Article XXIV of the GATT: Good, Bad, orBoth?

Kamal Saggi∗ and Halis Murat Yildiz†

Preliminary draft — comments welcome.

Abstract

Article XXIV of the General Agreement on Tariffs and Trade(GATT) provides an important exception to Article I (most favorednation clause) by permitting countries to enter into preferential freetrade agreements (PTAs). Does the existence of Article XXIV under-mine multilateral trade liberalization? Would aggregate world welfarebe higher if PTAs could not be formed? To answer these questions,this paper endogenizes the formation of free trade agreements (FTAs)in a three-country oligopoly model of intraindustry trade where coun-tries are asymmetric with respect to market sizes and production costs.Two tariff games are contrasted: one where countries have the optionto form FTAs and another where they do not. We show that free tradeis less likely to occur as an equilibrium outcome under the FTA optiongame and that the FTA option lowers world welfare when countriesare relatively symmetric. Also, the country with the largest market(and/or the highest cost) always benefits from the existence of theFTA option.Keywords: Multilateral Trade Liberalization, Free Trade Agree-

ments, GATT, Intraindustry Trade, Oilgopoly. JEL Classifications:F13, F12.

∗Department of Economics, Southern Methodist University, Dallas, TX 75275-0496.Phone: 214-768-3274; fax: 214-768-1821; e-mail: ksaggi@mail.smu.edu.

†Department of Economics, Ryerson University, 350 Victoria Street, Toronto, ON,Canada M5B 2K3. Phone: 416-979-5000 (ext 6689); fax: 416-979-5289; e-mail: hy-ildiz@ryerson.ca.

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1 Introduction

By permitting member countries of the World Trade Organization (WTO)to preferential trade agreement (PTA) wherein a group of member countriesof the WTO extend tariff concessions to each other that they do not extendto other members, Article XXIV of the General Agreement on Tariffs andTrade (GATT) provides an important exception to the most-favored-nation(MFN) clause (contained in Article I of GATT). Since the notion of non-discrimination as specified by the MFN clause is at the heart of the WTOsystem, the existence of Article XXIV has not been without controversy.1

Does the option of forming PTAs adversely affect incentives for multilateraltrade liberalization on the part of member countries of the WTO? Wouldn’tthe ultimate goal of GATT (i.e. multilateral free trade) be easier to obtain ifmember countries of theWTO had to strictly abide by Article I and could notform PTAs? The present paper addresses these questions in a three-countryoligopoly model of intraindustry trade wherein countries differ with respectto their market sizes and production costs.2 The underlying asymmetry inthe model sheds light on underlying characteristics that determine how thePTA option affects individual countries as well as on the welfare effects ofPTAs.That the above questions are important is evident from the fact that over

150 PTAs are in force today and almost all major countries participate insome type of a PTA or another (WTO, 2002). The trend toward the forma-tion of PTAs has intensified in recent years — most PTAs have been concludedin the last 10 years or so and since 1995 over 100 such agreements have beennotified to the WTO. Prominent examples of PTAs include the North Amer-ican Free Trade Agreement (NAFTA), the South American Common Market(MERCOSUR), the Association of South East Asian Nations (ASEAN) FreeTrade Area, the Andean Pact, and the numerous agreements of the European

1To minimize the potential harmful effects of PTAs Article XXIV article requires that:(i) a PTA must cover almost all trade between its members; (ii) PTA members must fullyeliminate tariffs and other trade restrictions on each other; and (iii) they should not raisetariffs (or any other trade restrictions) on non-members.

2These questions are related but not completely equivalent to the question posed byJagdish Bhagwati (1991): “Are PTAs building or stumbling blocks for multilateral tradeliberalization?” The difference is that in our approach, both preferential and multilateraltrade liberalization are endogenous and article XXIV is the underlying exogenous factor.See Bhagwati and Panagariya (1999) and Winters (1998) for overviews of the main policyquestions in the area.

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Union with other countries.3

Restricting attention to free trade agreements (FTAs), we evaluate theincentives countries have for multilateral trade liberalization under two sce-narios: one in which they can avail of the option to form FTAs and anotherwhere this option does not exist. Formally, the paper compares two tariffgames. The FTA game proceeds as follows. In the first stage, each countryannounces a set of countries with whom it wants to form a trade agreement.A bilateral FTA is formed if both countries want the agreement. Similarly,multilateral free trade emerges only when all countries want such an agree-ment. Next, given the constraints imposed by the policy regime in place,countries simultaneously choose their tariffs to maximize national welfare(defined as the sum of the local firm’s profits, consumer surplus, and tariffrevenue).4 Finally, firms compete in the product market in a Cournot fash-ion where individual country markets are assumed to be segmented. In theno FTA game, in stage one, countries must choose between participating inmultilateral free trade or utilizing individually optimal tariffs (i.e. no tradeagreement at all).From each country’s perspective, an FTA embodies the following trade-

off. On the one hand, joining an FTA implies that the domestic surplus islowered relative to the case where (optimally chosen) tariffs can be used. Onthe other hand, being part of an FTA increases export profits of members ineach other’s markets. Since countries are asymmetric, the loss in domesticsurplus and the gain from increased market access abroad generally differacross countries. In fact, a country’s loss in domestic surplus from an FTAincreases with own market size while the gain in export profits increaseswith the partner’s market size. As a result, an FTA between the largestand smallest countries is never stable. Furthermore, a country’s gain fromincreased market access abroad decreases with own cost whereas it increaseswith a partner’s cost. As a result, the country with the biggest market sizeand the one with the highest cost are the most FTA desirable partners fromthe viewpoint of other countries.

3The phrase ‘regional trade agreements’ is often used to describe trade liberalizationamongst a few countries. However, the phrase ‘preferential trade liberalization’ is more aptsince such liberalization need not occur only among geographically proximate countries(although it often does).

4Under bilateral FTAs, a country imposes optimally chosen tariffs on non-members andno tariffs on members. Under the multilateral trade agreement, all countries practice freetrade.

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Our approach is similar to that of Riezman (1999) who also asks whetherthe PTA option facilitates or hinders the achievement of global free trade.However, there are important differences between the two papers. First,our model differs substantially from Riezman (1999) who utilizes a simplegeneral equilibrium framework with fixed endowment levels. In his model,trade is inter-industry in nature and countries impose tariffs to improve theirterms of trade. By contrast, in the oligopoly model presented here trade isintraindustry in nature (as in Brander and Krugman, 1983) and countriesuse tariffs to extract rents from foreign firms (as in Brander and Spencer,1984). Second, and more importantly, our model allows us to address issuesrelated to asymmetries between countries; such is not the case in Riezman(1999). For example, our model permits an assessment of whether or notMFN facilitates multilateral free trade.5

While we ask questions related to those examined in Krishna (1998), theconceptual approach of our paper is quite different. Using a similar underly-ing trade model, Krishna (1998) explores the relationship between FTAs andmultilateral trade liberalization. In his model, tariffs are exogenously given,but FTAs are endogenous in the sense that only those FTAs that benefitproducers in member countries are considered. Krishna (1998) finds that theformation of FTAs undermines support for multilateral trade liberalization.The present paper supports this result because we show that FTAs reducethe likelihood of obtaining multilateral free trade. On the other hand, weargue that in a world in which the FTA option does not exist is not nec-essarily superior to one where it does exist: there are regions over whichmultilateral free trade cannot be obtained but welfare improving PTAs arefeasible. Shutting out FTAs would imply that such welfare gains would haveto be foregone. Furthermore, our analysis of cost asymmetries delivers aninteresting insight that we believe is truly novel to the literature: a patternof FTAs where the lowest cost country forms bilateral PTAs with the othertwo can be actually welfare superior to multilateral free trade.The ‘stumbling versus building block’ question posed by Bhagwati (1991)

has also been analyzed extensively in the literature through models that allowfor repeated interaction between countries — see Riezman (1991), Bagwell andStaiger (1997a, 1997b, and 1998a), Bond et. al. (2001), and Bond and Sy-

5It is also worth noting that Riezman (1999) uses the cooperative solution conceptof the core to illustrates his results via numerical examples whereas we analyze a non-cooperative game and analytically derive its sub-game perfect and coalition proof Nashequilibria.

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ropoulos (1996). In these models, cooperation is required to be self-enforcingin the sense that each country balances the current benefit of deviating fromthe cooperative tariff against the future losses caused by the breakdown ofmultilateral cooperation that results from its defection.6 In our model, anFTA is self-enforcing in the sense that it needs to be immune to crediblecoalitional deviations by both members and non-members.Levy (1997) focuses on political economy considerations that we abstract

from and finds that in the monopolistic competition model of intraindustrytrade in differentiated goods, PTAs can supplant multilateral trade liberal-ization.7 Unlike in the present paper, tariffs play virtually no role in Levy’sanalysis since only the choice between free trade (bilateral as well as multilat-eral) and autarky is considered. Freund (2000b) investigates how (exogenous)multilateral trade liberalization affects incentives for preferential trade liber-alization in the oligopoly trade model.8 Her main result is that multilateraltrade liberalization encourages the formation of PTAs and makes it morelikely that such agreements are non-credible.

2 Model

We develop a simple oligopoly model of trade in which each country has aunilateral incentive to impose rent extracting tariffs on those trading partnerswith whom it does not have any trade agreement. There are three countriesand two goods: x and y. Countries are asymmetric with respect to theirmarket size and production costs. Good x is produced by a single profit-maximizing firm in each country at a constant marginal cost in terms of thenumeraire good y.9 Preferences over the two goods are quasilinear:

Ui(xi, yi) = u(xi) + yi (1)

6The literature on PTAs is rather extensive and we only discuss closely related papers.The reader is referred to Bhagwati et. al. (1999) for a collection of many of the importantpapers in the area.

7See also Grossman and Helpman (1995) for a political economy model of trade agree-ments wherein trade protection is a function of contributions made by agents to theirrespective governments.

8By contrast, in our approach, all types of trade agreements are endogenously deter-mined.

9The gains from trade stem from reduced market power in the domestic industry. Tothis end, the monopoly assumption is not crucial but is the simplest way to representmarket power.

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Furthermore, u(xi) is assumed to be quadratic:

u(xi) = αiXi − X2i

2

where xi ≡ (xii, xji, xki) is country i’s consumption profile, andXi ≡P3

j=1 xji.Note that xji is country i’s consumption of country j’s product (or denotesthe output sold by country j’s firm in country i),Due to the quasilinear nature of the utility function, country i’s inverse

demand function is given by:

Pi(xi) = αi −X3

j=1xji (2)

where αi represents the market size of each country. Let country 1 have thelargest market for good x and country 3 the smallest:

α1 ≥ α2 ≥ α3 (3)

Consider a three stage game. In the first stage, each country announces aset of countries with whom it wants to form an agreement. An FTA betweentwo countries is formed if both countries want the agreement. Similarly, mul-tilateral free trade emerges only when all countries want such an agreement.Next, countries simultaneously choose their tariffs given the agreement(s)formed in the first stage. Finally, firms compete in the product market in aCournot fashion and markets are segmented so that each firm makes inde-pendent decisions regarding how much to sell in each market (as in Branderand Krugman (1983) and Brander and Spencer (1984)).In the absence of any trade agreement, firm j faces a specific tariff tji when

exporting to country i.10 Denote the vector of the tariff schedule of countryi by ti ≡ (tji, tki).11 Since Article I of GATT forbids tariff discrimination,in the absence of any FTAs we restrict attention to the case where tji =tki = ti for i, j, k. In section 5, we evaluate the contribution of MFN to tradeliberalization by allowing countries to tariff discriminate even in the absenceof any FTAs.12

10It is obvious that tii = 0 for all i .11We also assume that the countries do not impose tariffs on the numeraire good that

may be traded internationally in order to balance trade.12Note that, relative to discrimination, MFN treatment not only changes the optimal

tariffs in the absence of any trade agreements but also changes non-member countries’optimal tariffs under a bilateral FTA.

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Country j’s effective marginal cost of exporting to country i, denoted bycji, equals:

cji = cj + tji (4)

where cj denotes the marginal cost of production of country j’s firm. Letcountry 1 be the lowest cost producer and country 3 the highest:

c3 ≥ c2 ≥ c1 (5)

Country j’s profit function for exports to country i, denoted by Πji, can bewritten as:

Πji = xjiPi(Xi)− cjixji (6)

First order conditions for profit maximization yields equilibrium outputlevels:13

xii =αi − 3ci +

Pj,j 6=i cji

4and xji =

αi + ci − 3cji + cki4

, k 6= i, j. (7)

Similarly, equilibrium price in country i is easily calculated:

Pi =αi + ci +

Pj,j 6=i cji

4(8)

Using (7) and (8), equilibrium profits are:

Πii = x2ii and Πji = x2ji (9)

The following comparative statics are standard:

∂Πji

∂tji= −3xji

2< 0,

∂Πii

∂tji=

xii2

> 0, and∂Πki

∂tji=

xki2

> 0. (10)

Country i’s welfare function, Wi consists of four components: domestic con-sumer surplus Ui(Xi) − XiPi(Xi), domestic firm’s profits in home market(Πii), domestic firm’s export profits (Πij, j 6= i) and tariff revenue:

Wi = Ui(Xi)−XiPi(Xi) +Πii +Xj 6=i

Πij +Xj 6=i

tjixji (11)

13In order to guarantee market access to all exporting firms in any country under bothMFN and tariff discrimination, we assume the following condition 3c2 > 7c3 − 1.

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At the second stage of the FTA game, countries simultaneously choosetheir tariffs in order to maximize their own welfare given the agreement(s)formed in the first stage. Since markets are segmented and marginal costsare constant, strategic independence of trade policies obtains. As a result,own tariffs do not affect export profits and each country chooses an optimaltariff schedule, ti ≡ (tji, tki) in order to maximize:

maxCSi(tji, tki) +Πii(tji, tki) +Xz 6=i

tzixzi(tji, tki) (12)

Next, we derive optimal tariffs under various FTAs and explore theirformation.

3 Formation of trade agreements

We have two motivating questions. First, does the fact that countries canform FTAs make global free trade less likely to occur? Second, how does thevariation in market size and production cost across countries affect their in-centives for forming FTAs? To address these questions, we begin by derivingthe sub-game perfect Nash equilibria (SPNE) of the two games. However,to allow countries to deviate as a coalition, we also analyze Coalition ProofNash equilibria (CPNE) of the two games.While the model permits countries to be asymmetric along two dimensions

(production costs and market size), to highlight the role played by each typeof asymmetry, we consider each in isolation.

3.1 Equilibrium FTAs: the role of market size

From here till section 4, to focus on market size asymmetries we set ci = 0for all i. In addition, the following normalization is imposed throughout thepaper:14

α1 ≥ α2 = 1 ≥ α3 (13)

Under the status quo (i.e. no trade agreement), each country imposes itsoptimal MFN tariff on others. The optimal MFN tariff for country i is found

14Similarly, from section 4 onwards we focus on cost asymmetries and set α1 = α2 =α3 = 1.

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by imposing the constraint tji = tki on the above problem and it is given by15

ti(Φ) =3αi

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If countries i and j form the FTA (ij ), they abolish tariffs on each otherand choose their tariffs on country k’s independently. As a result, under(ij ), the problem in (12) is subject to the constraint tji = 0. The followingoptimal tariff levels are easily calculated under the different FTAs:

tji(jk) = tki(jk) = tji(Φ) =3αi

10(14)

andtji(ik) = tji(ki, kj ) =

αi

7(15)

As might be expected, when an FTA member i reduces its tariff on theother member j to zero, exports of the non-member k decrease. As a result,compared to the case of no agreement (Φ), a members incentive to imposea tariff on the non-member decreases since the non-member becomes a lessimportant source of rent-extraction. This result is known as the tariff com-plementarity effect in the literature (see Bagwell and Staiger 1997a, 1997b,and 1998a).16

3.1.1 SPNE of the FTA game

Under the FTA game, the strategy set of country i, denoted by Si, consistsof four duples of strategies (si) that involve countries with whom i wants toform an agreement:

Si = {{φ, φ}, {j, φ}, {φ, k}, {j, k}} (16)

where φ represents country i announcing in favor of ‘no agreement’. In orderto conserve notation, each agreement is denoted as follows: (i) Status quo Φ

15It turns out that even if a country is free to tariff discriminate, under market size asym-metry each country imposes a common tariff on the other two. However, the constraintimplied by MFN binds under cost asymmetry (see section 5 for further discussion).16A recent report by the World Bank (2000) argues that no clear evidence shows that

the formation of a PTA leads member countries to become more protectionist towardsnon-member countries. While such an outcome may be a consequence of Article XXIV,the tariff complementarity result implies that it could also be optimal for member countriesto voluntarily lower tariffs on non-members.

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— obtains when no two announcements match or when all announce φ; (ii)a bilateral FTA between countries i and j— (ij ) is formed iff two countriesannounce each other’s names j si and i sj; (iii) two independent FTAs inwhich i is the common member — (ij, ik) is formed iff (a) j si and i sj and (b)k si and i sk; and (iv) free trade — (123 ) obtains iff all countries announceeach others’ names.17

As is clear from the discussion above, member of an FTA can sign anindependent FTA with the non-member without needing consent of the othermember.18 Consider the following announcements:

s1 = {2, φ}, s2 = {1, 3}, s3 = {φ, 2} (18)

The above strategy vectors give rise to two independent FTAs: (21 ) and(23 ) of which country 2 is the common member.Note also that different strategy vectors may yield the same agreement(s)

when there is an asymmetry in terms of countries’ choices. To see this,suppose the strategy vector is given by:

s1 = {2, 3}, s2 = {1, 3}, s3 = {φ, 2} (19)

Even though country 1 announces country 3, country 3 wants to form an FTAonly with country 2.19 As a result, strategy vectors in (19) yields the sameagreements (21, 23 ) as the ones in (18). In order to eliminate redundantannouncements in the set of SPNE, it is assumed that FTA announcementscost each country ε (where ε > 0 is arbitrarily small).The following lemma summarizes the incentives of countries to form a

bilateral FTA:

Lemma 1: Country i’s incentive to form a bilateral FTA with countryj is increasing in the market size of country j whereas it is decreasing in itsown market size.17Formally, free trade obtains iff

s1 = {2, 3}, s2 = {1, 3}, s3 = {1, 2} (17)

18As indicated in Furusawa and Konishi (2003), this distinction creates an importantdifference between an FTA and a CU and leads to a sharp contrast to Yi (1996).19Under the open membership rule by Yi (1996), membership is open to all countries.

However, this rule does not seem to be appealing for discussions of PTAs since the forma-tion requires consent from both sides.

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The above lemma implies that the smallest country (3) always has anincentive to form an FTAwith the other two countries. Similarly, the mediumsize country (2) also benefits from an FTA with the largest country (1). Thetrade-off underlying FTAs is as follows: From each country’s perspective,joining an FTA is costly because its domestic surplus is lowered relative tothe case where it is free to use its optimal MFN tariff.20 On the other hand,being part of an FTA increases export profits of members in each other’smarkets. Consequently, the size of the larger member country plays a crucialrole in determining which bilateral FTAs can arise in equilibrium.What type of FTAs arise in equilibrium? We can show that unless country

j is too large relative to country i the bilateral FTA (ij ) is a SPNE:

(ij ) is SPNE for all αj s.t. 70αj ≤ 3√910αi (20)

From the perspective of countries 2 and 3, given that they call each other’snames, the marginal gain of gaining free access to an additional market (i.e.that of country 1) dominates the loss in domestic surplus from having anadditional FTA. As a result, when the smaller countries (2 and 3) call eachother’s name, they also announce the name of the largest country (1) inorder to form two independent FTAs. However, the largest country (1) hasan incentive to unilaterally deviate from such a pair of bilateral FTAs (inwhich it itself is not the common member). This can be explained as follows:Since the FTA partner for country 1 is the common member country (2 or3), country 1 does not enjoy any competitive advantage over the non-partnercountry implying that increase in its export profit from the FTA is small.Moreover, country 1 benefits from the tariff complementarity effect when itis not a member of an FTA.

W3(31, 32 ) ≥W3(23 ) but W1(23 ) ≥W1(31, 32 ). (21)

Similarly

W2(21, 23 ) ≥W2(23 ) but W1(23 ) ≥W1(21, 23 ). (22)

As a result, the two smaller countries (2 and 3) cannot form two indepen-dent FTAs (unless it is global free trade) so that (31, 32 ) and (21, 23 ) are

20Note that it is not obvious that an FTA is worse for domestic surplus relative to MFNsince even under MFN, a country is solving a constrained optimization problem in thatit must treat its trading partners the same. However, when two countries are symmetricwith respect to cost, it is optimal for the third country to not tariff discriminate so thatthe optimal MFN tariff is in fact its unrestricted optimal tariff.

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never SPNE. The only possible FTA that involves two independent bilateralFTAs is the one in which the largest country is the common member (12,13 ). Finally, global free trade (123) is a SPNE if all countries are relativelysymmetric with respect to their market size. We summarize these results inthe following proposition:

Proposition 1: FTAs (12), (13), (23), (12,13), (123) and status quo(Φ), are all SPNE iff the degree of asymmetry between countries is not toohigh (i.e. iff α3 ≥ α3 and α1 ≥ α1 ≥ α1). When countries are completelysymmetric with respect to market size (i.e. αi = 1 for all i), all FTAs areSPNE except for those that involve two independent FTAs.21

Why cannot two independent FTAs such as (12,13 ) arise in equilibriumwhen countries are completely symmetric? This is because each membercountry that belongs to only a single FTA (i.e. both countries 2 and 3)has an incentive to unilaterally deviate from its FTA with country 1 to takeadvantage of the tariff complementarity effect — the gain from tariff reductionsa non-member enjoys comes at no cost whereas the gain of free market accessin country 1 requires granting free access in return. In effect, each countrywith a single FTA prefers to free ride on the other two and is better off ifthe other two form an FTA rather than be part of one itself!Given that there exist multiple SPNE (including status quo Φ), we re-

fine the set of multiple SPNE by deriving Coalition-Proof Nash equilibrium(CPNE) of the FTA game. While the SPNE concept defines equilibrium onlyin terms of unilateral deviations, CPNE eliminates all non-credible deviationsby every conceivable coalition.22

3.1.2 Stable FTAs

We first clarify how the notion of CPNE applies in our model and then discussstable FTAs.21Explicit formulae for these market size thresholds are reported in the appendix.22As per Bernheim et al. (1987), an FTA is defined to be coalition-proof if and only if

it is Pareto efficient among self enforcing agreements. In turn, an FTA is self enforcing ifand only if no proper subset (coalition) of countries, taking the actions of its complementas fixed, can agree to deviate in a way that makes all of its members better off.

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The notion of CPNE In order to see how the concept of CPNE is appliedin our context, consider the following example:

s1 = {2, φ}, s2 = {1, φ}, s3 = {φ, φ} (23)

Suppose now that (12 ) is a SPNE and it is immune to any conceivabledeviation except for the deviation to (23 ):23

W2(23 ) > W2(12 ) and W3(23 ) > W3(12 ). (24)

In order for (12 ) to be a CPNE, it is necessary to check whether the jointdeviation of countries 2 and 3 from (12 ) to (23 ) is credible or not. If there isno incentive for any coalition of countries to further deviate from (23), thejoint deviation from (12 ) to (23 ) would be credible and (12 ) would not be aCPNE. But what if country 2 — a subset of the countries that deviate from(12) to (23) — do indeed has incentive to deviate further from (23) to (21, 23)taking country 1’s strategy as given (s1 = {2, φ} in the original agreement(12 ))? Suppose

W2(21, 23 ) > W2(23 ). (25)

Then the original deviation from (12 ) to (23) would be non-credible. As aresult, the FTA (12 ) would be a CPNE.Further note that there can be multiple FTAs that are CPNE simulta-

neously. Consider the above example again and suppose now that (23 ) isimmune to any conceivable deviations except for the joint deviation of coun-tries 1 and 3 to (13 ):

W1(13 ) > W1(23 ) and W3(13 ) > W1(23 ) (26)

Suppose further that country 3— a subset of the countries that deviate from(23 ) to (13)— has an incentive to deviate further from (13 ) to (31, 32 ), takingcountry 2’s strategy s2 = {φ, 3} in the original agreement (23 ) as given:

W3(31, 32 ) > W3(13 ) (27)

Under such a situation, (12 ) and (23 ) are both CPNE. Finally, follow-ing Dutta and Mutuswami (1997), we call an equilibrium FTA stable if itcorresponds to a CPNE.24

23It is clear that (12 ) is a SPNE since it is immune to unilateral deviations.24Furusawa and Konishi (2002) use a network formation model to endogenize free trade

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Stable FTAs under market size asymmetry Figure 1 shows stableFTAs in the (α3, α1) space:25

––Insert figure 1 here––

As seen from figure 1, when the largest country (1) is too large relativeto other countries, it does not have an incentive to form an FTA because ofthe unfavorable trade-off between loss in domestic surplus and gain in exportprofits. In this situation, the only possible stable agreement is (23 ) unlessthe smallest country (3) is too small relative to the medium size country (2).Otherwise, no agreement (Φ) is a CPNE. Similarly, if the smallest country (3)is too small, neither country 1 nor country 2 has an incentive to form an FTAwith country 3. In this case, if the size of the largest country (1) is similar tothe one of the medium size country (2), (12 ) is the stable equilibrium. Thefollowing is immediate:

Lemma 2: A bilateral FTA between the largest and smallest countries(13) is not stable.

It is important to note that only the bilateral FTAs that include thesimilar size countries, (12 ) and (23 ), are stable. The FTA (13 ) is not stablesince 1 and 2 have incentives to deviate from (13 ) to (12, 13 ). This deviationis not credible only within the market size parameter range over which thedeviation from (13 ) to no agreement (Φ) is credible. As a result, (13 ) isnever a CPNE. From inequalities in (21) and (??), since both (31, 32 ) and(21, 23) are not SPNE, they are trivially not in the set of CPNE as well.Moreover, (12, 13 ) is stable if countries 2 and 3 are not too small relativeto the largest country (1). Most importantly, free trade (123 ) obtains if andonly if market sizes of all countries are similar — in fact, free trade is theunique CPNE when countries are completely symmetric.26

agreements (FTAs). Given any FTA configuration, they examine whether a pair of coun-tries have incentives to sign another FTA, and whether a country has an incentive tocut an existing FTA. A network that is immune to these two incentives is called pairwisestable.25Throughout the paper, explicit functions used to obtain the figures can be found in

the appendix. Also we limit the range of country 1’s market size as follows while drawingthe figures for the case of market size asymmetry: 2 ≥ α126A similar result is also obtained by Furusawa and Konishi (2002) and they conclude

that FTAs are building blocs for free trade. However, our approach is different from

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3.2 Eliminating the FTA option

Under the no FTA option, bilateral agreements are not possible so countriescan either announce in favor of the status quo or in favor of free trade. Thestrategy set of country i, denoted by Si, consists of two duples of strategies(si):

Si = {{φ, φ}, {j, k}} (28)

Free Trade (123 ) occurs if and only if the following hold:27

W1(123 ) > W1(Φ), W2(123 ) > W2(Φ) and W3(123 ) > W3 (Φ). (29)

The set of CPNE of the no FTA game is represented in figure 2.

––Insert figure 2 here––

The comparison of figures 1 and 2 leads to the following proposition:

Proposition 2: Under both games, free trade (123) is found to be uniquelystable if and only if countries are relatively symmetric with respect to marketsize. However, free trade (123) is stable over a larger parameter space underthe no FTA game than under the FTA game.

As seen from figure 2, when countries do not have the option to formFTAs, global free trade (123 ) is stable in the light and dark blue regionswhile it is stable only in the dark blue region under the FTA game. As aresult, free trade is more likely to obtain under the no FTA game. Overthe light blue region, countries prefer free trade (123 ) to no agreement (Φ).However, an FTA option provides them an intermediate opportunity to forma trading bloc that is preferable to free trade (123 ).Further analysis of the two games yields some subtle results regarding the

welfare implications of FTAs in an asymmetric world. Two distinct regionsneed to be emphasized. In region I (12 ), (23 ), and (12, 13 ) are stable agree-ments under the FTA game while free trade (123 ) is the stable agreement

Furusawa and Konishi (2002) in an important way: Beside investigating whether FTAformation continues until free trade or not, we also ask whether the option of formingFTAs makes global free trade less likely to occur.27Note that the set of SPNE and CPNE are identical in the no FTA option game.

15

under the no FTA game. In region II, (12), (23 ), and (12, 13) are stableagreements under the FTA game, whereas no agreement (Φ) is the stableoutcome under the no FTA game. Note that the former (latter) region refersto the situation in which countries are relatively symmetric (asymmetric)with respect to the market size. Given these two distinct regions, we explorethe following questions: Which countries benefit (suffer) the most from theFTA option and what are the world welfare implications of FTAs?

Proposition 3: A comparison of the FTA game and the no FTA gameyields the following results: (i) over region I, the FTA option has beneficialwelfare effects for the largest country (1) but harmful effects for the smallestcountry (3) as well as for the world as a whole; (ii) the welfare impact on themedium size country (2) is ambiguous and it depends on the size distributionof countries: if the smallest country (3) is quite small and the medium sizecountry (2) is similar in size to the largest country (1), the FTA option hasbeneficial welfare effects for the medium sized country; however, if the largestcountry (1) is too large and the medium size country (2) is similar in sizeto the smallest country (3), the FTA option is harmful for the medium sizedcountry (2); and (iii) over region II, the FTA option has beneficial welfareeffects for all countries (and therefore for the world as a whole).

Proposition 3 implies that the largest country necessarily benefits fromthe FTA option. As indicated in lemma 1, smaller countries always haveincentive to form an FTA with the largest country (1). This gives the largestcountry (1) a special position in the FTA game that it ends up exploitingin equilibrium in that stable FTAs are those that benefit the largest country(1). On the other hand, country 3 has the weakest position in the FTA gamesince it offers free access to the smallest market. This makes the no FTAgame preferable for the smallest country (3) over region I. Note also that,over region I, if the smallest country (3) is too small relative to the mediumsize country (2) and the largest country (1) is similar in size as the mediumsize country (2), the stable FTAs are (12) or (12, 13 ) both of which aresuperior for the medium size country relative to free trade (123 ). However,if the largest country (1) is too large relative to the medium size country (2)and the smallest country (3) has a similar size as the medium size country(1), the resulting FTA is (23), which is inferior for the medium size country(2) relative to free trade (123). Furthermore, from the world welfare point of

16

view, free trade is always preferable to stable FTAs over region I. However,in region II, all forms of stable FTAs are preferable to no agreement (Φ). Asa result, when countries are relatively symmetric (asymmetric) with respectto the market size, FTA game has harmful (beneficial) impacts on the worldwelfare.We next compare the two games under cost asymmetry.

4 How cost asymmetry matters

As in the case of asymmetric market sizes, we investigate the following ques-tions under cost asymmetry. First, how does a country’s incentive to formFTAs depends upon its own cost of production relative to others? Second,does the option of pursuing FTAs undermine incentives for multilateral tradeliberalization? We begin with the FTA game and then analyze the no FTAgame. Throughout the analysis we assume that αi = 1 for all i and wenormalize c1 = 0.

4.1 Equilibrium FTAs

As per Article I of GATT (MFN), we impose the following constraint on theproblem in (12) under no agreement (Φ):

tji = tki = ti (30)

As a result, the optimal MFN tariff (ti(Φ)) under no agreement (Φ) is:

ti(Φ) =3−Pj cj

10(31)

The following tariff levels are found under the different FTAs:

tji(jk) = tki(jk) =6− 2ci + 3ck − 7cj

20(32)

andtji(ik) = tji(ki, kj ) =

3− 9cj + 7ck − ci21

(33)

17

4.1.1 Multiplicity of SPNE

Recall that a country’s incentive to form an FTA is determined by two coun-tervailing forces: an FTA increases export profits but it lowers domesticsurplus. If country i’s production cost is sufficiently lower than that of coun-try j then country j’s loss in domestic surplus from the FTA (ij) outweighsthe beneficial effects of improved access to country i’s market and the FTA(ij) is not a SPNE.

Lemma 3: Country i’s incentive to form an FTA with country j is in-creasing in country j’s cost whereas it is decreasing in own cost and that ofcountry k.

The above lemma implies that the low cost countries always has an in-centive to form an FTA with higher cost ones and the higher their costthe stronger is this incentive. Given the above incentives, the highest costcountry’s (3’s) decision is the crucial one in determining equilibrium FTAs.Moreover, once country i announces country j ’s name, it has always has anincentive to independently announce country k ’s name as well. This is be-cause an additional FTA results in an increase in the export profits due tothe better competitive position country i enjoys against each FTA partnerin the other partner’s market and this positive impact is always larger thanthe additional loss in domestic surplus caused due to the second FTA:

W1(12, 13 ) ≥W1(12 ) and W1(12, 13 ) ≥W1(13 ) (34)

W2(21, 23 ) ≥W2(12 ) and W2(21, 23 ) ≥W2(23 ) (35)

W3(31, 32 ) ≥W3(13 ) and W3(31, 32 ) ≥W3(23 ) (36)

However, country 3 has an incentive to unilaterally deviate from an agree-ment that involves two independent FTAs in which the other two countriesare common members since country 3 is at a competitive advantage — it doesnot gain much in its export markets while it loses a lot in its own market:

W3(12 ) ≥W3(12, 13 ) and W3(12 ) ≥W3(21, 23 ) for all c2, c3 (37)

Consequently, inequalities in (34), (35), (36) and (37) together implythat (12, 13) and (21, 23 ) are never SPNE. The only possible agreementthat involves two independent FTAs is the one in which the country 3 is thecommon member (31, 32 ).

18

Proposition 4: FTAs (12), (13), (23), (31, 32) and (123) and statusquo (Φ), are all SPNE iff the degree of cost asymmetry between countries isnot too high (i.e. iff c3 ≤ c3 and c2 ≥ c2 ≥ c2). Furthermore, if countriesare completely symmetric with respect to cost, all FTAs are SPNE except forthose that involve two independent FTAs.

Two independent FTAs cannot arise because when countries are com-pletely symmetric, the countries that belong to only FTA have a unilateralincentive to become a non-member: once again, the tariff complementarityeffect that these countries enjoy when they are not a member is greater thanthe gain from forming an FTA. Next, we describe stable FTAs under costasymmetry.

4.1.2 Stable FTAs

Figure 3 shows stable FTAs under cost asymmetry in the (c3, c2) space.

––Insert figure 3 here––

The following corollary is immediate:

Corollary 1: No agreement (Φ), and FTAs (23) and (31, 32) are notin the set of CPNE although they belong to the set of SPNE.

In other words, agreements that involve two independent FTAs are nevera CPNE. Recall that (12, 13 ) and (21, 23 ) are not even SPNE, so thatthey cannot be CPNE as well. If (31, 32) is formed, the joint deviationof countries 1 and 2 to free trade (123) is credible unless country 1 is tooefficient relative to country 2. Moreover, if the country 1 is too efficientrelative to country 2, then country (2) has an incentive to deviate form (31,32 ) to (13) and this deviation is credible. Consequently, (31, 32) is nevera stable agreement. Furthermore, the deviations from no agreement (Φ) to(12 ) and (23 ) are credible over the entire region so that no agreement (Φ)is never a stable equilibrium although it is a SPNE. Finally, the deviation ofcountries 1 and 2 deviate from (23 ) to (21, 23 ) is credible unless they arealmost symmetric with respect to their production costs. When all countrieshave relatively similar costs, they jointly deviate from (23 ) to global free

19

trade (123 ) and this is a credible deviation since (123 ) is immune to anyconceivable deviations over this range. As a result, (23 ) is never a CPNE.Figure 3 demonstrates that over the dark blue region, there are two

CPNE: (12 ) and (123). This region is determined by two non-credible de-viations. First, the joint deviation of countries 1 and 3 from (12 ) to (13)is not credible since country 1 always has an incentive to deviate further to(12, 13) (see inequality in (36)). Second, the deviation from (12 ) to (123)is not credible since countries 2 and 3 have incentives to deviate further to(23 ). As a result, (12 ) is a CPNE. Finally, over the same region, the onlypossible deviation from free trade (123 ) is the joint deviation of countries 2and 3 to (23 ) but this turns out to be non-credible since country 3 has anincentive to further deviate to (31, 32 ).Over the green region, there are two CPNE: (12 ) and (13 ). Three cred-

ible deviations from (13 ) determine the boundaries of the green region: (i)Countries 2 and 3 deviate to (31, 32 ), (ii) Country 3 deviates to no agreement(Φ) and (iii) All countries deviate to free trade (123 ). The yellow region isdetermined only by two credible deviations: (i) Country 2’s deviation to noagreement (Φ) and (ii) joint deviation of all countries to free trade (123).28

It is important to note that the region over which free trade (123 ) isstable is determined by the unilateral deviation of country 3 from (123) to(12 ). As a result, country 3’s choice is pivotal for the stability of free trade(123).Next, we examine which agreements arise in the CPNE if countries do

not have an FTA option.

4.2 No FTA game

Figure 4 shows stable FTAs under cost asymmetry in the (c3, c2) space.

––Insert figure 4 here––

A comparison of figures 3 and 4 shows that if countries can not formFTAs, free trade is achieved in the light blue region in figure 4; while it isnot the case under the FTA option. Thus, we have the following result.

28It is important to note that the region over which free trade (123 ) is stable is deter-mined by the unilateral deviation of country 3 from (123 ) to (12 ). As a result, country3’s choice is pivotal for the stability of free trade (123 ).

20

Proposition 5: Under both games (FTA and no FTA), free trade (123)is uniquely stable if and only if the countries are relatively symmetric withrespect to their production costs. However, even under cost asymmetry, freetrade (123) is stable over a larger parameter space under the no FTA gamethan under the FTA game.

The analysis of figure 3 and figure 4 provides additional results regard-ing the welfare implications of FTAs. Before doing that, it is important tonote again that (12) and (13) are the stable agreements under the FTA op-tion over the yellow region and the theory offers no guidance as to whichagreement ((12 ) or (13 )) might actually be observed. We suppose that the‘natural’ trading block (12) is the one that obtains as the stable agreement.29

Two distinct regions should be examined: region I: (12) is the stable agree-ments under the FTA option while free trade (123 ) is achieved as the stableagreement under the no FTA option, region II: (12 ) is the stable agreementunder the FTA option whereas no agreement (Φ) is the stable outcome underthe no FTA option. Given these distinct regions, we explore the followingquestions: Do the efficient or inefficient countries benefit from the FTA op-tion and what are the world welfare implications of having an FTA option?

Proposition 6: A comparison of the FTA game and the no FTA gameyields the following results: (i) over region I, the option to form FTAs hasbeneficial welfare effects for the highest cost country (3) but harmful welfareeffects for the other two countries as well as the world as a whole. (ii) overregion II, the FTA option has beneficial welfare effects for all countries (andtherefore the world as a whole).

Proposition 6 implies that the highest cost country always benefits fromthe FTA option. This result reflects the fact that market access to the highestcost country does not come at too high a price for the lower cost countries whoare at a competitive advantage. However, this stronger incentive of low costcountries actually turns into an advantage for the high cost country who endsup exploiting it in equilibrium. In fact, for the least efficient country, (12)

29If the stable agreement we observe over yellow region is (13 ), we have three distinctregions: region I: (13 ) is the stable agreement under the FTA game while free trade (123 )is achieved as the stable agreement under the no FTA game, region II: (12 ) is the stableagreement under the FTA option while free trade (123 ) is the stable one under the noFTA option, and region III: (12 ) is the stable agreement under the FTA option whereasno agreement (Φ) is the stable outcome under the no FTA option.

21

is always preferable to the stable agreements (123 ) and (Φ) under the FTAoption and no FTA option respectively. However, over region I, countries 1and 2 prefer free trade (123) that is not stable under the FTA option. As aresult, these countries are worse offwith the FTA option over region I and it isthe lowest cost country that loses the most from the FTA option. Over RegionII, when (12 ) is a CPNE, since there is no unilateral deviation of countries1 and 2 to Φ, they prefer (12 ) to Φ. Because of the tariff complementarityeffect, 3 also prefers (12 ) to Φ. Consequently, world welfare is higher under(12 ) than under Φ.Next, we examine the role of the most favored nation (MFN) principle in

the formation of trade agreements.

5 Role of MFN in trade agreements

If Article I (MFN) were not applicable, the problem in (12) under no agree-ment (Φ) is no longer subject to the symmetric treatment constraint in (31)and countries are free to tariff discriminate. The following optimal discrimi-natory tariff (tji(Φ)) is obtained under no agreement (Φ):

tji(Φ) =6− 2ci + 3ck − 7cj

20

It is important to note that inefficient (efficient) exporters benefit (suffer)from tariff discrimination relative to MFN:

tji(Φ)− ti(Φ) =ck − cj4

> 0 iff ck > cj (38)

It is straightforward to argue that a non-member country’s welfare under a

bilateral FTA is higher when its trade policy is not constrained by MFN.The following lemma explains the role of MFN in the two games:

Lemma 4: A country’s incentive to deviate from any agreement to noagreement (Φ) or to the ones in which it is a non-member is higher undertariff discrimination relative to MFN.

The above lemma argues that the region over which the agreements thatare stable under MFN treatment changes. Figure 5 shows stable agreementsunder the FTA option when countries are free to discriminate.

22

––Insert figure 5 here––

Similarly, stable agreements under the no FTA option are represented infigure 6.

––Insert figure 6 here––

A Comparison of figures 3-6 yields the following result:

Proposition 7: MFN contributes to trade liberalization in two ways: (i)Under both games, the region over which free trade (123) is stable is largerunder MFN than under tariff discrimination; (ii) under the FTA game, overthe region where free trade is not stable, (12) and (13) are stable over a largercost parameter space under MFN relative to tariff discrimination.

Since country 3 is pivotal and its welfare under (12 ) is higher underdiscrimination than under MFN, the region over which free trade (123) isstable is larger under MFN treatment. The same argument is valid for theno FTA option as well since the deviation of country 3 from free trade (123)to (Φ) determines the region over which free trade (123 ) is stable. Over theregion where free trade is not stable, since the deviations of the less efficientmember countries (2 and 3) from (12 ) and (13) to no agreement (Φ) arebinding for the stability of these bilateral FTAs, the region over which theyare stable is larger under MFN relative to tariff discrimination.The following insight emerges from the above analysis: Article I (MFN

treatment) facilitates the achievement of global free trade independent of therole of Article XXIV. However, when countries are not allowed to practiceArticle XXIV (no FTA option), the impact of MFN on the stability of freetrade is relatively larger.

6 Concluding remarks

This paper contributes to the long-standing debate regarding the effect ofFTAs on multilateral trade liberalization by analyzing two games: one wherecountries have the choice to pursue both FTAs and global free trade andanother where they cannot form FTAs. We find that the option to pursue

23

FTAs does lower the likelihood of achieving global free trade. In this sense,the exception made available by Article XXIV is in conflict with the GATT’smain goal of achieving global free trade. However, since both types of tradeliberalization is endogenous in our model, we also find that the option to formFTAs leads to welfare improving trade liberalization when global free tradecannot be achieved. In this sense, Article XXIV supports GATT’s maingoal — it can be better to have some preferential trade when multilateralliberalization is infeasible. In fact, the underlying asymmetry in our modeldelivers a surprising insight: the option to pursue FTAs can actually leadto an outcome that is welfare preferred to free trade when the FTAs formedfavor low cost producers relative to high cost ones.Our analysis further sharpens the stumbling block versus building block

debate by highlighting conditions under which the answer goes one way oranother. When the underlying asymmetry between countries is relativelysmall, the option to pursue FTAs does more harm than good. On the otherhand, when countries are quite asymmetric, multilateral free trade is harderto obtain and the FTAs are actually be desirable from a world welfare per-spective.Finally, we show that Article I (MFN treatment) facilitates the achieve-

ment of global free trade independent of the role of Article XXIV. However,when countries are not allowed to practice Article XXIV (no FTA option),the impact of MFN on the stability of free trade is relatively larger.

7 Appendix

All supporting calculations and proofs not provided in the text are givenbelow.Market Size AsymmetryFirst, we report the welfare levels of countries under different types of

agreements for the general case:

Wi(Φ) =40α2i + α2j + α2k

100

Wi(ij ) =35α2i + 8α

2j

98+

α2k100

, Wk(ij ) =40α2k100

+α2i + α2j49

(39)

Wi(ij ), (ik) =11α2i32

+4(α2j + α2k)

49, Wj(ij ), (ik) =

α2i16+5α2j14

+α2k49

(40)

24

Wi(ijk) =11α2i + 2(α

2j + α2k)

32(41)

In the following proofs, the critical α1 and α3 levels can be found followingthe proof of proposition 3.

Lemma 1Ii(ij ) is defined as the incentive of a country i to form an FTA with a

larger country j : Accordingly, the following is immediate:

Ii(ij ) =Wi(ij )−Wi(Φ) =351α2j − 210α2i

4900(42)

As a result:∂Ii(ij )∂αj

> 0 and∂Ii(ij )∂αi

< 0

Proposition 1Part (i): When countries are asymmetric (α1 > α2 = 1 > α3):

(12 ) is SPNE for all α1 s.t. α1 ≤ αa1

(13 ) is SPNE for all α1 s.t. α1 ≤ αa1α3

(23 ) is SPNE for all α3 s.t. α3 ≥ αa3

(12, 13 ) is SPNE if

a-) αc3 ≥ α3 ≥ αf

3 for all α1 s.t. αe1 ≥ α1 ≥ αh

1

andb-) α3 ≥ αc

3 for all α1 s.t. αd1 ≥ α1 ≥ αh

1

and finally,

(123 ) is SPNE if α3 ≥ αe3for all α1 s.t. α1 ≤ αb

1.

As a result, (Φ), (12 ), (13 ), (23), (12, 13 ) and (123 ) are SPNE simulta-neously if α3 ≥ α3 and α1 ≥ α1 ≥ α1 and this condition is restated as thefollowing combination:

a-) αg3 ≥ α3 ≥ αa

3αh1 for all α1 s.t. α1 ≤ αa

1α3

25

andb-) α3 ≥ αg

3 for all α1 s.t. αb1 ≥ α1 ≥ αh

1 .

Part (ii): When countries are completely symmetric (α1 = α2 = α3 = 1);(ij) is a SPNE since no member has an incentive to deviate unilaterally:

Wi(ij )−Wi(Φ) =Wj(ij )−Wj(Φ) =141

4900> 0

(123) is a SPNE since no country has an incentive to deviate unilaterally:

Wi(123 )−Wi(Φ) =39

800> 0

Figure 1Figure 1 represents the following set of CPNE:30

(i) Φ is a CPNE if α3 ≤ αa3 for all α1 s.t. α1 ≥ αa

1.(ii) (12 ) is a CPNE if α3 ≤ αb

3 for all α1 s.t. α1 ≤ αa1.

(iii) (23) is a CPNE if α3 ≥ αa3 for all α1 s.t. α1 ≥ αb

1.(iv) (12, 13) is a CPNE if (a) αc

3 ≥ α3 ≥ αb3 for all α1 s.t. α1 ≤ αc

1 and(b) αd

3 ≥ α3 ≥ αc3 for all α1 s.t. α1 ≤ αd

1.(v) (123 ) is a CPNE if α3 ≥ αe

3 for all α1 s.t. α1 ≤ αb1.

Lemma 2Given 2 ≥ α1 ≥ α2 = 1 ≥ α3:(13)−→(1 and 2)−→(12, 13 ): 1 and 2 always deviate:

W1(12 , 13 )−W1(13 ) ≥ 0, W2(12 , 13 )−W2(13 ) ≥ 0

and 2 has no incentives to deviate further but 1 has an incentive to deviatefurther to Φ if α1 ≥ αd

1 and to (12) if α1 ≥ αe1.

Consequently, the initial deviation of countries 1 and 2 from (13 ) to (12,13 ) is not self enforcing if (a) α3 < αc

3 and α1 ≥ αe1 and (b) α3 ≥ αc

3 andα1 ≥ αd

1. However, over this region 1 deviates from (13 ) to Φ if α1 > αa1 and

it is self-enforcing. As a result, (13 ) is never a CPNE.

Figure 230Detailed derivations are available upon request.

26

(i) Φ −→(1, 2 and 3 )−→(123 ): 3 always deviates, 2 deviates if α1 > αf1

and 1 deviates α1 > αg1. As a result Φ is a CPNE if α1 > αg

1.(ii) (123 )−→(1 or 2 or 3)−→ Φ: 3 never deviates, 1 deviates if α1 < αf

1

and 2 deviates if α1 > αg1. As a result, FT is a CPNE if α1 ≤ αg

1.

Proposition 2It is immediate from figures 1 and 2.

Proposition 3Over region I:When (12) is a CPNE (if α3 ≤ αb

3 for all α1 s.t. α1 ≤ αa1):

W1(12 )−W1(123 ) =3α21224

+15

784− 21α

23

400> 0

W2(12 )−W2(123 ) =3

224+15α21784

− 21α23

400> 0

W3(12 )−W3(123 ) =9α23160− 33(1 + α21)

784< 0

WW (123 )−WW (12 ) =15(1 +A21)

1568+39A23800

> 0

When (23 ) is a CPNE (if α3 ≥ αa3 for all α1 s.t. α1 ≥ αb

1):

W1(23 )−W1(123 ) =9α21160− 33(1 + α23)

784> 0

W2(23 )−W2(123 ) =3

224+15α23784

− 21α21

400< 0

W3(23 )−W3(123 ) =3α23224

+15

784− 21α

21

400< 0

WW (123 )−WW (23 ) =15(1 + α23)

1568+39α21800

> 0

When (12, 13) is a CPNE (if (a) αc3 ≥ α3 ≥ αb

3 for all α1 s.t. α1 ≤ αc1 and

(b) αd3 ≥ α3 ≥ αc

3 for all α1 s.t. α1 ≤ αd1):

W1(12 , 13 )−W1(123 ) =3α21224− 33α

23

784> 0

27

W2(12 , 13 )−W2(123 ) =15(1 + α23)

784> 0

W3(12 , 13 )−W3(123 ) =3A23224− 33

784< 0

WW (123 )−WW (12 , 13 ) =15(1 +A23)

1568> 0

Over region II:When (12 ) is a CPNE, since there is no unilateral deviation of countries

1 and 2 to Φ, they prefer (12 ) to Φ. Because of the tariff complementarityeffect, 3 also prefers (12 ) to Φ.When (23 ) is a CPNE, since there is no unilateral deviation of countries

2 and 3 to Φ, they prefer (23 ) to Φ. Because of the tariff complementarityeffect, 1 also prefers (23 ) to Φ.When (12, 13) is a CPNE, since there is no unilateral deviation of country

1 to Φ, it prefers (12, 13) to Φ, and the following holds:

W2(12 , 13 )−W2(Φ) =21α21400

+51α234900

− 3

70> 0

W3(12 , 13 )−W3(Φ) =21α21400

+51

4900− 3α

23

70> 0

It is trivial that since the welfare of all countries rises, world welfare increasesas well.

Critical α1 and α3 levels:

αa1 =

3√910

70, αb

1 =

p330 + 330α23

21, αc

1 =6√182

35, αd

1 =2p390 + 390α2335

αe1 =

6√182α335

, αf1 =

p210− 196α23

14, αg

1 =

p210 + 210α23

15, αh

1 =2√770

55

αa3 =

√910

39, αb

3 =5√182

156, αc

3 =

√5

4, αd

3 =

√154

22

αe3 =

√4070

110, αf

3 =

√770√182

858, αg

3 = 10

r11

1357

Lemma 3

28

Given that 15≥ ck ≥ cj ≥ ci = 0 and 3cj > 7ck − 1, when Ii(ij ) =

Wi(ij )−Wi(Φ),

Ii(ij )∂ci

=−768 + 218cj + 669ck

3150< 0,

Ii(ij )∂cj

=3882 + 1471cj − 6879ck

22050> 0

and

Ii(ij )∂ck

=−156− 2293cj + 657ck

7350< 0.

For the following proofs, the critical c2 and c3 levels can be found at theend of the appendix.

Proposition 4The proof of part (ii) is the same as the proof of part (ii) of the proposition

2.Part (i): When countries are asymmetric (1

5≥ c3 ≥ c2 ≥ c1 = 0 and

3c2 > 7c3 − 1):(12 ) is SPNE for all c2 s.t. c2 ≤ ca2

(13 ) is SPNE for all c2 s.t. c2 ≥ cb2

(23 ) is SPNE for all c2 s.t. c2 ≥ cc2

(31, 32 ) is SPNE for all c2 s.t. c2 ≤ cd2

and finally,

(123 ) is SPNE for all c2 s.t. c2 ≥ ce2.

As a result, (Φ), (12 ), (13 ), (23 ), (12, 13) and (123) are SPNE simultane-ously if c3 ≤ c3 ∼= 0.095 and cd2 ≥ c2 ≥ ce2.

Figure 3Figure 3 represents the following set of CPNE:31

a-) (12 ) is a CPNE if (i) c2 ≥ ce2 and c2 ≥ cf2 and (ii) c2 ≤ ce2 and c2 ≤ ca2.b-) (13 ) is a CPNE if c2 ≤ ce2, c2 ≥ cb2 and c2 ≥ cd2.

31Detailed derivations are available upon request.

29

c-) (123 ) is a CPNE if c2 ≥ ce2.

Corollary 1(i) Φ −→(1 and 2)−→(12 ): 1 always deviates, 2 deviates if c2 < ca2. As

a result, the deviation happens if c2 < ca2 and it is self-enforcing. Similarly,Φ −→(2 and 3)−→(23 ): 2 always deviates, 3 deviates if c2 > cc2. As a result,the deviation happens if c2 > cc2 and it is self-enforcing. These two conditions(c2 < ca2, c2 > cc2) cover entire region so that Φ is never a CPNE.(ii) (23 )−→(1 and 2)−→(21, 23 ): 2 always deviates, 1 deviates if c2 >

cg2. As a result, the deviation happens if c2 > cg2 and it is self-enforcing.Furthermore, if c2 < cg2, all countries deviate from (23 ) to free trade (123)and it is a self-enforcing deviation since free trade is strong Nash whenc2 < cg2. Consequently, (23) is never a CPNE.(iii) (31, 32)−→(1 and 2)−→(123 ): 1 always deviates, 2 deviates if c2 <

ch2 . As a result, the deviation happens if c2 > ch2 and it is self-enforcing whenc2 < ch2 . Note also that when c2 > ch2 , it is not even a SPNE. Consequently,(31, 32 ) is never a CPNE.

Figure 4(i) Φ −→(1, 2 and 3)−→(123 ): 1 and 2 always deviate, 3 deviates if

c2 >111c3−13

49. As a result Φ is a CPNE if c2 ≤ 111c3−13

49.

(ii) (123 )−→(1 or 2 or 3 )−→ Φ: 1 and 2 never deviate, 3 deviates ifc2 <

111c3−1349

. As a result, (123 ) is a CPNE if c2 ≥ 111c3−1349

.

Proposition 5It is immediate from figures 3 and 4.

Proposition 6Region I refers to the region over which c2 ≤ ce2 and c2 ≤ ca2 and (12 ) is

a CPNE under FTA option while free trade (123) is a CPNE under no FTAoption. Region II refers to the region over which c2 ≤ 111c3−13

49and (12 ) is a

CPNE under FTA option while no agreement (Φ) is a CPNE under no FTAoption. The following welfare comparison is immediate:Over Region I:

W1(123 ) > W1(12 ) for all c2 and c3

W2(123 ) > W2(12 ) for all c2 and c3

W3(123 ) < W3(12 ) iff c2 ≤ ce2

30

and

WW (123 ) > WW (12 ) for all c2 and c3.

Over Region II, when (12) is a CPNE, since there is no unilateral deviationof countries 1 and 2 to Φ, they prefer (12 ) to Φ. Because of the tariffcomplementarity effect, 3 also prefers (12) to Φ. Since welfare of all countriesare higher under (12) than under Φ, so is the world welfare.

Lemma 4It is obvious that welfare of the non-member country under a bilateral

FTA and also the welfare of countries under no agreement (Φ) is lower un-der MFN relative to discrimination since they are constrained to treat theirimporters symmetrically. The proof immediately follows this fact.

Figure 5The CPNE condition for (123 ) is determined by the deviation of the least

efficient country (3) to (12 ). Since MFN only changes the welfare under Φ,we obtain the same condition for (123 ) to be a CPNE:(123 ) is a CPNE if c2 ≥ cj2.On the other hand,(12) is a CPNE if (a) c2 ≥ cj2 and c2 ≥ ck2, (b) c2 ≤ cj2 and c2 ≤ cm2 .(13) is a CPNE if (a) c2 ≤ cj2, c2 ≥ cn2 and c2 ≥ cp2.

Figure 6Under discrimination:(i) Φ −→(1, 2 and 3)−→(123 ): 1 always deviates, 2 deviates if c2 ≤ cq2

and 3 deviates if c2 ≥ cr2. As a result Φ is a CPNE if c2 < cr2.(ii) (123 )−→(1 or 2 or 3)−→ Φ: 1 never deviates, 2 deviates if c2 > cq2,

and 3 deviates if c2 < cr2. As a result, (123 ) is a CPNE if c2 ≥ cr2.

Proposition 7It is immediate from the comparisons of both figure 3 with figure 5 and

figure 4 with figure 6.

Critical c2 and c3 levels:

ca2 =5376c3 − 4683 + 15

p109984− 233016c3 + 147889c232219

31

cb2 =156− 1792c3 + 5

p−10143 + 59682c3 + 147889c23657

cc2 =−1526c3 − 3882 + 15

p58681 + 113890c3 + 24857c231471

cd2 =1317 + 961c3 − 4

p110880− 305340c3 − 95970c234399

ce2 =−807 + 2029c3 + 16

p2295− 8625c3 + 9385c23291

cf2 =38829− 1463c3 − 120

p72058 + 6090c3 + 154756c2366703

cg2 =−843 + 441c3 + 4

p44730− 80220c3 − 60480c23559

ch2 =573 + 833c3 − 8

p1386 + 6762c3 + 12201c231775

cj2 =807− 2029c3 − 2

p200535− 1450170c3 + 2043935c23

689

ck2 =47649 + 64687c3 − 15

p4824862 + 16471560c3 + 20470744c23168133

cm2 =3(3857− 5√359086)

41839(2 + c3).

cn2 = −2 +(3857c3 − 5

√359086c3)

423

cp2 =1317 + 961c3 −

p1774080− 4885440c3 + 4931010c23

4399

cq1 =213 + 179c3 − 5

p924− 924c3 + 3086c23571

cr1 =87− 179c3 − 5

p426− 2592c3 + 3086c2379

32

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35

Figure 1: Equilibrium FTAs under Market Size Asymmetry

3α

1α

Free Trade

(12, 13)

(12)

(23)

No Agreement

Figure 2: Free Trade under Market Size Asymmetry

3α

1α

Free Trade under both scenarios

Free Trade under only no FTA option

No Agreement

Figure 3: Equilibrium FTAs under Cost Asymmetry and MFN

3c

2c

(12)

(13)

Free Trade

Lower threshold of 2c

Figure 4: Free Trade under Cost Asymmetry and MFN

2c

3c Lower threshold of 2c

No Agreement

Free Trade under only no FTA option

Free Trade under both scenarios

3c

2c

Free Trade

(12)

(13)

Figure 5: Equilibrium FTAs under Cost Asymmetry and discrimination

Lower threshold of 2c

Figure 6: Free Trade under Cost Asymmetry and discrimination

2c

3c

Free Trade under only no FTA option

Free Trade under both scenarios

No Agreement

Lower threshold of 2c