cost type) to misrepresent the true costs. Note that given assumption A3a and A3b, it is also profitable for a country to undertake unilateral actions, and given A4, it is optimal to take unilateral action, since there exist no means of transmitting information other than by the appropriate choice of qi . 5. Relaxing the assumptions The result stated in Proposition 1 builds on a strong assumption that costs are fully positively correlated. Let us investigate the role of correlation further. Let γ be the level of correlation of costs, i.e. γ = 1 means fully positive correlation. Common sense suggests

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Fig. 3. Reduction in correlation might increase net benefits for the low cost country.

that the higher the correlation, the more likely is unilateral action. The analysis in this paper tends to verify this intuition. Proposition 2. (a) (∂qiUA /∂γ) > 0: Lower correlation reduces qiUA . (b) There exits situations where, for a small decrease in correlation compared to γ = 1, the NB of undertaking a unilateral action increases. (c) For a sufficient decrease in correlation, NB is reduced and unilateral actions will not be profitable any longer. Given A2–A4, there exists a γ¯ > 0 such that for all γ ≤ γ, ¯ unilateral actions are not profitable. That lower correlation reduces qiUA is obvious. qiUA is defined as the level of reduction that exactly makes the high cost type indifferent between playing qiUA and getting a favorable updating of beliefs (i.e. being perceived as having low costs), or accepting being perceived as a high cost type. In the case where γ < 1, the net benefit from being perceived as having low costs is lowered, since the other countries will not reduce as much. Therefore, a smaller q than qiUA will make the high cost type indifferent. The conclusion of the proposition is that it is not guaranteed that a simple (monotonic) relationship exists between the level of correlation and the likelihood of unilateral action being profitable. An increased γ increases the reduction of the “others” in the case of revelation. On the other hand, in order to reveal information, a higher qiUA is necessary, given (∂qiUA /∂γ) > 0. Since the NB function is strictly concave in qi , a situation arises where for increased γ, the NB is decreased for the low cost type. Nothing in our assumption precludes the second effect from dominating the first. In Fig. 3 such a case is presented.15 Compared to Fig. 2, assume that costs are not fully correlated. Let NBi (θ, qi (γ), γ) be the NB for type θ when it is perceived of having low costs, and the correlation of costs is λ. The NB in the imperfectly correlated case, are the dotted NB lines, implying that when the 15

∗ ∗ In the figure, let RL i (γ) = (qi ∈ Qi |NBi (L, qi , γ) ≥ NBi (L, q(L, 1), 0)).

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country is perceived as having low costs, the resulting NB is smaller. The necessary amount in order to separate in the imperfect correlated case compared to the fully correlated case is reduced from qiUA (1) to qiUA (γ). In point B, the imperfectly correlation case, it requires a smaller increase in reductions in order to separate than in point A, the perfectly correlated case, but it also yields a lower positive response. In the Figure, point B yields higher NB to the low cost type than point A. This situation is more likely the steeper NB(L, q, 1) is at qUA , since reducing q then increases NB the most. For sufficiently small γ, unilateral actions are no longer profitable, the reason is that (∂[NB(L, q(γ), γ) − NB(L, q(L, 1), 0])/∂γ) → 0 for γ → 0 compared to D > 0.16 Assumption A3 is needed in order for one country to undertake unilateral actions. Instead of letting Di vary between countries, we could have that a country considering engaging in unilateral actions must form expectations about what the response of other countries will be. Assuming that countries hold different assessments about the reactions of the others, we get the following result: Result 3. The lower the estimated costs of becoming informed and the larger the expected response, the more likely that unilateral actions will be initiated. Why do different countries hold different beliefs? Could it be that countries with high international environmental profiles believe that if they reveal that costs are not as high as expected, other countries will be convinced of the necessity to make larger reductions in emissions?17 If so, then countries with high international environmental profiles will take unilateral actions, while countries with low such profiles will tend to make their strategies contingent on the actual achievements of other countries. This could also be supported by the presence of self-serving beliefs.18 Taken together it says that countries that value environmental protection highly also tend to believe that other countries do. Hence, the country most likely to engage in unilateral action is the one that has the most positive perception (expectation) about the response in terms of increased reductions aboard. But this will have serious consequences for the country undertaking the unilateral actions. Since it has the highest estimate, the real size of the response is likely to be smaller, and, ex post, the unilateral actions will probably not be (as) profitable. This resembles the well-known phenomenon called the winner’s curse from auction theory. This we restate as Result 4. 16 In the case of small positive correlation the high cost type will be revealed even without any signalling. This is an obvious consequence of the two-type signalling model, where the main reason why signalling is needed is to escape the shadow of the high cost type. For sufficiently small γ, the high cost type will not gain sufficiently to be compensated for the increased reductions and there will be no unilateral actions for D > 0. However, as ␥ increases the response increases and at some level the response is sufficient for the high cost type to gain enough to compensate for the increased reduction. 17 This hypothesis is based more on empirical evidence than on a theoretical foundation. The empirical evidence supporting it is best summarized by this quote from Rabin (1998, page 26): ‘a range of research suggests that once forming strong hypotheses, people are often too inattentive to new information contradicting their hypotheses. The form of anchoring does not necessarily imply that people misinterpret additional evidence, only that they ignore additional evidence. Psychological evidence reveals a stronger and more provocative phenomenon: people tend to misread evidence as additional support for initial hypotheses’. 18 For a discussion of such beliefs, see Dahl and Ransom (1999).

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Result 4. The curse of the country that initiates the unilateral action: since the country with the highest estimate of the response of the others will initiate the unilateral action, this country is likely to over-estimate the actual response. Hence, in the end, the country undertaking the unilateral action will be disappointed, and should consider updating its beliefs about the responses.

6. Alternative specification of the information structure We now offer an alternative specification of how information can be transmitted to other countries by use of a very simple public choice model. There are several reasons why we do this. It removes the necessity for assumption A4, yielding a more convincing argument for assumption A3b. It moreover gives a more satisfactory explanation for how “setting a good example” could be accomplished and why costs are correlated and how revelation of costs in one country changes incentives in other countries. We take into consideration the political process in the countries by building on a simple influential function approach inspired by Becker (1983).19 We assume that the decision about the level of environmental regulation in a country is determined by lobby activities of two pressure groups: an industrial group (IG) lobbying for no reductions and an environmental group (EG) lobbying for high reductions. According to Svendsen (1998), the EG try to maximize their influence through maximizing membership. Increasing membership increases payments and, hence, enables these groups to increase their lobbing activities. One way of increasing membership is to convince potential members of the importance of a strong EG. By pointing to achievements in other countries and arguing that these results are a consequence of strong EGs, the domestic EG has a strong argument that results in higher pressure on the decision-makers. On the other hand, an IG uses issues such as loss of international competitiveness and, consequently, increases in unemployment and reductions in exports as arguments against environmental regulation. Formally, let the utility for the IG be uIG = uIG (ci , qi ) of having costs of ci and a national reduction target of qi , while uEG = uEG (q) is the utility to the EG from total reductions.20 The higher the costs, the more the IG suffers if it has to make reductions, and the more this group is willing to lobby against reductions (the marginal gain from lobbying is increasing in ci ). On the other hand, the EG suffers because of global emissions but the level of costs has no effect on the utility of the EG.21 In order to integrate this public choice model into the signaling model, qi most be is the outcome of a maximizing process. This requires a re-interpretation of the cost and benefit functions in expression (1). One proposal is as follows: define a countrys’ wealth (utility), 19

See also Potters and Sloof (1996) for a survey of this type of model. That lobbying influences the decisions of policy-makers is well documented. Svendsen (1998) notes that all eight existing US permit market programs have been distorted politically through lobby activities. Haas et al. (1993) note that if there is one key variable accounting for policy change, it is the degree of domestic environmentalist pressure in major industrialized democracies, and not the decision making rules of the relevant institution. 21 Other specifications could be used, but what is important is how the cost estimates influence a countrys’ choice of reductions. 20

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wi , connected with the emission as a weighted sum of the utilities to the two groups, wi = λuIG (qi , ci )+(1−λ)uEG (q), hence wealth in country i is given by wi = wi (qi , q, ci ). Given this specification, define now qinc = arg max wi ((qi , q, ci ). In this way qi is chosen as the welfare maximizing choice of country i (as a trade-off between the conflicting preferences of two influential interest groups, and in optimum, balancing the benefit to the EG of the reductions with the costs of doing so for the IG). Given the above discussion, we have that (∂qinc /∂ρi ) < 0 and (∂qinc /∂q−i ) > 0. In all countries where the political decision-making process is as described above, industry has incentives to try to make policy-makers believe that costs are high. Compared to the model in Section 4, this better explains the assumption about the high correlation of costs, since the correlation is related to the political systems in a country. Given identical political systems, the incentives to believe that costs are high are also identical. It, moreover, also explains better how the emergence of new information can trigger positive responses in all these countries. This model can also be used to motivate why countries initially do not reduce (or reduce as if costs of further reductions are high). Assume that for ρo ∈ [0, ρ] ¯ a country will not engage in any reduction efforts, because, e.g. the IG will have almost full discretion over national policy (the marginal gain from pressure from the IG is relatively high) when costs are believed to be high with a high probability. Consequently, the IG will put sufficiently high pressure against national reductions such that this country acts as a high cost country. Importantly, as long as the government has no incentives to become informed, which is the case when its estimates of the responses of others are not sufficiently high, the decision makers have incentives to accept claims that costs are high. When a government has a pretty clear picture of the costs, then it needs an extremely high effort from the IG to change this picture. The chain of argument goes as follows: initially, the country holds a prior belief about its own costs and the costs others and the pressure from the IG to make no reductions is relatively effective, since ρ¯ < ρo . Now, the other country makes a cost revealing move and costs are low. The higher the correlation of costs, the more ‘informed’ the government becomes, and the less is the marginal effect of the pressure from the IG, in which case the pressure is reduced and the national reduction is increased.

7. Conclusions A main conclusion derived in this paper is that if reduction costs are correlated, then the transmission of information by use of a unilateral move makes sense. However, unilateral actions have not always been as successful as expected. One explanation offered in this paper is that the initiator of unilateral actions is the country with the highest expectation about its prospects of influencing other countries’ decision-making processes. Since the country holding the highest expectation is likely to overestimate the true state, it is likely to be disappointed. In conclusion, this paper both provides positive and negative prospects for unilateral actions as a means of moving towards an effective control of the international environmental problem. The analysis presented in this paper builds on the crucial assumption that unilateral actions concern the revelation of information about the cost side. For several reasons, we

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find it reasonable to expect that uncertainties relate to the cost side and not the damage side. Unilateral actions to cut back pollution reveal information about the efficiency and the costs of the measures employed. On the other hand, a unilateral action will not reveal the damage costs (or equally, the benefits from reductions). In particular, if considering a global pollution problem, the effect of one country on the total stock of pollution will probably be negligible, and no new information regarding damage cost functions is revealed. We also believe that signaling as a mechanism of information transmission in the way described in this paper is not unreasonable. The reason is that countries are only convinced by hard facts (and not by a report from a government hired consulting agency), simply because incentives are such that each country has an incentive to try to convince others that costs are low. However, only when a country has verified that costs are low by implementing the necessary measures, that is, by engaging in full-scale unilateral actions, can it possibly convince the other countries. As already noted in the introduction, another reason to undertake unilateral actions is the expectation of achieving a first mover advantage. The existence of such advantages clearly enhances the prospect of unilateral actions. In particular, the way unilateral actions are modelled in this paper, it clearly has a first mover advantage. In this case a country could reveal that costs are low, trigger higher reductions in other countries and at the same time increase the potential of the first mover advantages by enabling large-scale export possibilities. A country that engages in unilateral actions could therefore make its move more profitable by engaging in activities that yield first mover advantages. For example, in Denmark national subsidies of the windmill industry could turn out to be extremely profitable in the form of windmill exports, if a significant reduction of CO2 emissions is initiated globally. It has been argued that the emergence of substitute substances for CFC gasses changed certain EU countries’ strategies in the run-up to the Montreal Protocol, from being reluctant participants to taking the lead. If we include first mover advantages, the conclusion about the curse of the initiator of unilateral action might no longer be valid. If first mover advantages vary among the countries, then even if a country does not have high expectations (compared to some average for the countries) it might still initiate unilateral actions that also ex post turn out to be profitable.

Acknowledgements Special thanks go to A. Endres for valuable comments that have improved this paper considerably. Moreover, I would like to thank F. Jensen and participants at seminars in Monterrey and Kolding and three anonymous referees and Markus Lang for helping to improve the paper significantly. Finally, special thanks to P. Madsen for improving the English.

Appendix A Proof of result 1. Define qi = sup arg(NBi (H, qi , 1) = NBi (H, qi (H, 0), 0)). If there exists a qi satisfying 3.a with strict inequality, then existence is guaranteed. If NBi (L, qi , 1) >

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NBi (L, qi (L, 1), 0), then also NBi (L, qi , 1) > NBi (L, qi (H, 0), 0), since qi (L, 1) is the unique maximizer of NBi (L, qi , θ), which implies that if there exists a qi > qi (L, 0), such that NBi (L, qi , 1) − NBi (L, qi (H, 0), 0) > NBi (H, qi , 1) − NBi (H, qi (H, 0), 0)), as NBi (L, qi (L, 0), 0) > NBi (L, qi (H, 0), 0) then a separating equilibrium exists. But this is guaranteed via the single crossing condition.
Proof of result 2. Weak domination of qˆ iH for the high cost type in this case corresponds to the following inequality: maxp NBi (H, qˆ iH , ρ) ≤ minρ (NBi (H, qi (H, 0), ρ), ) ≥ NBi (H, qˆ iH , 1) ≤ NBi (H, qi (H, 0), 0), which is implied by 3.b. Define q¯ iL = max arg(NBi (L, qˆ iL , 1) = NBi (L, qi (L, 1), 0)). We now show that no qˆ iL = L q¯ i is weakly dominated. This amounts to showing that NBi (L, qˆ iL , 1) > NBi (L, qi (L, 0), 0). Use 3.a. NBi (L, qˆ iL , 1) ≥ NBi (L, qi (L, 1), 0) and the fact that NBi (L, qi , ρ) is decreasing in qi for qi > qi (L,1), for any qˆ iL = q¯ iL + ε, 3.b holds with strict inequality. Hence, no qˆ iL = q¯ iL can be weakly dominated. Therefore, given qˆ iL = q¯ iL + ε, posterior beliefs will be updated to ρ(ˆqiL ) = 1: given these new set of beliefs, no qi = qi + ε can be a separation equilibrium, and consequently, given this new set of beliefs, only qˆ iL = q¯ iL is an undominated separating equilibrium.
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