Emission Information Asymmetry in Optimal Carbon Tariff Design: Trade-Offs Between Environmental Efficacy and Energy Transition Goals

Abstract

Against the global rollout of Carbon Border Adjustment Mechanisms (CBAMs), carbon tariffs have emerged as a core tool for developed economies to internalize environmental externalities—especially for energy-intensive imports that dominate cross-border carbon flows. However, emission information asymmetry, a critical barrier to implementing cross-border energy and environmental policies, undermines the design of optimal carbon tariffs, as it distorts the link between tariff levels and actual fossil energy-related emissions. This study develops a two-country analytical model to examine how biased assessments of exporters’ carbon intensity influence optimal tariff settings, exporters’ strategic behavior, and aggregate carbon emissions—with a focus on energy-intensive production contexts. The results show that underestimating carbon intensity reduces exporters’ compliance costs, incentivizing emission concealment; this weakens tariffs’ environmental stringency and may raise global emissions. Overestimation, by contrast, inflates exporters’ marginal costs, discouraging green investment and causing emission displacement rather than reduction. The analysis highlights a policy feedback loop wherein misjudged emission information distorts both trade competitiveness and environmental performance. This study concludes that a transparent, accurate, and internationally verifiable carbon accounting system is essential: it not only facilitates the effective implementation of CBAM but also aligns optimal carbon tariffs with CBAM’s dual goals of climate action and trade equity, while supporting global energy transition efforts.

1. Introduction

Against the backdrop of escalating global climate pressures, the low-carbon transition of energy systems and carbon neutrality have become consensus goals of the international community—with energy-intensive sectors (e.g., steel, chemicals, power equipment) emerging as key targets for emission reduction, given their outsized contribution to fossil energy consumption and global carbon emissions. As the first institutional framework targeting “carbon leakage” while safeguarding trade fairness, the European Union’s Carbon Border Adjustment Mechanism (CBAM) marks a pivotal shift in carbon regulation: from a domestic environmental policy tool to a cross-border instrument that embeds climate costs into international trade of energy-intensive goods, where emission risks are tightly linked to fossil energy use [1,2,3]. By levying carbon tariffs on carbon-intensive imports, CBAM seeks to internalize environmental externalities and enhance the global effectiveness of climate action led by developed economies [4]. However, this mechanism also poses considerable challenges to export-oriented energy-intensive industries in developing countries—many of which still rely on coal, oil, and other fossil fuels for production, leading to inherently higher carbon intensity.

For a CBAM to function as an effective policy instrument, the accuracy and comparability of firms’ carbon emissions data have become fundamental prerequisites for tariff calculation [5]. Compared with their counterparts in developed countries, enterprises in developing economies often face significant limitations in carbon accounting, disclosure standards, and third-party verification, resulting in pronounced information asymmetry in global carbon data reporting [6,7]. This asymmetry not only increases compliance costs for exporters but also risks distorting the intended environmental and trade outcomes of CBAMs, potentially leading to unintended forms of green protectionism [8,9,10].

Beyond regulatory compliance, the degree of information disclosure is not merely a matter of compliance [11,12], but may also shape firm behavior in terms of production scale, pricing strategies, and carbon mitigation efforts [3,13]. Thus, understanding these mechanisms is crucial not only from a theoretical standpoint but also for policy design, as CBAM’s long-term success depends on how effectively it addresses these asymmetries in practice. Critical questions arise: Can enhanced transparency in emissions data stimulate low-carbon transformation? Does information asymmetry incentivize strategic behavior between exporters? How should the carbon-importing countries adjust their optimal tariff rates in response to different information environments? These questions remain underexplored in the existing literature, particularly regarding how micro-level strategic interactions between firms and policy design under information constraints shape the efficiency of carbon border policies.

To address this gap, this study develops a two-stage game-theoretic model under both symmetric and asymmetric information settings, focusing on the interaction between CBAM policy design and carbon information disclosure. We analyze how different information structures affect firm profits, production decisions, market prices, and total carbon emissions, and we derive the optimal carbon tariff rate under each scenario from the perspective of the importing country. In doing so, the paper links theoretical derivation with policy insights, providing implications that can inform real-world CBAM implementation once reliable emissions datasets become available.

2. Static Carbon Tariff Model Construction

2.1. Model Assumptions

Computable and applied analyses of the Carbon Border Adjustment Mechanism (CBAM)—most commonly computable general equilibrium and partial-equilibrium models—quantify leakage, trade and price effects, and incidence under alternative designs, thereby establishing policy salience for energy-intensive, trade-exposed sectors. These assessments, however, typically treat firm-level emissions as perfectly observed and thus abstract from information frictions. Parallel work on measurement, reporting, and verification (MRV) and carbon accounting (e.g., ISO 14064; GHG Protocol) has improved comparability, yet persistent cross-country differences in data quality, verification practices, system boundaries, and default factors generate non-trivial asymmetries that are central to CBAM implementation and compliance. Research on regulatory interaction under incomplete information (signals/beliefs, screening, mechanism design) clarifies how beliefs about private types shape policy and disclosure but seldom delivers closed-form border-tariff rules in oligopolistic product markets. Sectoral evidence for steel, chemicals, and cement documents high capital intensity, scale economies, and trade exposure that concentrate capacity in a few firms, consistent with Cournot-style oligopoly and non-negligible pass-through.

Against this background, the analysis embeds emission-information asymmetry in a two-country, two-firm Cournot setting and develops closed-form optimal CBAM tariffs under symmetric and asymmetric information, tracing how mismeasurement propagates to outputs, prices, profits, emissions, and welfare. This framework complements computable/applied assessments by providing a tractable basis that links MRV-driven data transparency to tariff design in oligopolistic EITE markets. The next subsection sets out the modeling assumptions.

To analyze the effects of carbon tariffs under conditions of emission information asymmetry, and in order to ensure that the mathematical model is both theoretically tractable and practically insightful, this section introduces several necessary simplifications and abstractions regarding key variables such as carbon emission costs and carbon tariffs. The model is constructed based on the following assumptions to enhance its analytical clarity and explanatory power.

Assumption 1: The carbon tariff game involves two countries: Country 1, which is subject to the carbon tariff, and Country 2, representing the European Union, which imposes the carbon tariff. The two countries differ in their carbon emission costs, with the tariff-imposing country (Country 2) facing relatively higher carbon costs. As a result, Country 2 levies a carbon tariff on imports from Country 1, where carbon costs are comparatively lower. The carbon tariff rate is denoted by $\mathit{T}(\mathit{T}>\mathbf{0})$.

Assumption 2: There are two types of electromechanical enterprises involved in the carbon tariff game. Firm 1 is located in the tariffed country (Country 1), and Firm 2 is located in the tariff-imposing country (Country 2). Both firms produce homogeneous electromechanical products. The per-unit carbon emissions of Firm 1 and Firm 2 are denoted by ${\mathit{A}}_{\mathbf{1}}$ and ${\mathit{A}}_{\mathbf{2}}$, respectively. The corresponding unit production costs are ${\mathit{B}}_{\mathbf{1}}$ and ${\mathit{B}}_{\mathbf{2}}$, and the unit carbon emission costs are ${\mathit{C}}_{\mathbf{1}}$ and ${\mathit{C}}_{\mathbf{2}}$, with ${\mathit{C}}_{\mathbf{1}}<{\mathit{C}}_{\mathbf{2}}$.

Assumption 3: The carbon tariff-imposing country (Country 2) imports electromechanical products from the tariffed country (Country 1). The output supplied to the market in Country 2 by Firm 1 and Firm 2 is denoted by ${\mathit{Q}}_{\mathbf{1}}$ and ${\mathit{Q}}_{\mathbf{2}}$, respectively. The inverse demand function in this market is given by $\mathit{P}=\mathit{a}-({\mathit{Q}}_{\mathbf{1}}+{\mathit{Q}}_{\mathbf{2}})$, where $\mathit{P}$ denotes the market price and $\mathit{a}$ is a positive constant representing market potential.

The definitions of all model parameters are detailed in

Table 1. Model parameters and their meanings.

Parameter	Definition
$T$	Carbon tariff rate
$A_1$	CO2 emissions per unit product of the electromechanical enterprise in the carbon tariff-targeted country
$A_2$	CO2 emissions per unit product of the electromechanical enterprise in the carbon tariff-imposing country
$B_1$	Production cost per unit product of the electromechanical enterprise in the carbon tariff-targeted country
$B_2$	Production cost per unit product of the electromechanical enterprise in the carbon tariff-imposing country
$C_1$	Carbon cost per unit of CO2 emitted by the electromechanical enterprise in the carbon tariff-targeted country
$C_2$	Carbon cost per unit of CO2 emitted by the electromechanical enterprise in the carbon tariff-imposing country
$Q_1$	Product supply quantity of the electromechanical enterprise in the carbon tariff-targeted country
$Q_2$	Product supply quantity of the electromechanical enterprise in the carbon tariff-imposing country

. Based on the above setup, this study further explores the strategic interactions under both symmetric and asymmetric information conditions, with a focus on the role of carbon emissions disclosure in shaping equilibrium outcomes.

2.2. Scenario 1: Game Under Asymmetric Information

In this scenario, the carbon tariff-imposed country (Country 1) and its domestic electromechanical firm (Firm 1) possess full knowledge of their carbon emissions data, which constitutes an information advantage. In contrast, the carbon tariff-imposing country (Country 2) and its domestic firm (Firm 2) lack timely access to this information and must rely on historical data or estimations to infer emissions levels. It is noteworthy that the carbon emissions data of Firm 2, located in the tariff-imposing country, is fully transparent and publicly accessible, allowing all stakeholders to readily obtain the relevant information.

Based on the modeling framework established in Section 2.1, this study introduces an additional assumption: the tariff-imposing country and its domestic firm estimate the per-unit carbon emissions of the exporting country’s product, denoted as ${\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}$. Under this condition, the two firms engage in a static Cournot competition under an environment of asymmetric information. Their respective profit functions are represented by ${\mathit{\pi }}_{\mathbf{1}}$ and ${\mathit{\pi }}_{\mathbf{2}}$.

Since the carbon tariff-imposing country (Country 2) and its domestic firm (Firm 2) cannot obtain real-time access to the carbon emission information of the exporting firm (Firm 1), they are only able to determine Firm 2’s output level ${\mathit{Q}}_{\mathbf{2}}$ and its corresponding maximum profit ${\mathit{\pi }}_{\mathbf{2}}$ by solving the Nash equilibrium of the two-player game. Under asymmetric information, Firm 2 must form an estimate of Firm 1’s output and profit, denoted by ${\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}$ and ${\mathit{\pi }}_{\mathbf{1}}^{\mathbf{\prime }}$, respectively. Based on this, the following equations can be derived.

$${}_{{\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}}{}^{\mathit{M}\mathit{A}\mathit{X}}{\mathit{\pi }}_{\mathbf{1}}^{\mathbf{\prime }}=(\mathit{a}-{\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}-{\mathit{Q}}_{\mathbf{2}}){\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}-({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}){\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}$$

(1)

$${}_{{\mathit{Q}}_{\mathbf{2}}}{}^{\mathit{M}\mathit{A}\mathit{X}}{\mathit{\pi }}_{\mathbf{2}}=(\mathit{a}-{\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}-{\mathit{Q}}_{\mathbf{2}}){\mathit{Q}}_{\mathbf{2}}-({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}}){\mathit{Q}}_{\mathbf{2}}$$

(2)

Based on Equations (1) and (2), the Nash equilibrium solution to this problem can be further derived as follows:

$${\mathit{Q}}_{\mathbf{1}}^{\mathbf{\prime }}={\displaystyle \frac{\mathit{a}-\mathbf{2}({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})+({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}$$

(3)

$${\mathit{Q}}_{\mathbf{2}}={\displaystyle \frac{\mathit{a}+({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})-\mathbf{2}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}$$

(4)

Since Firm 1, located in the tariffed country, possesses complete information regarding both firms’ carbon emissions, its profit is denoted by ${\mathit{\pi }}_{\mathbf{1}}$, and its profit maximization objective is given by:

$${}_{{\mathit{Q}}_{\mathbf{1}}}{}^{\mathit{M}\mathit{A}\mathit{X}}{\mathit{\pi }}_{\mathbf{1}}=(\mathit{a}-{\mathit{Q}}_{\mathbf{1}}-{\mathit{Q}}_{\mathbf{2}}){\mathit{Q}}_{\mathbf{1}}-({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}){\mathit{Q}}_{\mathbf{1}}$$

(5)

By substituting the constraint in Equation (4) into Equation (5) and taking the derivative with respect to ${\mathit{Q}}_{\mathbf{1}}$, the actual output of Firm 1 can be obtained as follows:

$${\mathit{Q}}_{\mathbf{1}}={\displaystyle \frac{\mathit{a}-\mathbf{2}({\mathit{B}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})+\mathbf{2}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}-{\displaystyle \frac{\mathbf{3}{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}-{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}}{\mathbf{6}}}$$

(6)

The total output can be derived from the above equations as follows:

$$\mathit{Q}={\mathit{Q}}_{\mathbf{1}}+{\mathit{Q}}_{\mathbf{2}}={\displaystyle \frac{\mathbf{2}\mathit{a}-({\mathit{B}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})-({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}+{\displaystyle \frac{{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}-\mathbf{3}{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}}{\mathbf{6}}}$$

(7)

Accordingly, the market price of electromechanical products in the carbon tariff-imposing country can be derived as follows:

$$\mathit{P}={\displaystyle \frac{\mathit{a}+({\mathit{B}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})+({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}-{\displaystyle \frac{{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}-\mathbf{3}{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}}{\mathbf{6}}}$$

(8)

In the case of asymmetric information, the carbon emission intensity of enterprises in the carbon tariff-targeted country (Country 1) is not fully observable by the tariff-imposing country (Country 2). The latter cannot accurately obtain the true carbon emission data of foreign firms, leading to uncertainty in its carbon tariff determination.

Under such information asymmetry, both firms compete à la Cournot in quantities. The carbon tariff affects Firm 1’s effective marginal cost, while Firm 2 faces only its domestic carbon cost. The profit functions of both firms are therefore written as follows:

$${\mathit{\pi }}_{\mathbf{1}}={\left[{\displaystyle \frac{\mathbf{2}\mathit{a}-\mathbf{3}({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})-({\mathit{B}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})+\mathbf{2}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{6}}}\right]}^{\mathbf{2}}$$

(9)

$${\mathit{\pi }}_{\mathbf{2}}=\left[{\displaystyle \frac{\mathbf{2}\mathit{a}+\mathbf{2}({\mathit{B}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})-\mathbf{4}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})-{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}+\mathbf{3}{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}}{\mathbf{6}}}\right]\times \left[{\displaystyle \frac{\mathit{a}+({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}+\mathit{T}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }})-\mathbf{2}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}\right]$$

(10)

2.3. Scenario 2: Game Under Symmetric Information

This subsection examines the scenario in which the electromechanical manufacturer in the tariffed country (Firm 1) voluntarily discloses carbon emission data related to its production processes. This leads to full transparency of environmental information between the two competing firms, enabling all stakeholders to access relevant data in real time.

Building upon Section 2.1, it is further assumed that under the symmetric information setting, the profits of the two firms are denoted by ${\mathit{\pi }}_{\mathbf{1}}^{~}$ and ${\mathit{\pi }}_{\mathbf{2}}^{~}$, and their respective outputs of electromechanical products are represented by ${\mathit{Q}}_{\mathbf{1}}^{~}$ and ${\mathit{Q}}_{\mathbf{2}}^{~}$. Based on this, a theoretical model of duopolistic competition is constructed.

The optimal profit of the electromechanical firm located in the tariffed country (Firm 1) is given by:

$${}_{{\mathit{Q}}_{\mathbf{1}}^{~}}{}^{\mathit{M}\mathit{A}\mathit{X}}{\mathit{\pi }}_{\mathbf{1}}^{~}=(\mathit{a}-{\mathit{Q}}_{\mathbf{1}}^{~}-{\mathit{Q}}_{\mathbf{2}}^{~}){\mathit{Q}}_{\mathbf{1}}^{~}-({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}}){\mathit{Q}}_{\mathbf{1}}^{~}$$

(11)

The optimal profit of the electromechanical firm located in the tariff-imposing country (Firm 2) is given by:

$${}_{{\mathit{Q}}_{\mathbf{2}}^{~}}{}^{\mathit{M}\mathit{A}\mathit{X}}{\mathit{\pi }}_{\mathbf{2}}^{~}=(\mathit{a}-{\mathit{Q}}_{\mathbf{1}}^{~}-{\mathit{Q}}_{\mathbf{2}}^{~}){\mathit{Q}}_{\mathbf{2}}^{~}-({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}}){\mathit{Q}}_{\mathbf{2}}^{~}$$

(12)

The Nash equilibrium outputs of Firm 1 and Firm 2 are:

$${\mathit{Q}}_{\mathbf{1}}^{~}={\displaystyle \frac{\mathit{a}+({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})-\mathbf{2}({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}})}{\mathbf{3}}}$$

(13)

$${\mathit{Q}}_{\mathbf{2}}^{~}={\displaystyle \frac{\mathit{a}-\mathbf{2}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})+({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}})}{\mathbf{3}}}$$

(14)

Accordingly, the total quantity supplied by Firm 1 and Firm 2 can be derived as:

$${\mathit{Q}}^{~}={\mathit{Q}}_{\mathbf{1}}^{~}+{\mathit{Q}}_{\mathbf{2}}^{~}={\displaystyle \frac{\mathbf{2}\mathit{a}-({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})-({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}})}{\mathbf{3}}}$$

(15)

The market price of electromechanical products in the carbon tariff-imposing country is:

$${\mathit{P}}^{~}={\displaystyle \frac{\mathit{a}+({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})+({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}})}{\mathbf{3}}}$$

(16)

Accordingly, the profits of Firm 1 in the tariffed country and Firm 2 in the tariff-imposing country are:

$${\mathit{\pi }}_{\mathbf{1}}^{~}={\left[{\displaystyle \frac{\mathit{a}-\mathbf{2}({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}})+({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}\right]}^{\mathbf{2}}$$

(17)

$${\mathit{\pi }}_{\mathbf{2}}^{~}={\left[{\displaystyle \frac{\mathit{a}+({\mathit{B}}_{\mathbf{1}}+{\mathit{C}}_{\mathbf{1}}{\mathit{A}}_{\mathbf{1}}+\mathit{T}{\mathit{A}}_{\mathbf{1}})-\mathbf{2}({\mathit{B}}_{\mathbf{2}}+{\mathit{C}}_{\mathbf{2}}{\mathit{A}}_{\mathbf{2}})}{\mathbf{3}}}\right]}^{\mathbf{2}}$$

(18)

2.4. Analysis of the Impact of Information Disclosure

Building on the analytical foundations established in Section 2.2 and Section 2.3, this section provides an in-depth examination of how export-oriented firms, subject to carbon tariff regulations, adjust the level of transparency in their greenhouse gas emissions disclosures, and how such adjustments influence various dimensions of their operational performance. Specifically, the analysis focuses on how changes in emissions information transparency affect key indicators such as production scale, operating profits, total greenhouse gas emissions, and market pricing dynamics.

Proposition 1.

If ${\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}<{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{\pi }}_{\mathbf{1}}>{\mathit{\pi }}_{\mathbf{1}}^{~},\mathit{I}\mathit{f}{\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}>{\mathit{A}}_{\mathbf{1}},$ then ${\mathit{\pi }}_{\mathbf{1}}<{\mathit{\pi }}_{\mathbf{1}}^{~}$.

Proof of Proposition 1.

Under asymmetric information, the profit of Firm 1 is given by:

$$\begin{array}{c}{\pi }_1={\left[{\displaystyle \frac{2a-3(B_1+C_1{A}_1+T{A}_1^{\prime })-(B_1+T{A}_1^{\prime }+C_1{A}_1^{\prime })+2(B_2+C_2{A}_2)}{6}}\right]}^2\\ ={\left[{\displaystyle \frac{a-2(B_1+C_1{A}_1+T{A}_1)+(B_2+C_2{A}_2)}{3}}+{\displaystyle \frac{(C_1+4T)(A_1-A_1^{\prime })}{6}}\right]}^2\end{array}$$

Under symmetric information, the profit of Firm 1 is:

$${\pi }_1^{~}={\left[{\displaystyle \frac{a-2(B_1+C_1{A}_1+T{A}_1)+(B_2+C_2{A}_2)}{3}}\right]}^2$$

It is evident that: If $A_1^{\prime }<A_1$, then ${\pi }_1>{\pi }_1^{~}$; if $A_1^{\prime }>A_1$, then ${\pi }_1<{\pi }_1^{~}$. This concludes the proof. □

Based on the conclusion of Proposition 1, if the carbon tariff-imposing country underestimates the true emission intensity of an exporting firm, the latter can exploit this information asymmetry by strategically withholding accurate carbon disclosures. This results in lower-than-appropriate tariff liabilities, enabling the firm to gain a cost advantage and earn profits above the competitive equilibrium level.

Conversely, if the imposing country overestimates the exporter’s emissions, the firm faces an inflated carbon tariff burden, eroding its profit margins and global competitiveness. To counter this, affected exporters may adopt a two-pronged strategy by systematically disclosing real-time emissions data from their production processes and seeking third-party verification from internationally recognized environmental assessment agencies [14,15]. This dual approach helps correct emission misjudgments and promotes a more equitable allocation of carbon tariff obligations.

Proposition 2.

If ${\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}<{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{Q}}_{\mathbf{1}}>{\mathit{Q}}_{\mathbf{1}}^{~}$ and ${\mathit{Q}}_{\mathbf{2}}<{\mathit{Q}}_{\mathbf{2}}^{~}$; if ${\mathit{A}}_{\mathbf{1}}^{\mathbf{\prime }}>{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{Q}}_{\mathbf{1}}<{\mathit{Q}}_{\mathbf{1}}^{~}$, ${\mathit{Q}}_{\mathbf{2}}>{\mathit{Q}}_{\mathbf{2}}^{~}$.

Proof of Proposition 2.

The differences in output levels of firms under the two information scenarios are given by:

$$\Delta Q_1=Q_1-Q_1^{~}={\displaystyle \frac{(C_1+4T)(A_1-A_1^{\prime })}{6}}$$

(19)

$$\Delta Q_2=Q_2-Q_2^{~}={\displaystyle \frac{(C_1+T)(A_1^{\prime }-A_1)}{3}}$$

(20)

When $A_1^{\prime }<A_1$, it is evident that:

$$\Delta Q_1=Q_1-Q_1^{~}={\displaystyle \frac{(C_1+4T)(A_1-A_1^{\prime })}{6}}>0$$

$$\Delta Q_2=Q_2-Q_2^{~}={\displaystyle \frac{(C_1+T)(A_1^{\prime }-A_1)}{3}}<0$$

That is, $Q_1>Q_1^{~}$ and $Q_2<Q_2^{~}$. Similarly, it can be proven that if $A_1^{\prime }>A_1$, then $Q_1<Q_1^{~}$ and $Q_2>Q_2^{~}$. This concludes the proof. □

Based on Proposition 2, under information asymmetry, deviations in carbon emission assessments by the tariff-imposing country can significantly reshape the production scales of both domestic and foreign electromechanical firms, thereby altering market competitiveness [16]. If the imposing country underestimates the actual carbon intensity of the exporting country’s firms, these exporters benefit from lower-than-deserved tariffs, gaining a cost advantage that enables them to expand output beyond the full-information equilibrium. In contrast, domestic firms facing relatively higher costs reduce their production.

Conversely, if carbon intensity is overestimated, exporters bear excessive tariffs, dampening their competitiveness and curbing production, while domestic firms capitalize on their relative advantage to expand output. These shifts distort market efficiency, heighten the risk of trade frictions, and threaten global supply chain stability. Thus, a transparent and scientifically robust carbon assessment framework is essential for ensuring fair competition and supporting green trade objectives.

To further explore the impact of information disclosure on carbon emission performance, we introduce two indicators: $\mathit{\lambda }$ and ${\mathit{\lambda }}^{~}$, representing the total carbon emissions generated by Firms 1 and 2 under asymmetric and symmetric information conditions, respectively. Specifically, $\mathit{\lambda }={\mathit{A}}_{\mathbf{1}}{\mathit{Q}}_{\mathbf{1}}+{\mathit{A}}_{\mathbf{2}}{\mathit{Q}}_{\mathbf{2}}$ and ${\mathit{\lambda }}^{~}={\mathit{A}}_{\mathbf{1}}{\mathit{Q}}_{\mathbf{1}}^{~}+{\mathit{A}}_{\mathbf{2}}{\mathit{Q}}_{\mathbf{2}}^{~}$. These indicators allow us to evaluate how deviations in carbon intensity assessment affect aggregate environmental outcomes. Based on this framework, we propose the following proposition.

Proposition 3.

When ${\mathit{A}}_{\mathbf{1}}>\mathbf{2}{\mathit{A}}_{\mathbf{2}}$, if ${\mathit{A}}_{\mathbf{1}}^{\prime }<{\mathit{A}}_{\mathbf{1}}$, then $\mathit{\lambda }>{\mathit{\lambda }}^{~}$; if ${\mathit{A}}_{\mathbf{1}}^{\prime }>{\mathit{A}}_{\mathbf{1}}$, then $\mathit{\lambda }<{\mathit{\lambda }}^{~}$.

Proof of Proposition 3.

The difference in total carbon emissions between the two information scenarios can be expressed as:

$$\begin{array}{cc}\hfill \Delta \lambda =\lambda -{\lambda }^{~}& =(A_1{Q}_1+A_2{Q}_2)-(A_1{Q}_1^{~}+A_2{Q}_2^{~})=A_1\Delta Q_1+A_2\Delta Q_2\hfill \\ & =(A_1-A_1^{\prime }){\displaystyle \frac{(C_1+4T)A_1-2(C_1+T)A_2}{6}}\hfill \end{array}$$

(21)

It is therefore evident that when condition $A_1>2A_2$ and condition $A_1^{\prime }<A_1$ are satisfied, condition $\Delta \lambda >0$ holds, implying $\lambda >{\lambda }^{~}$. Similarly, when condition $A_1>2A_2$ and condition $A_1^{\prime }>A_1$ are reversed, condition $\Delta \lambda <0$ is inverted, indicating $\lambda <{\lambda }^{~}$. This concludes the proof. □

Empirical evidence reveals substantial disparities in carbon emission efficiency between electromechanical enterprises in carbon tariff-imposing and exporting countries, with the latter often exhibiting significantly higher emissions per unit of output—largely due to technological gaps and energy structure differences [17,18].

Building on Proposition 3, under information asymmetry and when $A_1>2A_2$, an underestimation of exporters’ carbon intensity leads to artificially low tariffs, encouraging overproduction of carbon-intensive goods. Simultaneously, domestic firms may ease abatement efforts, resulting in increased total emissions.

Conversely, overestimation of exporters’ emissions raises their tariff burden, curbing high-emission production, while domestic firms gain competitive advantages and may invest more in clean technologies—ultimately reducing overall emissions. These findings highlight that carbon tariff effectiveness depends not only on policy design, but also critically on the accuracy of emissions data.

Proposition 4.

When ${\mathit{C}}_{\mathbf{1}}<\mathbf{2}\mathit{T}/\mathbf{3}$ and ${\mathit{A}}_{\mathbf{1}}^{\prime }<{\mathit{A}}_{\mathbf{1}}$, then $\mathit{P}>{\mathit{P}}^{~}$; when ${\mathit{C}}_{\mathbf{1}}<\mathbf{2}\mathit{T}/\mathbf{3}$ and ${\mathit{A}}_{\mathbf{1}}^{\prime }>{\mathit{A}}_{\mathbf{1}}$, then $\mathit{P}<{\mathit{P}}^{~}$.

Proof of Proposition 4.

Under the two scenarios, the price differential for electromechanical products is given by:

$$\Delta P=P-P^{~}=(A_1-A_1^{\prime })(T/3-C_1/2)$$

(22)

Clearly, when $C_1<2T/3\mathrm{and}{A}_1^{\prime }<A_1$, then $\Delta P>0$, implying $P>P^{~};\mathrm{converely},\mathrm{when}{C}_1<2T/3$ and $A_1^{\prime }>A_1,\mathrm{then}\Delta P<0,\mathrm{implying}P<P^{~}$. This concludes the proof. □

In the implementation of carbon tariff policies, many exporting countries face minimal or no domestic carbon pricing, making the inequality condition in Proposition 4 frequently applicable. When the tariff-imposing country underestimates the actual carbon intensity of imported electromechanical products, exporters gain unintended price advantages due to lower tariff costs. However, in response to consumer preference for low-carbon products and regulatory risk, domestic firms may raise prices, thereby pushing up market prices.

Conversely, overestimation of exporters’ emissions leads to higher tariff burdens, forcing them to lower export prices to maintain competitiveness, which depresses market prices. This pricing dynamic highlights the critical role of information asymmetry in shaping trade outcomes and reveals potential distortions in international competition. Thus, accurate and transparent carbon emissions assessment is essential to balance market fairness with environmental objectives [19].

Proposition 5.

When ${\mathit{C}}_{\mathbf{1}}<\mathbf{2}\mathit{T}$ and ${\mathit{A}}_{\mathbf{1}}^{\prime }<{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{\pi }}_{\mathbf{2}}<{\mathit{\pi }}_{\mathbf{2}}^{~}$; when ${\mathit{C}}_{\mathbf{1}}<\mathbf{2}\mathit{T}$ and ${\mathit{A}}_{\mathbf{1}}^{\prime }>{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{\pi }}_{\mathbf{2}}>{\mathit{\pi }}_{\mathbf{2}}^{~}$.

Proof of Proposition 5.

Under the two scenarios, the profit difference in the electromechanical enterprise in the tariff-imposing country is:

$$\Delta {\pi }_2={\pi }_2-{\pi }_2^{~}$$

(23)

Let:

$$E=\left[{\displaystyle \frac{2a-(B_1+C_1{A}_1^{\prime }+T{A}_1^{\prime })-4(B_2+C_2{A}_2)+3(B_1+C_1{A}_1+T{A}_1^{\prime })}{6}}\right]$$

(24)

$$H={\displaystyle \frac{a+(B_1+C_1{A}_1^{\prime }+T{A}_1^{\prime })-2(B_2+C_2{A}_2)}{3}}$$

(25)

$$S={\displaystyle \frac{a+(B_1+C_1{A}_1+T{A}_1)-2(B_2+C_2{A}_2)}{3}}$$

(26)

Then:

$$\Delta {\pi }_2={\pi }_2-{\pi }_2^{~}=EH-S^2$$

(27)

When $A_1^{\prime }<A_1$, it follows that $\mathrm{S}>\mathrm{H}\ge 0$. Furthermore, when $C_1<2T$ and $A_1^{\prime }<A_1$, we have: $E-S={\displaystyle \frac{(A_1-A_1^{\prime })(C_1-2T)}{6}}<0$. Thus, $S>E\ge 0$, implying $S^2>EH$, and hence $\Delta {\pi }_2>0$, i.e., ${\pi }_2<{\pi }_2^{~}$ Similarly, it can be shown that when $C_1<2T\mathrm{and}{A}_1^{\prime }>A_1,\mathrm{then}{\pi }_2>{\pi }_2^{*}$. This concludes the proof. □

Given that the condition $C_1<2T$ is easily met in practice, Proposition 5 suggests that when the importing country underestimates the carbon intensity of electromechanical products from the exporting country, the latter’s firms benefit from reduced tariff burdens. This cost advantage enhances their price competitiveness, allowing them to capture greater market share at the expense of domestic firms in the importing country.

Conversely, when carbon intensity is overestimated, exporters face excessive carbon costs, weakening their competitiveness. Domestic firms, in turn, gain from the relative cost advantage, boosting their market share and profitability. This dynamic underscores how the accuracy of emissions assessments critically shapes the economic outcomes of carbon tariff policies, and how information asymmetry can distort market competition. Hence, ensuring transparent and accurate carbon data is essential for both fair competition and the effectiveness of carbon border adjustment mechanisms [20].

3. Dynamic Carbon Tariff Game Model and Determination of the Optimal Tax Rate

The previous section analyzed how asymmetric carbon emission information from exporters influences firm profits, production scale, total emissions, and market prices under a fixed carbon tariff. Building on that framework, this section examines how the carbon tariff-imposing country determines the optimal tariff rate, comparing outcomes under perfect and asymmetric information to evaluate the impact on both sides of the game.

The analysis assumes that the tariff-imposing country seeks to optimize multiple objectives—not just protecting domestic industry but also maximizing social welfare, environmental outcomes, and fiscal revenue. Accordingly, the tariff rate is set through a comprehensive assessment of its effects on domestic firm competitiveness, consumer welfare, carbon externalities, and government income. The optimal rate balances these competing goals to maximize policy effectiveness under complex economic and environmental constraints.

3.1. Scenario 1: Dynamic Game Under Information Asymmetry

This study focuses on the decision-making mechanism for determining the optimal carbon tariff rate under conditions of asymmetric carbon emission information from electromechanical enterprises in the exporting country. The model adopts a two-stage dynamic game framework and utilizes backward induction to derive analytical solutions.

In the first stage of the game, the government of the tariff-imposing country sets the specific level of the carbon tariff. In the second stage, electromechanical firms from both countries engage in Cournot competition in the importing market after observing the announced tariff rate, while determining their respective supply quantities under asymmetric information conditions. The solution method for the second-stage equilibrium is consistent with that described in Section 2.2. In the first stage, however, the tariff-imposing government solves a specific optimization problem to achieve its policy objectives, as follows:

$${}_{T\ge 0}{}^{MAX}{\theta }_2={\pi }_2+{(Q_1+Q_2)}^2/2+T{A}_1^{\prime }{Q}_1^{\prime }$$

(28)

In this model, the objective function of the carbon tariff-imposing country comprises three key components. First is the effectiveness of the carbon tariff under information asymmetry, denoted by the utility function ${\theta }_2$. Second, the term ${(Q_1+Q_2)}^2/2$ reflects the policymaker’s valuation of domestic consumer surplus. Finally, the term $T{A}_1^{\prime }{Q}_1^{\prime }$ captures government fiscal revenue generated through the carbon tariff. Together, these three factors determine the policy preference and market intervention strategy of the importing country. Under this model, the optimal carbon tariff rate is given by:

$$T^{*}=(a-B_1-C_1{A}_1^{\prime })/3A_1^{\prime }$$

(29)

This value represents the optimal tariff level set by the importing country to fulfill its policy objectives under asymmetric information conditions. At this tariff rate, electromechanical firms from both the exporting and importing countries reach equilibrium output levels, denoted as $Q_1^{*}$ and $Q_2^{*}$, respectively. Simultaneously, the exporting country’s firms earn corresponding equilibrium profits ${\pi }_1^{*}$. These equilibrium outcomes reflect the combined effects of the carbon tariff policy on bilateral trade structures and firm-level operational performance.

$$Q_1^{*}=2a+(B_1+C_1{A}_1^{\prime })+6(B_2+C_2{A}_2)-9(B_1+C_1{A}_1)/18$$

(30)

$$Q_2^{*}=4a+2(B_1+C_1{A}_1^{\prime })-6(B_2+C_2{A}_2)/9$$

(31)

$${\mathsf{\pi }}_1^{*}={\left[2\mathrm{a}+({\mathrm{B}}_1+{\mathrm{C}}_1{\mathrm{A}}_1^{\prime })+6({\mathrm{B}}_2+{\mathrm{C}}_2{\mathrm{A}}_2)-9({\mathrm{B}}_1+{\mathrm{C}}_1{\mathrm{A}}_1)/18\right]}^2$$

(32)

3.2. Scenario 2: Dynamic Game Under Information Symmetry

Under conditions of information symmetry, determining the optimal carbon tariff rate for emissions from foreign electromechanical enterprises is a critical issue in the formulation of national environmental policy. This section constructs an optimization model to explore the mechanism for determining such an optimal tariff rate, as shown below:

$${}_{T^{~}}{}^{MAX}{\theta }_2^{~}={\pi }_2^{~}+{\left(Q_1^{~}{+Q}_2^{~}\right)}^2/2+T^{~}{A}_1{Q}_1^{~}$$

(33)

In this model, the objective function of the carbon tariff-imposing country consists of three key components. The first term, ${\theta }_2^{~}$, represents the utility derived under conditions of information symmetry. The second term, ${(Q_1^{~}+Q_2^{~})}^2/2$, reflects the policymaker’s evaluation of domestic consumer welfare. The final term, $T^{~}{A}_1{Q}_1^{~}$, captures the fiscal revenue obtained through the implementation of carbon tariffs. Together, these elements jointly determine the importing country’s policy choices and market interventions. Within this framework, the optimal carbon tariff rate is given by:

$$T^{~*}=(a-B_1-C_1{A}_1)/3A_1$$

(34)

This expression reflects the optimal tariff rate set by the importing country to fulfill its policy objectives under conditions of information symmetry. At this tariff level, electromechanical enterprises from both the exporting and importing countries reach an equilibrium output, denoted as $Q_1^{~*}$ and ${\mathrm{Q}}_2^{~\mathrm{*}}$, respectively. Simultaneously, the exporting country’s firms earn equilibrium profits ${\mathsf{\pi }}_1^{~\mathrm{*}}$. These equilibrium results embody the combined effects of carbon tariff policy on bilateral trade dynamics and firm performance.

$$Q_1^{~*}=a+3(B_2+C_2{A}_2)-4(B_1+C_1{A}_1)/9$$

(35)

$$Q_2^{~*}=4a-6(B_2+C_2{A}_2)+2(B_1+C_1{A}_1)/9$$

(36)

$${\pi }_1^{~\mathrm{*}}={\left[2a+3(B_2+C_2{A}_2)-4(B_1+C_1{A}_1)/9\right]}^2$$

(37)

3.3. Comparison of the Two Information Disclosure Scenarios

Proposition 6.

When ${\mathit{A}}_{\mathbf{1}}^{\prime }<{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{T}}^{*}>{\mathit{T}}^{~*}$, ${\mathit{Q}}_{\mathbf{1}}^{*}<{\mathit{Q}}_{\mathbf{1}}^{~*}$, ${\mathit{Q}}_{\mathbf{2}}^{*}<{\mathit{Q}}_{\mathbf{2}}^{~*}$, and ${\mathit{\pi }}_{\mathbf{1}}^{*}<{\mathit{\pi }}_{\mathbf{1}}^{~*}$; conversely, when ${\mathit{A}}_{\mathbf{1}}^{\prime }>{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{T}}^{*}<{\mathit{T}}^{~*}$, ${\mathit{Q}}_{\mathbf{1}}^{*}>{\mathit{Q}}_{\mathbf{1}}^{~*}$, ${\mathit{Q}}_{\mathbf{2}}^{*}>{\mathit{Q}}_{\mathbf{2}}^{~*}$, and ${\mathit{\pi }}_{\mathbf{1}}^{*}>{\mathit{\pi }}_{\mathbf{1}}^{~*}$.

Proof of Proposition 6.

Under these two scenarios, the difference in carbon tariff rates is given by:

$$\Delta T=T^{*}-T^{~*}=(a-B_1)(A_1-A_1^{\prime })/3A_1^{\prime }{A}_1>0$$

(38)

Difference in output for the exporting country’s electromechanical firm:

$$\Delta Q_1=Q_1^{*}-Q_1^{~*}=C_1(A_1^{\prime }-A_1)/18<0$$

(39)

Difference in output for the importing country’s electromechanical firm:

$$\Delta Q_2=Q_2^{*}-Q_2^{~*}={2C}_1(A_1^{\prime }-A_1)/9<0$$

(40)

Difference in profit for the exporting country’s electromechanical firm:

$$\Delta \pi ={\pi }_1^{*}-{\pi }_1^{~*}={\left(Q_1^{*}\right)}^2-{\left(Q_2^{~*}\right)}^2=(Q_1^{*}+Q_1^{~*})(Q_1^{*}-Q_1^{~*})<0$$

(41)

Clearly, if $A_1^{\prime }<A_1,\mathrm{then}{T}^{*}>T^{~*}$, $Q_1^{*}<Q_1^{~*}$, $Q_2^{*}<Q_2^{~*}$ and ${\pi }_1^{*}<{\pi }_1^{~*}.\mathrm{Similarly},\mathrm{if}{A}_1^{\prime }>A_1,\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}{T}^{*}<T^{~*},Q_1^{*}>Q_1^{~*},Q_2^{*}>Q_2^{~*},\mathrm{a}\mathrm{n}\mathrm{d}{\pi }_1^{*}>{\pi }_1^{~*}$. This concludes the proof. □

Building on Proposition 6, when the tariff-imposing country underestimates the carbon intensity of electromechanical products from the exporting country, exporters may conceal true emissions to gain a cost advantage. This misrepresentation leads to higher optimal carbon tariffs, increasing compliance burdens and reducing production scales in both countries. Conversely, overestimation of emissions may prompt the imposing country to lower tariffs, easing trade distortions and expanding output for both sides.

Furthermore, concealing emissions under underestimated assessments results in excessive tariffs and diminished exporter profits. However, when emissions are overestimated, strategic concealment can lead to tariff reductions, lower export costs, and improved profitability. This highlights the pivotal role of carbon data accuracy in shaping effective and fair carbon tariff policy under information asymmetry [21,22].

Let ${\lambda }^{*}$ and ${\lambda }^{~*}$ denote the total carbon emissions of Firms 1 and 2 under conditions of information asymmetry and symmetry, respectively. By definition: ${\lambda }^{*}=A_1{Q}_1^{*}+A_2{Q}_2^{*}$ and ${\lambda }^{~*}=A_1{Q}_1^{~*}+A_2{Q}_2^{~*}$. Based on this formulation, we propose the following:

Proposition 7.

If ${\mathit{A}}_{\mathbf{1}}^{\prime }<{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{\lambda }}^{*}<{\mathit{\lambda }}^{~*}$; conversely, if ${\mathit{A}}_{\mathbf{1}}^{\prime }>{\mathit{A}}_{\mathbf{1}}$, then ${\mathit{\lambda }}^{*}>{\mathit{\lambda }}^{~*}$.

Proof of Proposition 7.

Under the two scenarios, the difference in total carbon dioxide emissions is given by:

$$\Delta \lambda ={\lambda }^{*}-{\lambda }^{~*}=C_1(A_1^{\prime }-A_1)(A_1+4A_2)/18$$

(42)

Clearly, when $A_1^{\prime }<A_1, \Delta \lambda <0$, implying ${\lambda }^{*}<{\lambda }^{~*}$; conversely, when $A_1^{\prime }>A_1,\Delta \lambda >0$, implying ${\lambda }^{*}>{\lambda }^{~*}$. This concludes the proof. □

Proposition 7 highlights how information asymmetry in carbon intensity estimates can distort total emissions under carbon tariff regimes. When the tariff-imposing country underestimates the actual emissions of exported electromechanical goods, exporters are incentivized to conceal true emissions, lowering the reported total. Conversely, overestimation may prompt exporters to underreport, resulting in inflated unobserved emissions.

The model reveals a nuanced feedback mechanism: underestimation leads to lower tariffs, weakening the constraint on high-carbon production. While exporters may maintain output due to low carbon costs, domestic firms with higher costs reduce production, potentially offsetting emission gains. If emissions are overestimated, excessively high tariffs suppress exporters’ profits and investment in clean technology, while reducing domestic firms’ incentive to decarbonize—raising total emissions beyond levels under full information.

These findings underscore the critical role of data accuracy in determining the environmental efficacy of carbon tariffs. Inaccurate assessments—whether under- or overestimated—can both undermine intended climate goals and distort trade dynamics [23]. Thus, establishing a robust, internationally coordinated carbon accounting and verification system is essential. It helps mitigate carbon leakage, reduce market distortions, and ensure long-term alignment with global decarbonization objectives [24].

Building on the preceding proposition, this study further analyzes the relationship between the optimal carbon tariff and the carbon intensity coefficient. As shown in Equation (38), there is a negative correlation: when $A_1^{\prime }$ decreases, $\Delta T$ increases, and vice versa. Since $T^{*}$ is a fixed value, it also maintains a decreasing relationship with $A_1^{\prime }$. This suggests that under asymmetric information, lower estimated carbon intensity leads to higher optimal tariffs.

This outcome reflects the trade-offs faced by policymakers in balancing environmental goals with domestic economic stability. While higher tariffs can constrain carbon-intensive imports, they may also raise production costs and harm consumer welfare. When emissions are underestimated, tariffs may be raised to offset hidden environmental costs; if overestimated, excessive tariffs can trigger trade frictions, prompting downward adjustments to restore equilibrium.

Importantly, this inverse relationship exposes the limitations of carbon tariffs under information asymmetry. Misjudged emission levels not only distort price signals but risk decoupling tariffs from their intended role in climate governance. The findings highlight the urgency of establishing a transparent, internationally coordinated carbon accounting system to bridge information gaps and align carbon tariffs with global mitigation objectives.

Although the model presented here is theoretical and analytical in nature, its results have direct policy implications. For instance, the derived relationship between information bias and optimal tariff rates can be used by CBAM regulators to construct sensitivity scenarios for tariff design under different levels of data transparency. Moreover, the analytical framework can serve as a foundation for future numerical calibration once comparable firm-level emission datasets become available. In this way, the model bridges the gap between theoretical analysis and policy practice, offering a quantitative logic for decision-makers without requiring hypothetical data inputs at this stage.

Thus, rather than a case-specific simulation, this research provides a general analytical tool that policymakers and researchers can adapt for empirical extensions to different industrial contexts of CBAM implementation.

4. Conclusions and Recommendations

4.1. Conclusions

To balance climate change mitigation and industrial competitiveness, the European Union has introduced the CBAM, which imposes tariffs on carbon-intensive imports to address carbon leakage and safeguard the competitive position of domestic industries [25]. This study employs a game-theoretic framework under both symmetric and asymmetric information conditions to analyze how exporters’ carbon disclosure strategies influence policy design, market pricing, and cross-border emissions outcomes during CBAM implementation. The key findings are as follows:

First, under asymmetric information, electromechanical firms in the exporting country have strong incentives to conceal their carbon emissions data. When the importing country underestimates the true emission intensity of such firms, they can exploit this gap through strategic information hiding to gain excessive profits. Conversely, under an optimal tariff regime, if the importing country accurately estimates the firm’s actual carbon intensity, the firm’s ability to profit from concealment diminishes. Such information concealment leads to market resource misallocation and undermines the effectiveness of carbon tariff policies.

Second, information asymmetry significantly impacts the formulation of optimal carbon tariffs and the effectiveness of policy implementation. This study shows that when the importing country lacks accurate data on the actual emissions of electromechanical firms in the exporting country, the optimal tariff rate tends to exceed the level under full information. Overestimated tariffs not only compress exporting firms’ profit margins but may also cause a mismatch between policy objectives and real-world outcomes.

Third, carbon emission data asymmetry has systemic effects on both market participants and policy efficiency. These impacts mainly manifest in three aspects: (1) information bias on the part of the importing country when setting carbon tariffs affects the scientific basis of policy design; (2) information concealment by exporting firms poses moral hazard risks, weakening the environmental effectiveness of carbon tariffs and affecting firms’ profit margins and CO₂ emissions; (3) carbon data inaccuracy distorts the importing country’s price formation mechanism, disrupting efficient market resource allocation.

4.2. Recommendations

First, policymakers should establish transparent, standardized, and internationally recognized carbon accounting mechanisms. This includes promoting third-party verification, improving the interoperability of emissions data, and advancing international cooperation to ensure that carbon intensity assessments are accurate, consistent, and comparable across countries. Such efforts would directly address the root of information asymmetry in carbon border adjustment implementation [26,27]. In practical terms, regulatory bodies could develop a unified digital reporting system for CBAM-related trade data, coupled with automated cross-checking tools to prevent misreporting. This would ensure that emission information asymmetry is mitigated through verifiable data exchange between exporting and importing authorities.

Second, it is essential to design incentive-compatible mechanisms that encourage exporters to truthfully disclose their carbon emissions. By linking carbon tariffs more directly to verified emission data rather than relying on estimated benchmarks, authorities can reduce the profitability of concealment strategies. This approach enhances fairness and discourages strategic misreporting, thereby improving the environmental effectiveness of the policy [7,28]. For instance, tariff discounts or certification credits could be offered to exporters whose emission data are independently verified and publicly disclosed. This creates a market-based incentive that transforms transparency into a competitive advantage rather than a compliance burden.

Third, the determination of carbon tariff rates should carefully balance environmental objectives with trade competitiveness and consumer welfare. Policymakers are advised to adopt dynamic adjustment frameworks that can respond flexibly to changes in emissions data, production structures, and market conditions. This would prevent excessive carbon cost burdens, minimize trade frictions, and ensure that CBAM remains adaptive and effective in achieving both climate and economic goals [29,30]. Practically, this implies establishing a periodic tariff review mechanism—for example, updating CBAM tariff coefficients annually based on verified emission trends and trade elasticity indicators. Such adaptive calibration ensures that tariff policy remains responsive to evolving environmental and economic realities without relying on speculative simulations.

4.3. Limitations and Future Research Directions

This study develops a theoretical framework for analyzing carbon tariffs under conditions of information asymmetry, offering insights into their effects on firm behavior, emissions, and market outcomes. However, several limitations merit further exploration.

First, the two-country, two-firm abstraction abstracts from multi-country, multi-sector heterogeneity and networked supply chains. Extending the framework to a modular or general-equilibrium environment with input–output linkages would enhance external validity and allow heterogeneous MRV regimes to shape incidence along global value chains.

Second, the paper adopts a binary treatment of information—perfect symmetry versus asymmetry—whereas disclosure in practice is partial and probabilistic. A natural extension is to endogenize disclosure through signaling or Bayesian learning, with verified MRV and third-party certification reducing information noise and incentive-compatible schemes aligning tariffs with firm-level verified intensities rather than defaults. This would formalize the transparency mechanisms discussed in the recommendations and quantify their impact on misreporting, pass-through, and welfare.

Third, this study prioritizes a rigorous analytical framework, positioning numerical simulation as a subsequent phase. At this stage, simulations based on hypothetical data were deferred to avoid findings with limited representativeness. The current framework is, however, structured for future quantitative extension once systematic data becomes available, including parametric calibration, Monte Carlo sensitivity analyses, and dynamic simulations to assess policy feedback and firm behavior.

Finally, policy parameters are treated as fixed. Future work can analyze dynamic or adaptive tariff rules with regulatory feedback or learning, e.g., a periodic review mechanism that updates CBAM coefficients in light of verified emissions trends and trade-elasticity indicators. Such rules would operationalize the paper’s guidance on balancing environmental stringency with competitiveness and consumer welfare, while keeping the framework portable across sectors and data environments.

Addressing these limitations would not only refine the model’s predictive power but also provide more rigorous theoretical and empirical support for designing CBAMs that balance cross-border trade fairness with global energy transition goals—key priorities for both climate policy and energy sector development.