ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E24-2

Agreements on product standards
in a three-country model of international oligopoly
byAkihiko Yanase
Hiroshi Kurata
Yaqiong Lin

May 2024

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Agreements on product standards in a three-country model of international
oligopoly
Akihiko Yanasea Hiroshi Kuratab Yaqiong Linca, c

Nagoya Universityb

Tohoku Gakuin University

Abstract
This study extends the comparative institutional analysis of agreements on product standards developed by
Costinot (2008) to a three-country world, in which there are two member countries of an agreement on standards
and a nonmember country. We examine the comparative performance of two principles: national treatment (NT)and mutual recognition (MR). Assuming an international oligopoly with the traded goods generating consumption
externalities, we show that member countries prefer MR to NT for low externality levels and NT to MR for highexternality levels. Further, nonmember countries never prefer MR to NT. We also discuss whether a bilateralagreement on standards can be a building or stumbling block to a multilateral agreement by all three countries.
Keywords: product standards, national treatment, mutual recognition, consumption externality, domestic policy

aFaculty of Economics, Nagoya University. Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan. E-mail:yanase@soec.nagoya-u.ac.jp
bFaculty of Economics, Tohoku Gakuin University. 1-3-1 Tsuchitoi, Aoba-ku, Sendai 980-8511, Japan. E- mail:hkurata@mail.tohoku-gakuin.ac.jp
cGraduate School of Economics, Nagoya University. Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan. E-mail:linyaqiong2018@gmail.com

11 Introduction
Tariffs have been considered the main barriers to trade for a long time. For example, before the establishment of
the General Agreement on Tariffs and Trade (GATT) in 1948, the average world tariff was around 40% (Bown
and Irwin, 2015). However, the average applied tariff has been reduced to a sufficiently low level, that is, below
2.7%,1 through the efforts of the World Trade Organization (WTO) and GATT and by increasing regional trade
agreements (RTAs) and preferential trade agreements (PTAs), as claimed by Pascal Lamy, the Director-Generalof the WTO (2005–2013).2 Therefore, tariffs are no longer the main barriers to trade.
However, global integration is far from complete. The existence of various non-tariff barriers (NTBs) has
become a new issue impeding global free trade. Among all NTBs, product standards are regulatory instruments
widely used to protect safety and environmental quality, which might restrict imports or exports; some examples
are vehicle emissions and safety standards, restrictions on pesticide residues in agricultural goods, regulations onfood additives, and safety standards for electrical products. If countries implement different product standards
between domestic and imported goods arbitrarily, this can lead to trade disputes and even protectionism. Empiricalanalyses have shown that differing product standards have significant negative effects on trade. For example,
country-specific product standards reduce the average wages of exporting firms (Sánchez et al., 2008), decrease
the exports of developing countries (Disdier et al., 2008), cause diseconomies of scale, and affect decisions to enter
export markets (Chen et al., 2006). Wilson et al. (2002) provide evidence of heterogenous environmental
regulations among countries having negatively affected trade.
Conversely, reasonable and coordinated product standards, such as harmonized standards, can promote tradeflows, with many studies providing evidence of this effect. According to the literature, harmonized standards lower

1

2

The data are from the World Bank and can be accessed at https://data.worldbank.org/indicator/TM.TAX.MRCH.WM.AR.ZS

On July 16, 2012, Lamy made a speech titled “The universe of non-tariff measures has changed.”2the information asymmetries between firms and allow for a more efficient organization of inter-firm trade (Grajek,
2004), reduce country-specific adaptation costs and contribute to global trade growth (Schmidt and Steingress,2022), increase partner country export variety (Shepherd, 2007), and positively pull foreign direct investment andpush trade in developing nations (Clougherty and Grajek, 2008). Chen and Mattoo (2008), Baller (2007), Markand Bruno (2004), and Vancauteren and Weisbers (2011) show that, under mutual recognition (MR), regulation
harmonization could lead to more trade among member countries (e.g., intra-European Union [EU] trade).
For international organizations, imposing harmonized standards will prevent conflicts among countries.
However, it is not feasible to achieve harmonized standards considering the huge costs involved. As such, theWTO, EU, and RTAs have committed to two principles to solve the problem of countries’ arbitrary use of productstandards: national treatment (NT) and MR. The NT principle requires that the member countries of the agreement
do not apply discriminatory treatment to imported and domestic products or services, at least after the foreign goods
have entered the market. Some RTAs, such as the Comprehensive and Progressive Agreement for Trans-PacificPartnership (CPTPP), adopt the NT principle. The MR principle requires the member countries of an agreement
to mutually approve the results of the regulatory conditions implemented by other members as equivalent to theresults of those they have executed. The EU and the PTAs formed by it adopting the MR principle.
To explain these different approaches to standards agreements adopted by the WTO and EU, Costinot (2008)
analyzes the comparative performance of the two principles and finds that NT should be preferred over MR when
the amount of trade in goods characterized by high externality levels is large. Geng (2019) extends Costinot’s(2008) analysis with heterogeneous preferences toward positive and negative externalities and shows that NT isrelatively more welfare-enhancing than MR for countries with dissimilar preferences. These findings explain why
the WTO, CPTPP, and EU choose different types of standards agreements. Note that these studies compare MR
and NT only for bilateral agreements. However, multilateral agreements are now prevalent, and many bilateralagreements extend to multilateral ones. Accordingly, this study compares the performances of NT and MR
principles in multilateral agreements and analyzes whether bilateral agreements lead to multilateral ones.

3

No studies have hitherto compared the performance of two regimes in multilateral trade agreements. However,this issue is not only of practical significance for the real economy but also has theoretical implications. Most pasteconomic analyses have focused on the role of the NT principle in bilateral agreements. For example, Gulati andRoy (2008) and Geng (2022) analyze the optimal policy settings of tariff, non-tariff measures, and domestic
instruments. Ferrara et al. (2019) compare the effects of discriminating and non-discriminating tariffs on theenvironment. Further, Battigalli and Maggi (2003) and Bagwell and Staiger (2001b) justify whether the rule of NT
is equipped to handle disputes. Staiger and Sykes (2011) verify whether there are excessive non-discriminatory
regulations under the WTO’s legal framework. Meanwhile, Mei (2018) assesses which of the non-discriminatory
and harmonization standards could lead to international efficiency. Bagwell and Staiger (2001a) discuss how NT
cooperates with the most favored-nation-principle. Finally, Ederington (2001) analyzes how to deal with domestic
regulatory policies when considering trade policies.
A few studies focus on NT and MR simultaneously. Costinot (2008) and Geng (2019) compare theperformance of NT with that of MR. Further, Grossman et al. (2021) analyze how to coordinate countries’
regulatory policies under NT and MR. While the above studies consider bilateral agreements, some studies use athree-country model to analyze the effects of endogenous product standards in multilateral agreements (Takaradaet al., 2020; Kawabata and Takarada, 2021; Yanase and Kurata, 2022). However, they only focus on the NT
principle. Therefore, the literature fails to identify the clear implications of product standards under multilateralagreements and the comparative performance of the NT and MR principles. This study thus aims to cover this gap
in the literature.
Specifically, we extend Costinot’s (2008) model with negative externalities to a three-country model. Our
three-country framework discusses whether bilateral agreements can be a building or stumbling block tomultilateral agreements under the respective regimes. We find that, if the level of externalities is in a specific range,
multilateral agreements on standards can be achieved via bilateral agreements, irrespective of whether theagreement is based on NT or MR. However, this building block outcome is only a small subset of all possible4

outcomes; otherwise, the bilateral agreements of member and nonmember countries will block a multilateralagreement on standards.
Following Ferrara et al.’s (2019) assumption, we assume that the member countries of a bilateral agreement on
standards can choose discriminatory standards for the imported goods produced by a nonmember country. One
may argue that WTO member countries are prohibited from using regulatory policies to discriminate against
foreign producers. Therefore, the assumption that member countries can implement standard policies in a
discriminatory manner is not realistic. However, based on the following considerations, the assumption of
discriminatory regulations is reasonable. First, GATT Article XX presents potential exceptions, outlining cases inwhich members can breach the general WTO principles, particularly regarding health and the environment. Ferrara
et al. (2019) adopt discriminatory regulations to examine the role of NT and consider prominent Article XX
exceptions when goods are vertically differentiated and generate consumption externalities. Second, GATT Article
XXIV allows the formation of a PTA, provided that the members of that agreement do not impose higher or more
restrictive trade barriers on nonmembers. Therefore, as long as the heterogeneous standards among members andnonmembers of a PTA do not lead to higher or more restrictive trade barriers for nonmembers, this assumption
does not violate the WTO rule.
International law scholars highlight the limitations of strictly extending the WTO rule to issues relating to NTBs.
For example, Hoekman and Mavroidis (2015) explain why, in a world where tariffs become gradually obsolete
and markets are being segmented through NTBs, it is unrealistic to expect deep integration to occur at the WTO
level. Mavroidis (2015) also argues that non-discrimination is ill-equipped to deal effectively with regulatory
barriers in a near-tariff-free world. Considering these arguments, we assume that GATT Article XXIV can beapplied to the “deep” integration considered in this study.
The remainder of this paper is organized as follows. In Section 2, we set up our three-country model and derive
the policy game equilibrium without any agreements on standards. Section 3 considers bilateral agreements andderives the policy game equilibria for the respective institutional arrangements—NT and MR. We also examine5the welfare effects of bilateral agreements on member and nonmember countries. In Section 4, we derive theoutcomes when all three countries conclude multilateral agreements, while Section 5 discusses whether bilateralagreements can be extended to multilateral ones. Section 6 summarizes the study, and Section 7 concludes thepaper.

2 The Model
We consider three countries, denoted by A, B, and C, each respectively having one firm denoted by a, b, and c that
produces a homogeneous product. All countries share the same preferences and technologies. Following Costinot(2008), firms can produce two types of products: H (high pollution) type, which incurs zero-unit production cost
but whose consumption generates 𝜃 > 0 units of pollution, and L (low pollution) type, whose unit cost is 𝑐 >0 and whose consumption generates no pollution. We consider a mass of consumers, each buying at most one
unit of a product, and they are indifferent between the two types of products. Pollution damage occurs at the locationof consumption, and there is no spillover of pollution damage across countries.
Consumers are heterogeneous concerning their consumption benefits, and the utility of type 𝜈 ∈ [0,1] consumer
living in country J is given by𝑢(𝑣) = 2𝑣 − 𝑝! − 𝜙!
−𝜙 !

if 𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 buys either version,
if 𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 buys nothing,(1)

𝐽 = 𝐴, 𝐵, 𝐶, where 𝜈 is uniformly distributed with support [0, 1]; 𝑝 is the price of the product; and 𝜙 ! isthe pollution damage in country 𝐽. Denoting firm 𝑘’s sales in country 𝐽 by 𝑞"! (𝑘 = 𝑎, 𝑏, 𝑐; 𝐽 = 𝐴, 𝐵, 𝐶), thepollution damage in country J is represented by 𝜙 ! = ∑"#$,&,' 𝜃"! 𝑞"! , where 𝜃"! ∈ {0, 𝜃}. As consumers with𝜈 ≥ 𝑝 will buy the product and pollution damage is a pure externality, consumers’ utility maximization behavior
derives the inverse demand as 𝑃(𝑄 ! ) = 1 − 𝑄 ! , 𝐽 = 𝐴, 𝐵, 𝐶, where 𝑄 ! denotes consumption in country J andis equal to ∑"#$,&,' 𝑞"! .
6

We assume that the markets are segmented and that the three firms compete in quantity in each country’s
market. Assuming no tariffs or transport costs, we define firm 𝑘’s profit earned in country 𝐽’s market (𝑘 =𝑎, 𝑏, 𝑐; 𝐽 = 𝐴, 𝐵, 𝐶) as
𝜋"! = \𝑃 ! (𝑄 ! ) − 𝑐"! ]𝑞"! = ^1 − 𝑄 ! − 𝑐"! _𝑞"! ,(2)

where 𝑐"! ∈ {0, 𝑐 } denotes the unit production cost of the good produced by firm 𝑘 and consumed in country
𝐽.
Country 𝐽’s government can regulate its market by setting standards 𝜎"! ∈ {𝐻, 𝐿} for each of firm 𝑘’s
products (𝑘 = 𝑎, 𝑏, 𝑐), and each firm can sell in country 𝐽’s market if and only if its product version satisfies theminimum quality standard. That is, if 𝜎"! = 𝐻, firm 𝑘 can sell both the 𝐻 and 𝐿 types (i.e., there is no
regulation), but it chooses to produce and sell 𝐻 type because the unit cost is zero; by contrast, if 𝜎"! = 𝐿, firm𝑗 must produce and sell the 𝐿 type product.
The following two-stage game represents our model. In the first stage, the government of each country sets
product standards for each good. In the second stage, given the standards of the respective products, firms engage
in Cournot competition in each country’s market. We solve the game by backward induction to derive the subgame
perfect Nash equilibrium.

2.1 Cournot–Nash equilibrium
In stage 2, given the standards policy in the respective countries, the firms play the Cournot game in each country’s
market. In country 𝐽’s market, firm k chooses 𝑞"! to maximize (2), taking 𝑞"! , 𝑖 ≠ 𝑘 as given. From the firstorder conditions for profit maximization, the Cournot equilibrium outputs can be obtained as 𝑞"! = (1 − 3𝑐"! +∑ 𝑐(! )/4, 𝑘, 𝑖 = 𝑎, 𝑏, 𝑐. The equilibrium sales and price in country J are then derived as 𝑄 ! = (3 −()"∑ 𝑐"! )/4 and 𝑃(𝑄 ! ) = (1 +"#$,&,'∑ 𝑐"! )/4, respectively.

"#$,&,'

7

Country 𝐽’s welfare is given by the sum of consumer surplus (inclusive of pollution damages) and the domestic
firm’s profits (from domestic sales and exports). From (1), consumer surplus can be written as 𝐶𝑆! =(𝑄 ! )* /2 − 𝜙 ! . As for the equilibrium profits, (2) can be rewritten as 𝜋"! = (𝑞"! )* in the Cournot–Nashequilibrium. Therefore, substituting the equilibrium outputs and sales into the expressions for consumer surplus
and firm profits, country 𝐽’s welfare can be represented as
𝑆𝑊 ! = 𝐶𝑆! + n

=

(01

∑

!"#,%,&

0*

'

'! )(

− ∑"∈$,&,' 𝜃"!

+#,,-,.

'𝜋!+'510'! 6∑)*! ')7+ ∑+#,,-,.

(510'+, 6∑)*! '), )(
58

.

(3)

Throughout this paper, we assume that there are no political factors that affect governments’ standards policies. As
such, we assume each government’s objective function is its national welfare, 𝑆𝑊 ! , 𝐽 = 𝐴, 𝐵, 𝐶 . We also
propose the following assumption.3
Assumption 1 𝑐 < 1/5.

2.2 Noncooperative policy equilibrium without agreements
As a benchmark for the subsequent analysis, we start with the situation in which governments noncooperatively
determine their standards without making any agreements among countries. In the absence of agreements onstandards, in stage 1, country J’s government chooses the standards for the products consumed in that country,(𝜎$! , 𝜎&! , 𝜎'! ), to maximize country J ’s social welfare, taking other countries’ standards, (𝜎$+ , 𝜎&+ , 𝜎'+ ), 𝐾 ≠ 𝐽,
as given. There are three regimes for each government to choose from: (i) full regulation (FR), under which 𝜎"! =3

It can be easily verified that, under Assumption 1, all firms choose positive export levels.

8

𝐿 for 𝑘 = 𝑎, 𝑏, 𝑐; (ii) no regulation (NR), under which 𝜎"! = 𝐻 for 𝑘 = 𝑎, 𝑏, 𝑐; and (iii) discrimination (D),under which 𝜎9! = 𝐻 and 𝜎"! = 𝐿 for 𝑘 ≠ 𝑗.4
Although governments seek to maximize their respective welfare, (3) indicates that export profits depend only
on other countries’ standards. This means that governments choose standards to maximize their respective
domestic component of social welfare, which is the sum of the consumer surplus and the domestic firm’s profit
from domestic sales:𝐶𝑆!

+ 𝜋9! =

(01∑!"#,%,&

'

'! )(

0*

− ∑"∈$,&,' 𝜃"!

''

510'! 6∑)*! ')
7

'

+

'

(510'+ 6∑)*+ ') )(
58

.

(4)

By comparing domestic welfare under the respective strategies for standards policy, we
obtain the following proposition.
Proposition 1 In an unconstrained noncooperative standards game without any international agreements, theequilibrium standards regime implies:
・NR for 0 ≤ 𝜃 < 𝜃 : ;:・D for 𝜃 : ≤ 𝜃 > 𝜃 ; and・FR for 𝜃:≤ 𝜃,'(510'):'(5;6')

where 𝜃 : ≡ 7(51') and 𝜃 ≡ ;(56*').
Proof See the Appendix.
The intuition behind Proposition 1 is as follows. When choosing standards, each government faces thefollowing trade-off: A more stringent standards policy results in decreased consumption and domestic profit, but
pollution damage decreases in that country. If pollution damage 𝜃 is low, the former effect dominates; however,4

Strictly speaking, the discrimination regime D here should be termed as “negative discrimination”. Because the government discriminates against foreign firmsby setting more stringent standards. We may consider another type of discriminatory standard’s regime, namely “positive discrimination,” under which the""government sets less stringent standards on foreign products than domestic ones; 𝜎! = 𝐿 and 𝜎# = 𝐻 for 𝑘 ≠ 𝑗. However, we can verify that, under
Assumption 1, positive discrimination will never be an equilibrium outcome. Therefore, throughout this paper, we regard the negative discrimination case as
the discrimination regime.
9

if 𝜃 is high, the latter effect dominates. If 𝜃 is moderate, the discrimination strategy can increase domestic profit
while reducing pollution damage.

3 Bilateral Agreements on Standards Policy
Here, we consider a situation in which two of the three countries, namely countries A and B, conclude an agreementthat requires a commitment to the rigid rule regarding their standards policy. We consider two rules for standard
agreements: NT and MR. As previously mentioned, NT means that the same standards should be applied to both
the domestic product and the product imported from the member country of the agreement. MR means that control
over standards on the exported product is transferred from the importer to the exporter member country, meaningthat the exporter country sets the standards, and the importer country has to accept them.
We consider a form of agreement with the least degree of integration, meaning that standards are still
determined by each member country of the agreement noncooperatively, rather than member countries
harmonizing their standards to maximize joint welfare.5 That is, we assume that member countries A and B, whenfacing a constraint imposed by NT or MR, determine their respective standards to maximize their respective
welfare. Country C, an outsider to the agreement, also determines its standards noncooperatively. As country C’s
optimal standards are independent of the other countries’ standards, Proposition 1 holds for country C even in thepresence of bilateral agreements.

3.1 Policy game under NT
As in the unconstrained noncooperative case, export profits only depend on the foreign standards under NT.
Therefore, for countries A and B, the government’s problem in stage 1 is to choose the standards policy that

5This is similar to a relationship between a free trade agreement (FTA) and a customs union (CU) in terms of the determination of tariffs; each member countryof an FTA determines its external tariffs independently, whereas, under a CU, member countries jointly set common external tariffs.
10maximizes the domestic welfare in (4), subject to the constraint that the same standards should be applied to thedomestic product and the one imported from the member country; that is, the constraint is 𝜎$! = 𝜎&! ∈{𝐻, 𝐿}, 𝐽 = 𝐴, 𝐵.
Again, there are three regimes for member countries’ governments to choose from. As in the no-agreementcase, these governments (𝐽 = 𝐴, 𝐵) have an option to choose: (i) full regulation, under which 𝜎"! = 𝐿 for 𝑘 =𝑎, 𝑏, 𝑐 or (ii) no regulation, under which 𝜎"! = 𝐻 for 𝑘 = 𝑎, 𝑏, 𝑐. In addition, they may choose a standards
policy that discriminates against nonmember country C, which we simply call (iii) discrimination, under which𝜎"! = 𝐻 for 𝑘 = 𝑎, 𝑏 and 𝜎'! = 𝐿, 𝐽 = 𝐴, 𝐵.6
The following proposition characterizes the optimal standards policy.
Proposition 2 Under a bilateral agreement on a standards policy with NT, member countries’ equilibrium
standards regime implies:
・NR for 0 ≤ 𝜃 < 𝜃;<

・D for 𝜃 ≤ 𝜃 < 𝜃 ; and・FR for 𝜃<≤ 𝜃,'(*10')<'(=1*')

where 𝜃 ≡ ;(51*') and 𝜃 ≡ 7(56') .
Proof See the Appendix.

6

As discussed in Section 1, we assume that GATT Article XXIV, which allows the formation of a preferential trade agreement, provided that the members of

this agreement do not impose higher or more restrictive trade barriers on nonmembers, can be applied to the “deep” integration considered in this study. It canbe verified that any shifts in standards policies in the course of a transition from the unconstrained noncooperative policy equilibrium to a bilateral agreement
on standards do not make member countries’ standards on imports from the nonmember country more stringent.
11

3.2 Policy game under MR
Under MR, each member country transfers the right to control imports to the other member (i.e., exporter) country.
This means that country A’s government determines, in addition to 𝜎$, and 𝜎', , the standard on firm a’s productexported to country B, that is, 𝜎$- . Analogously, country B’s government determines 𝜎&, in addition to 𝜎&- and𝜎'- . Moreover, each member country faces the constraint that the same policy should be applied to the domesticallyconsumed product and the one produced by the same firm and exported to another member country; that is,𝜎9, = 𝜎9- must hold for 𝑗 = 𝑎, 𝑏.
Unlike under the NT regime, each member country’s standards policy affects the export profit earned in anothermember country, as well as consumer surplus and domestic profit. Therefore, the objective function of thegovernment in each member country 𝐽 = 𝐴, 𝐵 with domestic firm 𝑗 = 𝑎, 𝑏 is given by
𝐶𝑆! + 𝜋9, + 𝜋9-

=

(01

∑

!"#,%,&

0*

'

'! )(

− ∑"∈$,&,' 𝜃"!

''

510'! 6∑)*! ')7+ ∑+#,,-(510'+, 6∑)*! '), )(
58

.

(5)

The government’s problem is to maximize (5) subject to 𝜎9, = 𝜎9- .
The government in each member country has the following strategies for standards: (i) full regulation, under which
𝜎9, = 𝜎9- = 𝜎9. = L for (𝑗, 𝐽) ∈ {(𝑎, 𝐴), (𝑏, 𝐵)}; (ii) no regulation, under which 𝜎9, = 𝜎9- = 𝜎9. = 𝐻 for(𝑗, 𝐽) ∈ {(𝑎, 𝐴), (𝑏, 𝐵)}; and (iii) discrimination against country C, under which 𝜎9, = 𝜎9- = 𝐻 and 𝜎.! = 𝐿
for (𝑗, 𝐽) ∈ {(𝑎, 𝐴), (𝑏, 𝐵)}.
From (5), under MR, one member country’s optimal standards depend on the other member country’s
standards. This means that, unlike the previous policy regimes, we first need to derive each member country’s best
response strategy and then obtain the Nash equilibrium of the standard game. As we will see below, both member

12countries’ standards are strategic complements in the MR game. This particular feature of MR leaves room (in our
setting with discrete policy choices) for multiple Nash equilibria (see also the Appendix). Therefore, to compare
the outcomes under MR with those under NT, we need to refine the equilibrium in the MR game. We follow
Costinot (2008) to restrict our attention to the Pareto efficient or “most cooperative” equilibrium. That is, if one
equilibrium is strictly preferred over any other by both countries, we assume that they can coordinate on thisequilibrium. The most cooperative equilibrium in the MR game can be characterized by the following proposition.
Proposition 3 Under a bilateral agreement on standards policy with MR, member countries’ equilibrium
standards regime in the most-cooperative equilibrium implies:
・NR for 0 ≤ 𝜃 < 𝜃;>・D (against the nonmember) for 𝜃 ≤ 𝜃 < 𝜃 ; and・FR for 𝜃
>

>

≤ 𝜃,
(0?6@')'

where 𝜃 ≡ ;(56*') .
Proof See the Appendix.
3.3 Comparison between NT and MR<:>

Comparing the threshold values of 𝜃, we can verify that 𝜃 : < 𝜃 < 𝜃 < 𝜃 < 𝜃 . That is, compared to thecase without agreements on standards, the threshold value of 𝜃 above which the member countries begin to shift
from discrimination to full regulation is lower under NT and higher under MR (see Figure 1). This means that the13member countries tend to choose more stringent standards under NT. By contrast, they tend to choose less stringent
standards under MR.7

Figure 1 Summary of policy game outcomes
The intuition behind these differences in the stringency of member countries’ standards between types ofstandards agreements can be interpreted as follows. In our three-country model, the unconstrained benchmark
allows each country’s government to discriminate against both of its exporters, but under NT, each member country
can discriminate against only the exporter in the nonmember country. This reduces the domestic firm’s costadvantage compared to its foreign rivals under NT. As the member countries’ objective function is expressed by(4) both under the benchmark and NT cases, these countries evaluate the importance of pollution externalities to agreater extent under NT, leading to more stringent standards.
Under MR, each member country loses control over the standards of the imported product from anothermember country but instead gains control over the standards of the product exported to its partner’s market.
Therefore, the government in each member country considers the domestic firm’s profit earned in its partner’s

7

In his two-country model, Costinot (2008) considers the result under NT as “green protectionism,” while the result under MR is considered a “race to thebottom.” In our three-country model, member countries’ standards have similar properties.

14

market, as well as its domestic profit, and has an incentive to loosen the regulation on the domestic firm to promote
exports to that market. In addition, member countries do not consider the externalities generated by the domestic
firm in foreign countries. Therefore, under MR, the member countries choose less stringent standards than underthe benchmark case.
>

From Figure 1, if the environmental externality is negligible (i.e., 𝜃 < 𝜃 : ) or very severe (i.e., 𝜃 ≥ 𝜃 ),both types of standards agreement achieve the same outcomes as the unconstrained noncooperative equilibrium.
<>

In addition, NT and MR induce member countries to choose different policies only if 𝜃 ≤ 𝜃 < 𝜃 . This
indicates that the welfare effects of these agreements, which are discussed below, differ only if 𝜃 is in this range.
We now present the welfare effects of the standards agreements on the respective countries. We begin with thewelfare effects on member countries. Let us denote member country 𝐽’s welfare, which is the sum of consumer
surplus 𝐶𝑆! and domestic firm j’s total profits, 𝜋9 = ∑+#,,-,. 𝜋9+ , under the unconstraint noncooperativeequilibrium, NT, and MR by 𝑆𝑊!< and 𝑆𝑊!> , respectively, for (𝑗, 𝐽) ∈ {(𝑎, 𝐴), (𝑏, 𝐵)}. Then, the welfare
gains (or losses) in each member country under the respective standards regimes (i.e., 𝑆𝑊!< − 𝑆𝑊!: under the
NT regime and 𝑆𝑊!> − 𝑆𝑊!: under the MR regime) can be illustrated as in Figure 2.

15

Figure 2 Welfare comparison of member countries
We obtain the following proposition from Figure 2.
Proposition 4 For the member countries of the standards agreement, (i) NT and MR are indifferent when 𝜃 <
𝜃

<

>

<

>

and 𝜃 ≤ 𝜃; (ii) MR is preferred over NT when 𝜃 ≤ 𝜃 < 𝜃 ; and (iii) NT is preferred over MR when>(@1*')'𝜃 ≤ 𝜃 < 𝜃 , where 𝜃 ≡ 7(56') .
The intuition behind Proposition 4 can be interpreted as follows. As shown in Figure 1, for 𝜃 : < 𝜃 < 𝜃, themember countries of a standards agreement choose discrimination in the absence of an agreement but choose notto regulate all products both under NT and MR. This policy change increases the domestic firm’s profits but leads
to higher pollution externalities. However, as the value of 𝜃 is small, the former positive effect outweighs thelatter negative one. For 𝜃 < 𝜃 < 𝜃 < , the member countries discriminate against the exporter from thenonmember country both under NT and MR by regulating that firm. This leads to a cost advantage for the domestic<>

firm and, thus, has a positive effect on member countries’ welfare. If 𝜃 is between 𝜃 and 𝜃 , NT and MR makemember countries choose different standards policies; NT leads them to choose stricter standards, and MR leads<:

them to choose looser standards. For 𝜃 ≤ 𝜃 < 𝜃 , member countries choose full regulation under NT whilestill discriminating against nonmembers under MR. Owing to the increase in firms’ costs, NT results in lower
consumption and profits for the domestic firm, making the member countries worse off compared to in the noagreement case. Meanwhile, a full regulation policy removes environmental externalities and leads to a welfare:>

gain under NT as 𝜃 increases. For 𝜃 ≤ 𝜃 < 𝜃 , all countries choose full regulation under both the NT andbenchmark situations, meaning that the member countries achieve the same welfare level. By contrast, member
countries continue to discriminate against nonmember countries under MR. The domestic firm in each member
country has a cost advantage compared to the firm in the nonmember country, contributing to member countries’
welfare gains under MR. Simultaneously, not regulating member countries’ firms leads to more pollution and, thus,

16

welfare losses. Since the value of 𝜃 is sufficiently high in the current situation, the latter negative effect outweighs
the former positive one, resulting in a net loss for member countries under MR.
We now consider the welfare effects of bilateral agreements on standards for the nonmember country of eachtype of agreement. Figure 3 illustrates the net gain in nonmember country C’s welfare compared to that under thebenchmark scenario of unconstrained noncooperative equilibrium (i.e., 𝑆𝑊.< − 𝑆𝑊.: under NT and 𝑆𝑊.< −𝑆𝑊.: under MR). For 𝜃 : < 𝜃 < 𝜃, the member countries lift the regulation on imported goods as they movefrom D to NR, while the nonmember country continues to implement D. Consequently, the nonmember country
becomes better off compared to the benchmark case. However, for 𝜃 < 𝜃 < 𝜃 < , member countries move fromNR to D, which discriminates against the nonmember. This policy change benefits firms in the member countries<

at the cost of firm c’s export profits. Therefore, the nonmember country’s welfare decreases drastically. For 𝜃 ≤:𝜃 < 𝜃 , while the member countries continue to discriminate against imports from nonmember countries underMR, they shift from D to FR under NT. This means that, under NT, firm c regains the same competitiveness in theexport markets as firms a and b, which is beneficial to the nonmember country. This advantage of the NT regime:

for the nonmember country disappears as all countries choose FR for 𝜃 ≥ 𝜃 . However, under MR, thenonmember country further becomes worse off because the threshold value of 𝜃 above which the member
countries begin to shift from D to FR is higher under MR. That is, member countries continue to discriminate
against the nonmember country, which chooses FR and, thus, its domestic firm loses competitiveness in the export
markets.

17

Figure 3 Welfare comparison of the nonmember country
From Figure 3, for the nonmember country, the bilateral agreement on standards based on MR cannot be
preferred over the one based on NT, as demonstrated by the following proposition.
Proposition 5 For a nonmember country outside the standards agreement, (i) NT and MR are indifferent when
𝜃<𝜃

<

>

<

>

and 𝜃 ≤ 𝜃 and (ii) NT is preferred over MR when 𝜃 ≤ 𝜃 < 𝜃 .

The nonmember country can never prefer MR to NT because the threshold level of θ at which the member
countries start to implement full regulation is lower under NT and higher under MR. For the values of 𝜃 belowthat threshold, member countries choose to discriminate against the nonmember. In other words, compared to theno-agreement benchmark, NT makes member countries implement a less discriminatory standards policy, while
MR leads to more discriminatory standards by members.
Combining Propositions 4 and 5, preferential agreement over standards policy can benefit all countries only
when 𝜃 : < 𝜃 < 𝜃 (under both NT and MR) and 𝜃 ≤ 𝜃 < 𝜃
standards agreements make at least one country worse off.

4 Multilateral Agreements
18:(under NT only). For other values of 𝜃, theWe now discuss what outcomes can be obtained when the bilateral agreements on standards are expanded tomultilateral ones. Assume that country C joins the agreement, which can be of either the NT or MR type and, thus,
the standards and policies are harmonized globally.
Each type of multilateral agreement can be characterized as follows. Under NT, the government in each country
controls the standards on the products sold in the domestic market, that is, (𝜎$! , 𝜎&! , 𝜎'! ), such that 𝜎$! = 𝜎&! = 𝜎'!
for 𝐽 = 𝐴, 𝐵, 𝐶. Under MR, each country’s government controls the standards on the products produced by thedomestic firm, that is, (𝜎9, , 𝜎9- , 𝜎9. ), such that 𝜎9, = 𝜎9- = 𝜎9. for 𝑗 = 𝑎, 𝑏, 𝑐. Irrespective of the type ofagreement, the governments treat all countries equally, meaning that discrimination cannot be a possible strategy.
We assume that each government seeks to maximize its own welfare.8

4.1 Outcomes under NT
Under NT, as in the case of the bilateral agreement, the export profits that the domestic firm earns are beyond thecontrol of the national government because they only depend on other countries’ standards. Thus, the governmentschoose standards to maximize their respective domestic components of social welfare, as given by (4). In addition,
as explained above, the governments cannot implement discriminatory standards; hence, their possible strategy iseither (i) full regulation, under which 𝜎"! = 𝐿, or (ii) no regulation, under which 𝜎"! = 𝐻 for 𝑘 = 𝑎, 𝑏, 𝑐 and
𝐽 = 𝐴, 𝐵, 𝐶. The following proposition represents the solution to this policy game.
Proposition 6 Under a multilateral agreement on standards based on NT, the equilibrium standards regime
implies:8

It can be easily verified that if the governments were to cooperate on the standards policies to maximize their joint welfare, NT and MR achieve identicalsolutions for the globally optimal standards.

19• NR for 0 ≤ 𝜃 < 𝜃 ∗< , and• FR for 𝜃 ∗< ≤ 𝜃, where 𝜃 ∗< ≡55'(*1')*7.

Proof See the Appendix.
:

As demonstrated in the proof of Proposition 1, 𝜃 ∗< is greater than 𝜃 : and smaller than 𝜃 . We can also
verify that 𝜃 < 𝜃 ∗< < 𝜃<

for any 𝑐 < 1/5 (see also Figure 4 (a)). That is, the threshold value of 𝜃 at which

the governments start to implement full regulation is lower under the multilateral agreement than under the bilateralagreement. This means that a multilateral agreement based on NT induces the government to implement a more
stringent standards policy. The intuition is as follows. Under the bilateral agreement on standards, member
countries still had an option to discriminate against the exporter from the nonmember country. However,discriminatory standards are not available under the multilateral agreement. As the governments cannot raise thedomestic firm’s export profits through the standards policies under NT, the importance of pollution externalities
increases under the multilateral agreement. They thus have an incentive to regulate products, even for lower
externality values.

(a) Agreements based on NT

20

(b) Agreements based on MR
Figure 4 Summary of optimal standards under multilateral agreements

4.2 Outcomes under MR
In the case of a multilateral agreement with MR, each country’s standards policy affects the export profits of othercountries. This means that governments’ objective function is social welfare 𝑆𝑊 ! given by (3), 𝐽 = 𝐴, 𝐵, 𝐶.
Their possible strategy is either (i) full regulation, 𝜎9+ = 𝐿 or (ii) no regulation (NR), under which 𝜎9+ = 𝐻 for
𝑗 = 𝑎, 𝑏, 𝑐 and 𝐾 = 𝐴, 𝐵, 𝐶. Since the objective function of country 𝐽’s government, 𝑆𝑊 ! , depends on theother two countries’ standards policies, the optimal standards for country J’s government, (𝜎9, , 𝜎9- , 𝜎9. ), also
depend on those countries’ standards. Therefore, we first need to derive each member country’s best response
strategies and then obtain the Nash equilibrium of the standard game. Again, there can be multiple Nash equilibria,
and we focus on the most cooperative equilibrium, which can be characterized by the following proposition.
Proposition 7 Under a multilateral agreement on standards based on MR, the equilibrium standards regime in
the most-cooperative equilibrium implies:• NR for 0 ≤ 𝜃 < 𝜃 ∗> , and'(7*650')• FR for 𝜃 ∗> ≤ 0, where 𝜃 ∗> ≡ ;(56*') .
Proof See the Appendix.

21>It can be verified that 𝜃 ∗> is greater than 𝜃 ; the threshold value of θ at which the governments start
implementing full regulation is higher under the multilateral agreement than under the bilateral one. This meansthat a multilateral agreement based on MR induces the government to implement a less stringent standards policy.
Intuitively, compared to the bilateral agreement under MR, the multilateral agreement further reduces governments’control over the standards on imported products but increases their control over the standards on the domestic
firm’s export products. By loosening the regulation on the domestic firm, each country can gain from the increased
exports; the resulting externalities only affect foreign welfare and not domestic welfare. Thus, under the multilateralagreement on standards policy based on MR, the governments do not impose regulations unless the level ofexternalities is exceptionally high.

5 Can Bilateral Agreements be a Building Block to Multilateral Agreements?
We now compare each country’s welfare under multilateral agreements with that under bilateral agreements. Basedon the comparison, we discuss whether the respective types of multilateral agreements can be a building or
stumbling block to multilateral agreements.

5.1 NT-based agreement
As the bilateral and multilateral agreements achieve the same outcomes for 𝜃 < 𝜃 : (under which all countries:

choose NR) and 𝜃 ≤ 𝜃 (under which all countries choose FR), we begin with a comparison of the welfare:

between the two types of agreements for the case when 𝜃 ≤ 𝜃 < 𝜃. In this case, the member countries of thebilateral agreement choose NR and do so under the multilateral agreement as well, whereas the nonmember
country chooses D under the bilateral agreement and NR under the multilateral agreement. As the nonmember
country lifts its discriminatory measures after joining the multilateral agreement, the domestic firm’s cost advantage
reduces. By contrast, member countries’ firms no longer suffer the cost disadvantage after the multilateral22:agreement. Therefore, for 𝜃 ≤ 𝜃 < 𝜃 , switching from a bilateral to multilateral one makes the member
countries better off and the nonmember worse off.
For 𝜃 ≤ 𝜃 < 𝜃 ∗< , the members of the bilateral agreement choose D against the nonmember, and thenonmember chooses D, while all countries choose NR under the multilateral agreement. The nonmember
country’s policy response to a change from a bilateral to a multilateral agreement is the same as the one when
𝜃 : ≤ 𝜃 < 𝜃. Therefore, this change harms the nonmember’s welfare. However, the member countries also lift
the discriminatory measure against the nonmember, eliminating the cost disadvantage of the nonmember country’s
firm and, thus, improving its welfare. This positive effect outweighs the former negative effect, and the nonmember
country becomes better off. For member countries’ firms, these two effects caused by the change from the bilateral
to the multilateral agreement work in the opposite direction; the nonmember country’s policy change from D to
NR benefits member countries’ firms, but member countries’ policy change from D against the nonmember to NR
harms these firms. In addition, as all firms produce polluting goods under the multilateral agreement, pollution
damage increases. Consequently, the member countries become better off after the transition from the bilateral tothe multilateral agreement if θ is smaller than a threshold level, denoted by 𝜃 B ∈ ^𝜃, 𝜃 ∗< _, but they become worse
off if 𝜃 > 𝜃 B .
<For 𝜃 ∗< ≤ 𝜃 < 𝜃 , the members of the bilateral agreement choose D against the nonmember, and thenonmember chooses D, while all countries choose FR under the multilateral agreement. Under the multilateralagreement, all firms now face stricter standards and, thus, their costs increase. In addition, since countries remove
discriminatory measures under the multilateral agreement, the cost advantage of domestic firms disappears.
Simultaneously, as an exporter, each firm’s cost disadvantage also disappears. In this three-country model, firm a,for example, has already been as competitive as firm b in country B’s market, and the change from the bilateral tothe multilateral agreement only improves firm a’s competitiveness in country C’s market. Therefore, the member
countries become worse off after the conclusion of the multilateral agreement. By contrast, for firm c, a transition

23

from the bilateral to the multilateral agreement helps it regain its competitiveness in the markets of both countries
A and B. Since the governments implemented full regulation under the multilateral agreement, the countries now
incur no environmental damages. As the level of 𝜃 is relatively high in this case, the nonmember country becomes
better off.
<:

Finally, for 𝜃 ≤ 𝜃 < 𝜃 , the members of the bilateral agreement choose FR and the nonmember chooses
D, while all countries choose FR under the multilateral agreement. In this case, member countries’ firms regain
competitiveness in the nonmember country’s market, while the nonmember country’s firm loses its cost advantage
in the domestic market. As such, the change from a bilateral to a multilateral agreement makes the member
countries better off and the nonmember country worse off.

5.2 MR-based agreement
We now consider the case of the MR-based agreement. In light of (4), the same outcomes are obtained under thebilateral and multilateral agreements for 𝜃 < 𝜃 : (under which all countries choose NR) and 𝜃 ∗> ≤ 𝜃 (underwhich all countries choose FR). Consider case 𝜃 : < 𝜃 < 𝜃, under which the member countries of the bilateralagreement choose NR and also do so under the multilateral agreement, whereas the nonmember country chooses
D under the bilateral agreement but chooses NR under the multilateral agreement. This case has already been
discussed for the NT-based agreement; that is, a transition from the bilateral to the multilateral agreement makes
the member country better off but the nonmember country worse off.
:For 𝜃 ≤ 𝜃 < 𝜃 , the members of the bilateral agreement choose D against the nonmember, and thenonmember chooses D, while all countries choose NR under the multilateral agreement. This case is also the sameas that under the NT-based agreement for 𝜃 ≤ 𝜃 < 𝜃 ∗< . That is, as already discussed, there is a threshold value𝜃 B ∈ ^𝜃, 𝜃 ∗< _ such that a change from a bilateral to a multilateral agreement makes the member countries better24:

off only if 𝜃 < 𝜃 B , while the nonmember country is unambiguously better off. For 𝜃 B ≤ 𝜃 < 𝜃 , the membersof the bilateral agreement become worse off after the conclusion of the multilateral agreement.
:

For 𝜃 ≤ 𝜃 < 𝜃 , the members of the bilateral agreement choose D against the nonmember, and thenonmember chooses FR, while all countries choose NR under the multilateral agreement. As member countries’
firms have already been unregulated and lose their cost advantage over the nonmember country’s firm after theconclusion of the multilateral agreement, these firms’ profits decrease. By contrast, the nonmember country’s firm
regains its competitiveness in the export markets. However, this positive effect on the nonmember country’s
welfare is outweighed by the increase in pollution damage, as the value of 𝜃 is already high in this case. Thus, atransition from a bilateral to a multilateral agreement makes all countries worse off.
Finally, for 𝜃 ≤ 𝜃 < 𝜃 ∗> , all countries choose FR under the bilateral agreement, while all countries choose
NR under the multilateral agreement. Firms do not need to comply with standards to enjoy higher profits after theconclusion of the multilateral agreement. Nonetheless, the value of 𝜃 is so high that the damage from negative
externalities outweighs the positive effects on firm profits. As such, a change from a bilateral to a multilateralagreement makes all countries worse off.

6 Discussion
A multilateral agreement on standards via a bilateral one can be achieved only if it is not blocked by the member
or nonmember countries of the bilateral agreement. Summarizing the above discussion for the respective types ofstandards agreements, this is possible only if 𝜃 ≤ 𝜃 < 𝜃 B , where 𝜃 B is smaller than 𝜃 ∗< . In this case, both themembers and nonmembers of the bilateral agreements, irrespective of whether the agreements are based on NT or
MR, become better off after concluding the multilateral agreement. Otherwise, a transition from a bilateral to a
multilateral agreement on standards causes welfare losses to either the nonmember or member countries and, thus,
the multilateral agreement will be blocked by these countries.

25

The member countries of a bilateral agreement are assumed to conclude the agreement. The discussion ismeaningful only if the members have an incentive to conclude the bilateral agreement. However, as illustrated in
Figure 2, the member countries gain from the conclusion of the bilateral agreement when 𝜃 ∈ ^𝜃, 𝜃 B _. That is,for 𝜃 ≤ 𝜃 < 𝜃 B , a multilateral agreement on standards can be achieved via an agreement concluded by two of
the three countries. Starting from a noncooperative equilibrium of standards policies, two of the three countries willconclude a bilateral agreement on standards and, then, the remaining country has an incentive to join the agreement,
which also enhances member countries’ welfare. Therefore, we obtain the following proposition.
Proposition 8 A bilateral agreement on standards, irrespective of whether it is based on NT or MR, can be abuilding block to a multilateral agreement only if 𝜃 ∈ ^𝜃, 𝜃 B _.
How can Proposition 8 be interpreted? Does it offer a positive message with regard to achieving the harmonizationof standards at the global level? We are rather pessimistic about it for the following reasons. First, interval^𝜃, 𝜃 B _ in Proposition 8 is only a small subset of the possible values of 𝜃. Second, for the externality parametersatisfying 𝜃 ∈ ^𝜃, 𝜃 B _, the respective countries choose discriminatory standards under bilateral agreements, andshift to less stringent standards policies after concluding the multilateral agreement. However, as previously
discussed, implementing a discriminatory standards policy might go against the non-discrimination principle in the
WTO law, even if preferential agreements are allowed. Moreover, the multilateral agreement results in a “race tothe bottom,” which the agreement does not aim for.

7 Conclusion
This study extended Costinot’s (2008) comparative analysis of the agreements on product standards to a threecountry model. By considering a bilateral agreement between a subset of the world economy, we discussed thecomparative performance of the different regimes of standards agreements, namely NT and MR, for both themember and nonmember countries of the agreements.

26

We have shown that the equilibrium standards depend on the value of the externality parameter, 𝜃. The
patterns of the equilibrium standards in the unconstrained noncooperative standards game without any international
agreements and in the bilateral agreement on standards under NT are the same, but the threshold values of 𝜃 differ:no regulation for small values of 𝜃, discrimination for intermediate values of 𝜃, and full regulation for large valuesof 𝜃. Compared to the case without agreements on standards, we have shown that the threshold value of 𝜃 above
which the member countries begin to shift from a discrimination strategy to full regulation is lower under NT andhigher under MR; this means that member countries tend to choose more stringent standards under NT, whereas
they tend to choose less stringent standards under MR. We also examined the welfare gains from bilateralagreements for both member and nonmember countries. For member countries, for small values of 𝜃, MR ispreferred over NT, while for large values of 𝜃, NT is preferred over MR. We have also shown that a nonmember
country can never prefer MR to NT.
We further considered multinational agreements on standards. For NT-based agreements, the threshold valueof 𝜃 at which governments start to implement full regulation is lower under the multilateral agreement than underthe bilateral agreement; this suggests that a multilateral agreement based on NT induces the government toimplement a more stringent standards policy. By contrast, for MR-based agreements on standards, the thresholdvalue of 𝜃 at which the governments start implementing full regulation is higher under the multilateral agreement
than under the bilateral one. This means that a multilateral agreement based on MR induces the government toimplement a less stringent standards policy. We have also shown that there exists a range of 𝜃 for which themultilateral agreement on standards can be achieved via agreements concluded by two of the three countries.
Specifically, starting from a noncooperative equilibrium of standards policies, two of the three countries willconclude a bilateral agreement on standards and then, the remaining country has an incentive to join the agreement,
which also enhances member countries’ welfare. Otherwise, a multilateral agreement on standards will be blocked
by the member countries or a nonmember country of the bilateral agreement.

27

Some noteworthy extensions of the analysis warrant further study. First, future studies should consider the caseof asymmetric countries (i.e., developed countries and developing countries). In this study, we considered threesymmetric countries join the trade agreements. In future studies, we will consider asymmetric countries to join theagreements. Second, this research considered the impact of non-tariff barriers. While under some trade agreements,
the tariff is still in force. Thus, future study will consider import tariffs and export subsidies (two traditional trade
instruments) together with product standards.

Acknowledgements
The authors would like to thank Anna Matzner, Yasuhiro Takarada, and the conference participants at the
University of Bari and Aix-Marseille School of Economics.
This work has been financially supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid
for Scientific Research (B) (No. 20H01492) and (C) (No. 23K01407), and JSPS KAKENHI Grant Number
2422J14642 and 2422KJ1568.

Declarations
The authors declare no potential conflict of interest regarding the publication of this work.
The authors declare no use of generative AI and AI-assisted technologies in the writing process.

28

Appendix
A.1 Proof of Proposition 1
As export profits depend on other countries’ standards, the government’s objective in each country is to maximize
the domestic component of national welfare, i.e., the sum of consumer surplus and domestic profit, represented by(4). If country J’s government implements full regulation (FR), 𝑐"! = 𝑐 and 𝜃"! = 0 for k = a, b, c. Thus, (4)can be rewritten as
𝐶𝑆! + 𝜋9! =55(51')(

（A.1）

0*

If the government chooses no regulation (NR), 𝑐"! = 0 and 𝜃"! = 𝜃 for k = a, b, c, and (4) becomes55

0C

𝐶𝑆! + 𝜋9! = 0* − 7（A.2）

If the government chooses Discrimination (D), it holds that (𝑐"! , 𝜃"! ) = (0, θ) and (𝑐"! , 𝜃"! ) = (𝑐, 0) for 𝑗 ≠ 𝑘.
Then, (4) can be rewritten as
𝐶𝑆! + 𝜋9! =(01*')(
0*

−𝜃

56*'
7

+

(56*')((A.3)

58

Comparing the welfare under different standards policies, we obtain the following threshold values for θ:
55

𝐹𝑅 ≻ 𝑁𝑅 iff 𝜃 > *7 𝑐(2 − 𝑐) ≡ 𝜃5 ;'(5;6')𝐹𝑅 ≻ 𝐷 iff 𝜃 > ;(56*') ≡ 𝜃* ;'(510')𝑁𝑅 ≻ 𝐷 iff 𝜃 < 7(51') ≡ 𝜃0 .
It can be easily verified that under Assumption 1 (i.e., c < 1/5), 𝜃0 < 𝜃5 < 𝜃* holds. Then, the optimal standards
policy for country J under the unconstrained noncooperative policy game can be represented by Figure A.1.
From Figure A.1, country J’s government finds it optimal to choose NR for 0 ≤ θ < 𝜃0 , D
for 𝜃0 ≤ θ < 𝜃* , and FR for 𝜃* ≤ θ. Considering that the three countries are symmetric, governments in all:

countries have the same choice for optimal standards. Redefining 𝜃0 and 𝜃* by 𝜃 : and 𝜃 respectively, we
obtain the statement of Proposition 1.

29

Figure A.1: Optimal standards in the unconstrained noncooperative equilibrium

A.2 Proof of Proposition 2
As in the unconstrained noncooperative case, export profits depend only on the foreign standards under NT; thus,
the member countries choose standards to maximize domestic welfare. Let us focus on country A. If country A’s
government chooses FR, 𝑐9, = 0 and 𝜃9, = 𝜃 for j = a, b, c holds and, thus, its domestic welfare is the same as(A.1). If NR is chosen, 𝑐9, = 0 and 𝜃9, = 𝜃 for j = a, b, c hold, meaning that the domestic welfare is the sameas (A.2). If country A’s government discriminates against country C regarding the standards policy, (𝑐$, , 𝜃$, )=(𝑐&, , 𝜃&, ) = (0, θ) and (𝑐', , 𝜃', ) = (c, 0) hold, and (4) can be rewritten as
𝐶𝑆 , + 𝜋$, =(01')(
0*56'− 2𝜃 7 +(56')(
58

.

(A.4)

Comparing the welfare under different standards policies, we obtain the threshold values for θ as follows. The
comparison between FR and NR is the same as that in the unconstrained noncooperative case; that is, FR ≻ NR if
and only if θ > 𝜃5 , where 𝜃5 is defined in the proof of Proposition 1. From (A.1), (A.2), and (A.4), we obtain theother threshold values'(=1*')𝐹𝑅 ≻ 𝐷 iff 𝜃 > 7(56') ≡ 𝜃*D ;'(*10')𝑁𝑅 ≻ 𝐷 iff 𝜃 < ;(51*') ≡ 𝜃0D .
It can be verified that 𝜃0D < 𝜃5 <𝜃*D holds if c<1/5.

30

Figure A.2: Bilateral agreement on standards based on NT principle
From Figure A.2, country A’s government finds it optimal to choose NR for 0 ≤ θ < 𝜃0D , D for 𝜃0D ≤ θ < 𝜃*D ,and FR for 𝜃*D ≤ θ. With symmetry, country B’s government follows the same choice for optimal standards.
<

Redefining 𝜃0D and 𝜃*D by 𝜃 and 𝜃 , respectively, we obtain the statement of Proposition 2.

A.3 Proof of Proposition 3
We first prove the following lemma.
Lemma A.1 Under a bilateral agreement of standards policy with MR, the member countries’ equilibrium
standards regime implies that:・No regulation for 0 ≤ 𝜃 < 𝜃;・Discrimination (against the nonmember) for 𝜃 ≤ 𝜃 < 𝜃

>

and

>

・Discrimination or Full regulation for 𝜃 ≤ 𝜃 < 𝜃 B and・Full regulation for 𝜃 B ≤ 𝜃,>

(0?6@')'

where 𝜃 ≡ ;(56*') and 𝜃 B =5=(*1')';.

Proof Let us consider country A’s government, whose objective function is given by (5). If the government
chooses FR, 𝑐$, = 𝑐$- = 𝑐', = c and 𝜃$, = 𝜃', = 𝜃 but 𝜃&, depends on country B’s strategy. Thus, (5) canbe rewritten as31𝐶𝑆 , + 𝜋$, + 𝜋$=(01*'1'%- )(
0*

− 𝜃&,

56*'10'%7+(51*'6'%- )(+58(510'6'%. 6'&. )(

(A.5)

58

If NR is chosen, 𝑐$, = 𝑐$- = 𝑐', = 0 and 𝜃$, = 𝜃', = 𝜃, and (5) can be rewritten as
𝐶𝑆 , + 𝜋$, + 𝜋$- =(01'%- )(
0*

− 2𝜃

56'%7

− 𝜃&,

510'%-+

7(56'%- )(58+(56'%. 6'&. )(
58

.

(A.6)

If country A’s government discriminates against country C regarding the standards policy, (𝑐$, , 𝜃$, )= (𝑐$- , 𝜃$- ) =(0, θ) and (𝑐', , 𝜃', ) = (c, 0) hold. Thus, (5) can be rewritten as
𝐶𝑆 , + 𝜋$, + 𝜋$=(01'1'%- )(0*−𝜃

56'6'%7− 𝜃&,

56'10'%7+(56'6'%- )(58+(56'%. 6'&. )(
58

(A.7)

Let us begin with country A’s best response strategy when country B uses FR, which means 𝑐&, = 𝑐'- = 𝑐 and𝜃&, = 0. Then, (A.5), (A.6), and (A.7) can further be rewritten as
50(51')(
0*(01')(
0*56'−𝜃 * +(01*')(0*−𝜃;(56')(
58
56*'
7

+

+

(56*')(
58(56*')(
;

, and

,

respectively. Comparing the above expressions one after another, we obtain the threshold values of θ when FR ischosen in country B:'(581')𝐹𝑅 ≻ 𝑁𝑅 iff 𝜃 > ;(56') ≡ 𝜃5EF ;'(0?6@')𝐹𝑅 ≻ 𝐷 iff 𝜃 > ;(56*') ≡ 𝜃*EF ;𝑁𝑅 ≻ 𝐷 iff 𝜃 <'(*1G');≡ 𝜃0EF .

It can be verified that 𝜃0EF < 𝜃5EF < 𝜃*EF under the assumption c < 1/5. Then, we have a similar pattern to Figures
A.1 and A.2 regarding the best response strategy of country A’s government; that is, when country B’s standards

32policy is FR, country A find it optimal to choose NR for 0 ≤ θ < 𝜃0EF , D for 𝜃0EF ≤ θ < 𝜃*EF , and FR for 𝜃*EF ≤θ.
We next consider country A’s best response strategy when country B uses NR, which means 𝑐&, = 𝑐&- = 𝑐'- =0 and 𝜃&, = 𝜃. Eqs. (A.5), (A.6), and (A.7) can be rewritten as(3 − 2𝑐)*
1 + 2𝑐 (1 − 2𝑐)* (1 − 3𝑐)*
−𝜃
+
+
32
4
16
16
50
0*

0C

− 7 , and(3 − 𝑐)*
1 + 𝑐 (1 + 𝑐)*
1
−𝜃
+
+
32
4
16
16
respectively. The threshold values can be calculated as follows:
𝐹𝑅 ≻ 𝑁𝑅 iff 𝜃 >𝐹𝑅 ≻ 𝐷 iff 𝜃 >'(5815=');(51')

0'(5?1G');≡ 𝜃5<F ;≡ 𝜃*<F ;'(*10')𝑁𝑅 ≻ 𝐷 iff 𝜃 < ;(51*') ≡ 𝜃0<F .
We have 𝜃0<F < 𝜃5<F < 𝜃*<F under the assumption c < 1/5. Again, country A’s best response strategies when NR
is implemented in country B are NR for 0 ≤ θ < 𝜃0EF ,D for 𝜃0EF ≤ θ < 𝜃*EF ,and FR for 𝜃*EF ≤ θ.
Finally, let us consider country A’s best response strategy when country B uses D, which means 𝑐&, = 𝑐&- = 0,𝑐'- = 𝑐 and 𝜃&, = 𝜃. Eqs. (A.5), (A.6), and (A.7) can be rewritten as(3 − 2𝑐)*
1 + 2𝑐 (1 − 2𝑐)*
−𝜃
+
32
4
8
50

0C

− 7 +
0*
(01')(
0*(56')(
58

56'−𝜃 * +, and(56')(

respectively. The threshold values can be calculated as follows:

33

;

,

'(581G')𝐹𝑅 ≻ 𝑁𝑅 iff 𝜃 > ;(51') ≡ 𝜃5H ;𝐹𝑅 ≻ 𝐷 iff 𝜃 >5='(*1');≡ 𝜃*H ;'(*10')𝑁𝑅 ≻ 𝐷 iff 𝜃 < ;(51*') ≡ 𝜃0H .
Note that 𝜃0<F = 𝜃0H . Because 𝜃0H < 𝜃5H < 𝜃*H holds under Assumption 1, country A’s best response
strategies when country B uses D, are NR for 0 ≤ θ < 𝜃0H , D for 𝜃0H ≤ θ < 𝜃*H , and FR for 𝜃*H ≤ θ.
Comparing the lower bounds of the threshold values under different strategies, we can verify that 𝜃0EF −𝜃0<F = 𝜃0EF − 𝜃0H < 0. Comparing the upper bounds of the threshold values, we have 𝜃*EF < 𝜃*<F < 𝜃*H ;moreover, we can verify that 𝜃0<F = 𝜃0H < 𝜃*EF . Thus, we can summarize country A’s best response strategies
by Figure A.3. By symmetry, country B’s best response strategies are the same as Figure A.3, with A replaced by
B.

Figure A.3: Summary of member country A’s best response strategies
From Figure A.3, it immediately follows that the Nash equilibrium standards for the member countries are uniquelydetermined for 0 ≤ θ <𝜃0<F = 𝜃0H , in which NR is the Nash equilibrium standards, for 𝜃0<F = 𝜃0H ≤ θ < 𝜃*EF , inwhich D is the Nash equilibrium standards, and for 𝜃*H ≤ θ, in which FR is the Nash equilibrium standards. For
𝜃0EF ≤ θ < 𝜃*<F , there are two Nash equilibria, D and FR. In view of Proposition 2, 𝜃0<F = 𝜃0H is equal to 𝜃.
>

Then, by redefining 𝜃*EF and 𝜃*H by 𝜃 and θ′, respectively, we obtain the statement of the lemma34

As there are multiple Nash equilibria when 𝜃>≤ θ < θ′, we make a refinement of equilibrium using the following

lemma.
Lemma A.2 In the most cooperative equilibrium under MR regime, the member countries will coordinate on FR>

when θ ∈ [𝜃 , θ′].
Proof We begin with the derivation of optimal standards when the member countries jointly determine theirstandards to maximize the sum of their welfare. As the export profits earned in country C depend only on country
C’s standards, the member countries A and B choose (𝜎$, , 𝜎&, , 𝜎', ) and (𝜎$- , 𝜎&- , 𝜎'- ) to maximize thefollowing objective function:
𝐶𝑆 , + 𝜋$, + 𝜋$- + 𝐶𝑆 - + 𝜋&, + 𝜋&= n (𝐶𝑆! + 𝜋$! + 𝜋&! )!#,,-= ∑!#,,-[(01∑!"#,%,&

0*

'

'! )(

'

'

510'! 6∑)*! ')− ∑"∈$,&,' 𝜃"!

7+ ∑"#$,&''(510'! 6∑)*! ') )(
58

].

(A.8)

However, because the two member countries are symmetric, the joint-welfare maximization problem is equivalent
to choosing country A’s standards policy (𝜎$, , 𝜎&, , 𝜎', ) that maximizes
𝐶𝑆 , + 𝜋$, + 𝜋&,
=

(01

∑

!"#,%,&0*'!- )(− ∑"#$,&,' 𝜃",

510'!- 6∑)*! ')7+ ∑9#$,&(510'+- 6∑)*! ')- )(
58

.

(A.9)

We consider four strategies regarding country A’s choice of standards: (i) full regulation (FR) in which(𝜎$, , 𝜎&, , 𝜎', ) = (L, L, L), (ii) no regulation (NR) in which (𝜎$, , 𝜎&, , 𝜎', ) = (H, H, H), (iii) discrimination (D) in
which(𝜎$, , 𝜎&, , 𝜎', )= (H, L, L), and (iv) discrimination against country C (DC) in which (𝜎$, , 𝜎&, , 𝜎', ) = (H, H,
L). In the respective regimes, (A.9) can be rewritten as follows
𝐹𝑅: 𝐶𝑆 , + 𝜋$, + 𝜋$- =35

50(51')(
0*;(A.10)

50

0C

𝐹𝑅: 𝐶𝑆 , + 𝜋$, + 𝜋$- = 0* − 7 ;𝐷: 𝐶𝑆 , + 𝜋$, + 𝜋$- =5017'(01=')0*

𝐷𝐶: 𝐶𝑆 , + 𝜋$, + 𝜋$- =−𝜃506'(*6=')0*(A.11)
56*'
7

;

56'

−𝜃 * .

(A.12)(A.13)

Note that by comparing (A.11) and (A.13), NR ≺ DC always holds. This means that NR cannot be an optimal
policy, and thus it suffices to compare FR, D, and DC to obtain the following threshold values for θ:@'(*6')𝐹𝑅 ≻ 𝐷 iff 𝜃 > ;(51') ≡ 𝜃5& ;'(@1*')𝐹𝑅 ≻ 𝐷𝐶 iff 𝜃 < 7(56') ≡ 𝜃*& ;𝐷 ≻ 𝐷𝐶 iff 𝜃 <'(5715=');≡ 𝜃0& .

Note also that NR ≺ DC always holds for any θ > 0.
It can be verified that 𝜃0& < 𝜃5& < 𝜃*& . Then, the optimal standards policy for the member countries under bilateral
cooperation can be represented by Figure A.4; that is, the member countries’ governments find it optimal to choose
DC for 0 ≤ θ <𝜃*& and FR for 𝜃*& ≤ θ.
>I
It can be verified that 𝜃*& is smaller than 𝜃 . This means that for θ ∈ [θ , θ′], the member countries have an

incentive to coordinate on FR even though there are multiple Nash equilibria in the policy game under MR.
Proof of Proposition 3 In light of Lemma A.2, Lemma A.1 is modified to Proposition 3.

Figure A.4: Optimal standards under bilateral cooperation

A.4

Comparison of welfare between unconstrained noncooperative solution andbilateral agreements
36

From Propositions 1 to 3, we observe that the respective countries’ equilibrium standards vary as the value of θchanges, as shown by Figure 1. Table 1 summarizes the equilibrium standards (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ;
𝜎$. , 𝜎&. , 𝜎'. ) under respective standards regimes, where H and L represent (H, H, H) and (L, L, L), respectively.

Table 1: Summary of the equilibrium standards (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. )Case 1 (𝟎 ≤ 𝜽 < 𝜽𝑼 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. )=(H, H, H; H, H, H; H, H, H) under all regimes, meaningthat 𝑆𝑊!: = 𝑆𝑊!< = 𝑆𝑊!> for J = A, B, C. In other words, 𝑆𝑊!< − 𝑆𝑊!: = 𝑆𝑊!> − 𝑆𝑊!: = 0 for both
member and nonmember countries.
Case 2 (𝜽𝑼 ≤ 𝜽 < 𝜽)In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) =(H, L, L; L, H, L; L, L, H) under unconstrained
noncooperative equilibrium. Because (𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ; 𝑐$. , 𝑐&. , 𝑐'. ) = (0, c, c; c, 0, c; c, c, 0) and(𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (θ, 0, 0; 0, θ, 0; 0, 0, θ),𝑆𝑊,: = 𝑆𝑊-< = 𝑆𝑊.> =(3 − 2𝑐)*
1 + 2𝑐 (1 + 2𝑐)* (1 − 2𝑐)*
−𝜃
+
+
32
4
16
8

holds.
Under NT and MR, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (H, H, H; H, H, H; L, L, H) holds. Since(𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ;𝑐$. , 𝑐&. , 𝑐'. ) = (0, 0, 0; 0, 0, 0; c, c, 0) and (𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (θ,θ, θ; θ, θ, θ; 0, 0, θ), the respective countries’ welfare can be represented as follows:37

𝑆𝑊!< = 𝑆𝑊!> =13 3𝜃 1 (1 − 2𝑐)*−
+ +, 𝐽 = 𝐴, 𝐵,
32 4 816

𝑆𝑊.< = 𝑆𝑊.> =(01*')(
0*

−𝜃

56*'
7

+

(56*')(
58

5

+ ;.

Therefore, it follows that
𝑆𝑊!< − 𝑆𝑊!: = 𝑆𝑊!> − 𝑆𝑊!: ='(01=');

𝑆𝑊.< − 𝑆𝑊.: = 𝑆𝑊.> − 𝑆𝑊.: =51'− 𝜃 * , 𝐽 = 𝐴, 𝐵'(51')*> 0.

𝑵

Case 3 (𝜽 ≤ θ < 𝜽 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (H, L, L; L, H, L; L, L, H) under unconstrained
noncooperative equilibrium. Therefore, each country’s welfare is the same as in case 2:

𝑆𝑊,: = 𝑆𝑊-< = 𝑆𝑊.> =(3 − 2𝑐)*
1 + 2𝑐 (1 + 2𝑐)* (1 − 2𝑐)*
−𝜃
+
+
32
4
16
8

Under NT and MR, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. = (H, H, L; H, H, L; L, L, H) holds. This means that(𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ;𝑐$. , 𝑐&. , 𝑐'. )= (0, 0, c; 0, 0, c; c, c, 0) and (𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (θ,θ, 0; 0, θ, θ; 0, 0, θ) and, thus, the respective countries’ welfare can be represented as follows:
𝑆𝑊!< = 𝑆𝑊!> =(3 − 2𝑐)*
1 + 𝑐 (1 + 𝑐)* (1 − 2𝑐)*−𝜃++
, 𝐽 = 𝐴, 𝐵,
32
2
8
16

𝑆𝑊.< = 𝑆𝑊.> =(01*')(
0*

−𝜃

56*'
7

+

(510')(;+(56*')(
58.

Therefore, it follows that
𝑆𝑊!< − 𝑆𝑊!: = 𝑆𝑊!> − 𝑆𝑊!: ='(5715=')0*𝑆𝑊.< − 𝑆𝑊.: = 𝑆𝑊.> − 𝑆𝑊.: = −38C− 7 , 𝐽 = 𝐴, 𝐵'(*1=')
;

< 0.

𝑵

𝑼

Case 4 (𝜽 ≤ θ < 𝜽 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) =(H, L, L; L, H, L; L, L, H) under unconstrained
noncooperative equilibrium. Therefore, each country’s welfare is the same as in Case 2:

𝑆𝑊,: = 𝑆𝑊-< = 𝑆𝑊.> =(3 − 2𝑐)*
1 + 2𝑐 (1 + 2𝑐)* (1 − 2𝑐)*
−𝜃
+
+
32
4
16
8

Under NT, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (L, L, L; L, L, L; L, L, H) holds. Considering that(𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ;𝑐$. , 𝑐&. , 𝑐'. ) = (c, c, c; c, c, c; c, c, 0) and (𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (0,0, 0; 0, 0, 0; 0, 0, θ), the respective countries’ welfare can be represented as follows:9(1 − 𝑐)* (1 − 𝑐)* (1 − 2𝑐)*++
, 𝐽 = 𝐴, 𝐵,
32
8
16

𝑆𝑊,< = 𝑆𝑊-< =𝑆𝑊.< =(01*')(
0*

−𝜃

56*'
7

+

(51')(;+(56*')(
58.

Under MR, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (H, H, L; H, H, L; L, L, H) holds. Then, the expressions
for the respective countries’ welfare are the same as those in Case 3:

𝑆𝑊,> = 𝑆𝑊-> =(3 − 𝑐)*
1 + 𝑐 (1 − 𝑐)* (1 − 2𝑐)*−𝜃++
, 𝐽 = 𝐴, 𝐵,
32
2
8
16

𝑆𝑊.> =(01*')(
0*

−𝜃

56*'

+

7

(510')(;+(56*')(
58.

Therefore, we obtain the following results regarding the comparison of the respective countries’ welfare under NTwith that under the unconstrained noncooperative equilibrium:
𝑆𝑊!< − 𝑆𝑊!: =1@'(*6')0*

𝑆𝑊.< − 𝑆𝑊.: =

39

+𝜃

56*'
7

'(*10');, 𝐽 = 𝐴, 𝐵

> 0.

As for the comparison of the respective countries’ welfare under MR with that under the unconstrained
noncooperative equilibrium, we obtain the following results:
𝑆𝑊!> − 𝑆𝑊!: =𝑐(14 − 15𝑐) 𝜃− , 𝐽 = 𝐴, 𝐵
32
4

𝑆𝑊.> − 𝑆𝑊.: = −𝑼𝑐(2 − 5𝑐)
< 0.
8

𝑴

Case 5 (𝜽 ≤ θ < 𝜽 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) =(L, L, L; L, L, L; L, L, L) under unconstrained
noncooperative equilibrium and NT. Since (𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ;𝑐$. , 𝑐&. , 𝑐'. ) = (c, c, c; c, c, c; c, c, c) and(𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (0, 0, 0; 0, 0, 0; 0, 0, 0), it follows that

𝑆𝑊!: = 𝑆𝑊!< =9(1 − 𝑐)* 3(1 − 𝑐)* 15(1 − 𝑐)*+=, 𝐽 = 𝐴, 𝐵, 𝐶.
32
16
32

Therefore, we obtain the following result regarding the comparison of welfare:𝑆𝑊!: = 𝑆𝑊!< , 𝐽 = 𝐴, 𝐵, 𝐶.
Under MR, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (H, H, L; H, H, L; L, L, L) holds. Thismeans(𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ;𝑐$. , 𝑐&. , 𝑐'. ) = (0, 0, c; 0, 0, c; c, c, c) and (𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. )= (θ, θ, 0; θ, θ, 0; 0, 0, 0), the respective countries’ welfare can be represented as follows:

𝑆𝑊,> = 𝑆𝑊-> =(3 − 𝑐)*
1 + 𝑐 (1 + 𝑐)* (1 − 𝑐)*
−𝜃
+
+
,
32
2
8
16

𝑆𝑊.> =

G(51')(
0*+(510')(;+(51')(
58.

Therefore, it follows that
𝑆𝑊!> − 𝑆𝑊!: =𝑐(7 − 2𝑐)1+𝑐−𝜃
, 𝐽 = 𝐴, 𝐵
8240

𝑆𝑊.> − 𝑆𝑊.: = −'(51*')*< 0.

𝑴

Case 6 (𝜽 ≤ θ)
In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. )=(L, L, L; L, L, L; L, L, L) under all regimes, meaning that
𝑆𝑊!> = 𝑆𝑊!< = 𝑆𝑊!: for all J = A, B, C. In other words, 𝑆𝑊!> − 𝑆𝑊!: = 𝑆𝑊!< − 𝑆𝑊!: = 0 for both
member and nonmember countries.

A.5 Proof of Proposition 6
As the objective function of each country’s government is (4) and the government’s choice is either FR or NR, we
can refer to the discussion in the proof of Proposition 1; that is, FR is preferred to NR if and only if θ >and vice versa. Letting 𝜃 ∗< ≡55'(*1')*7

55'(*1')*7,, we obtain the statement of the proposition.

A.6 Proof of Proposition 7
We first prove the following lemma.
Lemma A.3 Under a multilateral agreement of standards policy with MR, each country’s equilibrium standards
are as follows:• No regulation for 0 ≤ θ <𝜃5> ,• No regulation or Full regulation for 𝜃5> ≤ θ <𝜃*> and• Full regulation for 𝜃*> ≤ θ,
where 𝜃5> ≡ (42 + 13c) c/8(1 + 2c) and 𝜃*> ≡ (42 − 55c) c/8(1 − 2c).

41

Proof Let us consider country A’s government, whose objective function is given by (3). To consider country A’s
best response strategy, we need to calculate country A’s welfare when (i) both countries B and C choose FR, (ii)both countries B and C choose NR, and (iii) one country chooses FR and the other country chooses NR.
Starting from the case when both countries B and C choose FR (i.e., 𝑐&! = 𝑐'! = 𝑐 and θ&! = θ'! = 0 for J = A,B, C), country A’s welfare can be calculated as

𝑆𝑊 , =

15(1 − 𝑐)*32

if country A chooses FR (i.e., 𝑐$! = c and θ$! = 0 for J = A, B, C), and𝑆𝑊 , =(3 − 2𝑐)*
1 + 2𝑐(1 + 2𝑐)*
−𝜃
+3
32
4
16

If it chooses NR (i.e., 𝑐$! = 0 and θ$! = θ for J = A, B, C). Comparing the levels of 𝑆𝑊 , under different
strategies, it follows that'(7*650')

FR≻NR iff 𝜃 > ;(56*') ≡ 𝜃5> .
We next consider the case when both countries B and C choose NR (i.e., 𝑐&! = 𝑐'! = 0 and θ&! = θ'! = θ for
J = A, B, C) Then, country A’s welfare can be calculated as3(1 − 3𝑐)*
1 + 𝑐 (3 − 𝑐)*
𝑆𝑊 =
−𝜃
+
16
2
32
,

if country A chooses FR, and𝑆𝑊 , =

15 3
− 𝜃
32 4

if it chooses NR. Comparing the levels of SWA, it follows that'(7*1==')FR≻NR iff 𝜃 > ;(51*') ≡ 𝜃*> .

42

Finally, let us consider the case when one country, say B, chooses FR while the other country, say C, chooses NR((i.e., 𝑐&! = 𝑐, 𝑐'! = 0, θ&! = 0 and θ'! = θ for J = A, B, C). Then, country A’s welfare can be calculated as3(1 − 3𝑐)*
1 + 2𝑐 (3 − 2𝑐)*
𝑆𝑊 =
−𝜃
+
16
4
32
,

if country A chooses FR, and3(1 + 𝑐)*
1 + 𝑐 (3 − 𝑐)*
𝑆𝑊 =
−𝜃
+
16
2
32
,

if it chooses NR. Comparing the levels of SWA, it follows that
FR≻NR iff 𝜃 >*5'(*1');≡ 𝜃0> .

Comparing the threshold values of θ, we obtain 𝜃5> < 𝜃0> < 𝜃*> . Thus, we can summarize country A’s best
response strategies by Figure A.5. By symmetry, countries B and C follow a similar pattern of best response
strategies.

Figure A.5: Summary of country A’s best response strategies

43

From Figure A.5, it immediately follows that the Nash equilibrium standards for each country are uniquelydetermined for 0 ≤ θ < 𝜃5> , in which NR is the Nash equilibrium standards and for 𝜃*> ≤ θ, in which FR is the
Nash equilibrium standards. For 𝜃5> ≤ θ < 𝜃*> , there are two Nash equilibria, NR and FR. Then, we obtain thestatement of the lemma.
As there are multiple Nash equilibria when 𝜃5> ≤ θ < 𝜃*> , we make a refinement of equilibrium using thefollowing lemma.
Lemma A.4 In the most cooperative equilibrium under MR regime, the countries will coordinate on FR when θ∈ [𝜃5> , 𝜃*> ].
Proof We begin with the derivation of optimal standards when the countries jointly determine their standards tomaximize the sum of their welfare, ∑!#,,-,. 𝑆𝑊 ! . However, since all countries are symmetric, the joint-welfare
maximization problem is equivalent to choosing country J’s standards policy (𝜎$! , 𝜎&! , 𝜎'! ) ) that maximizes
𝐶𝑆! + n 𝜋"!
"#$,&,'=(01∑!"#,%,&

0*

'

'! )(

− ∑"∈$,&,' 𝜃"!

''

510'! 6∑)*! ')7+ ∑"#$,&,'''(510'! 6∑)*! ') )(58.

(A.14)

We consider the following strategies regarding country J’s choice of standards: (i) full regulation (FR) in which𝜎"! = L for k = a, b, c, (ii) no regulation (NR) in which 𝜎"! = H for k = a, b, c, and (iii) discrimination (D) in which
𝜎9! = H and 𝜎"! = L for k ̸= j. In the respective regimes, (A.14) can be rewritten as follows:
FR: 𝐶𝑆! + ∑"#$,&,' 𝜋"! =5=(51')(;(A.15)

NR: 𝐶𝑆! + ∑"#$,&,' 𝜋"! = 0* − 7 𝜃;

(A.16)(01*')(

D: 𝐶𝑆! + ∑"#$,&,' 𝜋"! =

0*

0*
5=

0

−𝜃

56*'
7

+3

From (A.15), (A.16) and (A.17), we obtain the following threshold values for 𝜃

44(56*')(
58(A.17)

𝐹𝑅 ≻ 𝑁𝑅 iff 𝜃 >='(*1');≡ 𝜃5∗ ;'(5?650')

𝐹𝑅 ≻ 𝐷 iff 𝜃 < ;(56*') ≡ 𝜃*∗ ;'(=1@')𝑁𝑅 ≻ 𝐷 iff 𝜃 < 7(51') ≡ 𝜃0∗ .
It can be easily verified that under Assumption 1, 𝜃*∗ < 𝜃5∗ < 𝜃0∗ holds. Then, the optimal standards policy underinternational cooperation can be represented by Figure A.6; that is, NR is chosen for 0 ≤ θ< 𝜃5∗ and FR is chosenfor 𝜃5∗ ≤θ.
It can be verified that 𝜃5∗ is smaller than 𝜃5> . This means that for θ ∈ [𝜃5> , 𝜃*> ] the countries have an incentive
to coordinate on FR even though there are multiple Nash equilibria in the policy game under MR.
Proof of Proposition 7
In light of Lemma A.4, Lemma A.3 is modified to the statement that the most cooperative equilibrium outcome is
to choose NR for 0 ≤ θ < 𝜃5> and FR for 𝜃5> ≤ θ. By redefining 𝜃5> by 𝜃 ∗> , we obtain the statement of
Proposition 7.

Figure A.6: Optimal standards in the cooperative solution

A.7 Comparison of welfare between bilateral and multilateral agreements

45

From Propositions 1, 2, 3, 6, and 7, we obtain the respective countries’ equilibrium standards under bilateral andmultilateral standards regimes depending on the value of θ, as shown in Figure 4. Tables 2 and 3 summarize theequilibrium standards (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) under NT and MR, respectively.

Table 2: Summary of the equilibrium standards (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) based on NT

Table 3: Summary of the equilibrium standards (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) based on MR
Let us begin with the comparison of each country’s welfare under bilateral and multilateral agreements based on
NT. We have already denoted country J’s welfare under the bilateral agreement based on NT by 𝑆𝑊!< , and let us
denote its welfare under multilateral agreement by 𝑆𝑊!<> J = A, B, C.
Case 1N (𝟎 ≤ 𝜽 < 𝜽𝑼 )In this case, 𝜎"! = H for k= a, b, c and J =A, B, C under all regimes, meaning that 𝑆𝑊!< = 𝑆𝑊!<> for J = A, B,
C. In other words, a shift from bilateral to the multilateral agreement has no effect on both member and nonmember
countries’ welfare.
46

Case 2N (𝜽𝑼 ≤ 𝜽 < 𝜽)In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (H, H, H; H, H, H; L, L, H) holds under the NT-based
bilateral agreement. Since (𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ; 𝑐$. , 𝑐&. , 𝑐'. ) = (0, 0, 0; 0, 0, 0; c, c, 0), and(𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (θ, θ, θ; θ, θ, θ; 0, 0, θ) the respective countries’ welfare can be
represented as follows:

𝑆𝑊!< =

13 3𝜃 (1 − 2𝑐)*−+
, 𝐽 = 𝐴, 𝐵,
32 4
16

𝑆𝑊.< =(01*')(
0*

−𝜃

56*'
7

+

(56*')(
58

5

+ ;.

Under the NT-based multilateral agreement, 𝜎"! = H holds, which means 𝑐"! = 0 and θ"! = θ for k = a, b, c and J= A, B, C. Each country’s welfare is given by
𝑆𝑊!<> =15 3𝜃−, 𝐽 = 𝐴, 𝐵, 𝐶
32 4

Therefore, we obtain the following results regarding the comparison of welfare:𝑆𝑊!<> − 𝑆𝑊!< =𝑐(1 − 𝑐)
> 0, 𝐽 = 𝐴, 𝐵
4

𝑆𝑊.<> − 𝑆𝑊.< =−3𝑐 * + 4𝑐𝜃 + 𝑐 − 4𝜃.
8

It can be verified that 𝑆𝑊.<> − 𝑆𝑊.< is equal to 0 when θ = 𝜃 : and monotonically decreasing in θ. Thus,
𝑆𝑊.<> − 𝑆𝑊.< < 0 for 𝜃 : ≤ 𝜃 < 𝜃.
Case 3N (𝜽 ≤ 𝜽 < 𝜽∗𝑵 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = ( H, H, L; H, H, L; L, L, H) holds under the NT-based
bilateral agreement. Because (𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ; 𝑐$. , 𝑐&. , 𝑐'. ) = (0, 0, c; 0, 0, c; c, c, 0) and47

(𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. )= (θ, θ, 0; 0, θ, θ; 0, 0, θ), the respective countries’ welfare can be
represented as follows:
𝑆𝑊!< =(3 − 2𝑐)*
1 + 𝑐 (1 + 𝑐)* (1 − 2𝑐)*−𝜃++
, 𝐽 = 𝐴, 𝐵,
32
2
8
16
𝑆𝑊.< =(01*')(
0*

−𝜃

56*'
7

+

(510')(;+(56*')(
58.

As 𝜎"! = H holds for k = a, b, c and J = A, B, C under the NT-based multilateral agreement, each country’s welfare
5=0C

is given by 𝑆𝑊!<> =0* − 7 , J = A, B, C. Therefore, it follows that
𝑆𝑊!<> − 𝑆𝑊!< =𝑐(6 − 13𝑐) − 8𝜃(1 − 2𝑐), 𝐽 = 𝐴, 𝐵
32

𝑆𝑊.<> − 𝑆𝑊.< =𝑐(7 − 12𝑐) − 4𝜃(1 − 𝑐).
8

It can be verified that 𝑆𝑊!< − 𝑆𝑊!<> is monotonically decreasing in θ, and 𝑆𝑊!< − 𝑆𝑊!<> is positive if
𝜃 = 𝜃 but negative if 𝜃 = 𝜃 ∗< , J = A, B. Thus, there exists a threshold value θ′ such that 𝑆𝑊!< − 𝑆𝑊!<> = 0.
This threshold value is explicitly derived as θ′ = c (6 − 13c)/8(1 − 2c). As for the sign of 𝑆𝑊.< − 𝑆𝑊.<> it canbe verified that although the 𝑆𝑊.<> − 𝑆𝑊.< is monotonically decreasing in θ, the sign of this expression ispositive for all θ ∈ [𝜃, 𝜃 ∗< ].
𝑵

Case 4N (𝜽∗𝑵 ≤ 𝜽 < 𝜽 )In this case, the expressions for the respective countries’ welfare under the NT-based bilateral agreement are thesame as those in Case 3N. However, under the multilateral agreement, 𝜎"! = L holds, and thus 𝑐"! = c and θ"! =0 for k = a, b, c and J = A, B, C. Each country’s welfare is given by

𝑆𝑊!<> =

15(1 − 𝑐)*, 𝐽 = 𝐴, 𝐵, 𝐶.
32

Therefore, we obtain the following results regarding the comparison of welfare:48

𝑆𝑊!<> − 𝑆𝑊!< =8𝜃(1 + 𝑐) − (12 − 𝑐)𝑐, 𝐽 = 𝐴, 𝐵
16

𝑆𝑊.<> − 𝑆𝑊.< = 𝜃

1 + 2𝑐 𝑐(2 + 33𝑐)
−
.
4
32

It can be verified that 𝑆𝑊!<> − 𝑆𝑊!< is negative, J = A, B, while 𝑆𝑊.<> − 𝑆𝑊.< is positive for all θ ∈ [𝜃 ∗< ,
<

𝜃 ].
𝑵

𝑼

Case 5N (𝜽 ≤ 𝜽 < 𝜽 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. ) = (L, L, L; L, L, L; L, L, H) holds under the NT-based
bilateral agreement. This means that (𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ; 𝑐$. , 𝑐&. , 𝑐'. ) = (c, c, c; c, c, c; c, c, 0) and(𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (0, 0, 0; 0, 0, 0; 0, 0, θ) and, thus, the respective countries’ welfare canbe represented as follows:

𝑆𝑊!< =
𝑆𝑊.< =

13(1 − 𝑐)* (1 − 2𝑐)*+
, 𝐽 = 𝐴, 𝐵.
32
16(01*')(
0*

−𝜃

56*'
7

+

(51')(;+(56*')(
58.

As 𝜎"! = L holds for k = a, b, c and J = A, B, C under the NT-based multilateral agreement, each country’s welfare
5=(51')(

is given by 𝑆𝑊!< =0*,J = A, B, C. Therefore, it follows that
𝑆𝑊!<> − 𝑆𝑊!< =(2 − 3𝑐)𝑐> 0, 𝐽 = 𝐴, 𝐵
16

𝑆𝑊.<> − 𝑆𝑊.< =8(1 + 2𝑐)𝜃 − 𝑐(18 + 𝑐).
32:

It can be verified that𝑆𝑊.<> − 𝑆𝑊.< is monotonically increasing in θ and equal to 0 if θ = 𝜃 . Thus, the sign of<:𝑆𝑊.<> − 𝑆𝑊.< is negative for 𝜃 ≤ 𝜃 < 𝜃 .
𝑼Case 6N (𝜽 ≤ 𝜽)49

In this case, 𝜎"! = L for k = a, b, c and J = A, B, C under all regimes, meaning that 𝑆𝑊!<> − 𝑆𝑊!< for J= A, B,
C.
We next consider the case of standards agreements based on MR. We have already denoted country J’s welfare
under the MR-based bilateral agreement by 𝑆𝑊!> , and let us denote its welfare under multilateral agreement by
𝑆𝑊!>> , J = A, B, C.
From Tables 2 and 3, we can easily verify that the outcomes under Cases (1M), (2M), (3M), and (6M) are the sameas Cases (1N), (2N), (3N), and (6N), respectively. Therefore, we omit the analysis of welfare comparison for thesecases.
𝑼

𝑴

Case 4M ( 𝜽 ≤ 𝜽 < 𝜽 )In this case, (𝜎$, , 𝜎&, , 𝜎', ; 𝜎$- , 𝜎&- , 𝜎'- ; 𝜎$. , 𝜎&. , 𝜎'. )=(H, H, L; H, H, L; L, L, L) holds under the MR-based
bilateral agreement. This means that (𝑐$, , 𝑐&, , 𝑐', ; 𝑐$- , 𝑐&- , 𝑐'- ;𝑐$. , 𝑐&. , 𝑐'. ) = (0, 0, c; 0, 0, c; c, c, c) and(𝜃$, , 𝜃&, , 𝜃', ; 𝜃$- , 𝜃&- , 𝜃'- ; 𝜃$. , 𝜃&. , 𝜃'. ) = (θ, θ, 0; θ, θ, 0; 0, 0, 0) and thus, it follows that

𝑆𝑊!> =(3 − 𝑐)*
1 + 𝑐 (1 + 𝑐)* (1 − 𝑐)*−𝜃++, 𝐽 = 𝐴, 𝐵.
32
2
8
16

𝑆𝑊.> =

11(1 − 𝑐)* (1 − 3𝑐)*
+
.
32
8

Under the MR-based multilateral agreement, 𝜎"! = H holds, which means 𝑐"! = 0 and θ"! = θ for k = a, b, c and
5=0C

J = A, B, C. Each country’s welfare is thus given by 𝑆𝑊!>> =0* − 7 , J = A, B, C. Therefore, we obtain thefollowing results regarding the comparison of welfare:𝑆𝑊!>> − 𝑆𝑊!> =𝑐(2 − 7𝑐) − 8𝜃(1 − 2𝑐), 𝐽 = 𝐴, 𝐵
32

𝑆𝑊.<> − 𝑆𝑊.< =(46 − 47𝑐)𝑐 − 24𝜃
.
32
50

𝑼

It can be verified that the signs of the above expressions are both negative for 𝜽 ≤ 𝜽 < 𝜽

𝑴

.

𝑴

Case 5M (𝜽 ≤ 𝜽 < 𝜽∗𝑴 )In this case, under the MR-based bilateral agreement, 𝜎"! = L holds, which means 𝑐"! = c and θ"! = 0 for k = a,b, c and J = A, B, C, for k = a, b, c and J = A, B, C. Each country’s welfare is𝑆𝑊!> =

15(1 − 𝑐)*, 𝐽 = 𝐴, 𝐵, 𝐶
32

Under the MR-based multilateral agreement, 𝜎"! = L holds, which means 𝑐"! = 0 and θ"! = θ for k = a, b, c
and J = A, B, C. Each country’s welfare is
𝑆𝑊!>> =

3(5 − 8𝜃), 𝐽 = 𝐴, 𝐵, 𝐶.
32

Thus, it follows that
𝑆𝑊!>> − 𝑆𝑊!> =0[=(*1')'1;C]0*.
>

It can be verified that the above equation is monotonically decreasing in θ and is negative if θ = 𝜃 . Thus,>

𝑆𝑊!>> − 𝑆𝑊!> < 0 for 𝜃 ≤ 𝜃 < 𝜃 ∗>51

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