The Farsighted Stability of Global Trade Policy Arrangements

In this paper, we study and compare the stability of trade policy arrangements in two different regulatory scenarios, one with and one without Preferential Trade Agreements (PTAs), i.e. current vs. modified WTO rules. Unlike the existing literature, our paper considers an extensive choice set of trade constellations, containing both available PTAs, Customs Unions (CUs) and Free Trade Agreements (FTAs), as well as Multilateral Trade Agreements (MTAs), while assuming unlimited farsightedness of the negotiating parties. With symmetric countries and under both the current and the modified WTO rules, the Global Free Trade (GFT) regime emerges as the unique stable outcome. In the case of asymmetry, the results are driven by the relative size of the countries. If the world is in the vicinity of symmetry and two out of three countries are close to identical while relatively smaller than the other one, the area where the GFT regime is stable increases when prohibiting PTAs. However, when two similar countries are relatively larger, the availability of PTAs is conducive to the stability of the GFT regime. Finally, if the world is further away from symmetry, full trade liberalization is not attainable at all and an area where the Most-Favoured-Nation (MFN) regime is stable appears in the scenario without PTAs. Thus, the direction of the effect of PTAs on trade liberalization depends on the degree of asymmetry among countries.


Introduction
Following the General Agreement on Tariffs and Trade (GATT) of 1947, an ever increasing number of signatory countries liberalised their trade policies primarily via two channels: bilateral and multilateral negotiations. To the present day, there have been eight rounds of multilateral trade negotiations with the current ninth one, the Doha Round, still ongoing. Starting in force in the 1980ies, the world has seen an ever-increasing number of Preferential Trade Agreements (PTAs) concluded by bilateral negotiations. Currently, about forty percent of all countries/territories are a member of more than five PTAs, and about a quarter participates in more than ten. 1 The World Trade Organization (WTO), successor of the GATT since 1995, provides the set of rules for the trade liberalisation process of a significant number of countries. 2 Its Article I acts as the foundation for any multilateral trade liberalisation by formulating the so-called Most-Favoured-Nation (MFN) principle: Any concession granted to one member needs to be extended to all other members of the WTO. 3 In this paper, trade policy arrangements that are consistent with the MFN principle are referred to as Multilateral Trade Agreements (MTAs) in the spirit of said principle. 4 Contrary to the core MFN principle, Article XXIV Paragraph 5 explicitly allows countries to form PTAs, specifically Customs Unions (CUs) and Free Trade Agreements (FTAs), that do not need to extend the concessions granted within the arrangement to other countries. 5 However, Article XXIV Paragraph 5 Subparagraph (a), (b), and (c) each require that these are without (negative) influence on other trade relations.
The (direction of the) influence of Article XXIV Paragraph 5 on the development of trade policy arrangements is a controversial topic and has been the focus of many contributions. 6 In this tradition, the primary purpose of this paper is the analysis of the stability of different trade policy arrangements in two scenarios: one with PTAs in line with the current WTO rules, and an alternative scenario without PTAs (modified WTO rules). In addition, we examine whether PTAs act as 'building blocks' or 'stumbling blocks' on the path towards global free trade (Bhagwati (1993)).
The existing literature usually considers a limited set of trade agreements or assumes limited farsightedness of the negotiating countries. While this allows for a cleaner description of the model and interpretation of its results, it raises the question whether these restrictions significantly influence the analysis, and to what 1 extent such frameworks capture reality. In our view, certain empirical observations favour an extensive choice set of trade policy regimes and full farsightedness. In fact, over past rounds of multilateral trade negotiations, many countries were simultaneously involved in several trade liberalisation processes. 7 Moreover, such trade negotiations are usually complicated processes with significant impact on the countries' economies, and thus decisionmakers usually commission studies to quantify the effects, and try to anticipate strategic actions by the trade partners involved. 8 Extending the analysis to a broad set of trade policy arrangements, and taking into account the farsightedness of decision-makers is one of the contributions of this paper.
In our analysis, we thus consider an extensive set of trade agreements, containing PTAs -both CUs and FTAs -as well as MTAs. Next, endogenizing the formation of trade agreements, each country ranks them based on a three-country two-good general equilibrium model of international trade. 9 The stability of all trade agreements is then examined using these rankings together with the concept of 'consistent sets' as stable outcomes -a concept developed by Chwe (1994). As a result, our work expands the set of trade agreements under consideration and also extends the farsightedness of the negotiating parties in comparison to the existing literature. In fact, to the best of our knowledge, no other paper considers a choice set as extensive as ours.
Our analysis shows that the effect of PTAs on trade liberalisation depends on the size distribution of the countries in terms of endowments. 10 As long as the countries are almost equal in size, Global Free Trade (GFT) emerges as the unique stable outcome under both the existing and the alternative institutional arrangement (with vs. without PTAs). However, when two countries are considerably smaller than the third, a modified WTO arrangement that does not allow PTAs would facilitate the stability of GFT. This results from the suppression of the exclusion incentive (when PTAs are available) of the small countries versus the large. By contrast, if two countries are relatively larger than the third, a modified WTO without PTAs would actually reduce the extent to which GFT is stable. The argument here is the free-riding incentive of the small country when PTAs are not available, and we show that this is due to the non-availability of CUs. When the world is further away from symmetry, full trade liberalisation is not attainable at all, and abolishing the exception for PTAs can result in the worst possible outcome from the perspective of overall world welfare, the non-cooperative MFN regime.
include unlimited consideration of the future by the participants while simultaneously avoiding emptiness of the stable set that plagues other (more) restrictive solution concepts. 12 It is closely related to the stability concept proposed in Herings, Mauleon and Vannetelbosch (2009) and its extension (HMV (2014)). As noted by the authors, their criterion constitutes a stricter version, which in specific cases (that include our model) coincides.
The remainder of the paper is organised as follows. Section 2 specifies the model. Section 3 analyses the findings, and Section 4 offers concluding remarks.

Model
In this section, we start by presenting the trade policy arrangements we consider, and introduce the transition graphs that show how countries can move from one policy regime to another, individually or in coalitions. Subsequently, we provide the necessary theoretical and intuitive details of the stability notion we use, including the solution concept. Finally, we present the underlying trade model that determines countries' preferences over trade policy regimes and parametrise the model. Free Trade to come in three different forms: a CU, FTA, or MTA of three members. 13 In addition, there is the case of two over-lapping FTAs in a hub-and-spoke structure -adding another three regimes. In total, 12 It is also resistant to the criticism of Ray and Vohra (2015) about the sovereignty of coalitions as their main issues concerned with feasibility and distribution do not apply to our framework. Furthermore, their specific criticism about the explanatory power of Chwe's approach only applies to transferable utility games. 13 While their welfare level is equal, their position in the network (cf. Section 2.2) need not be, and for our concept of stability it is important which group of countries can create or destroy specific trade agreements (see Appendix C.2). Where applicable, we group all three together and refer to them as 'GFT'.
we thus have 16 different global trade policy regimes and define the set of global trade policy constellations Under each of these trade agreements, tariffs are bounded by zero from below, and from above by the MFN-tariff, which we discuss in more detail in Appendix B.2. The national policymaker in country i thus ] ∀j. 14 Conditional on trade agreement, the choice of tariffs is restricted further, as we discuss now.
In the baseline case, which we denote by MFN, countries do not liberalise their trade relations, but satisfy the non-discrimination principle. Each country i unilaterally chooses its (optimal) tariffs, solving When countries i and j form a customs union CU (i, j) together, each of them removes any trade restriction on the partner country, and they jointly impose an optimal tariff on country k. Their optimization problem Country k, finally, simply follows and applies the MFN principle (as before). Once all three countries enter a single CU together, the (common) optimisation problem is trivial because internal tariffs are restricted to zero. We denote this scenario by CUGFT.
In case countries i and j form an F T A(i, j), each of them again removes any trade restriction on the other country, and unilaterally imposes an optimal tariff on the outsider country k. The (representative) optimisation problem of country i (and j) is . The optimisation problem of country k is identical to that of the third country in case of a CU.
Furthermore, if country i forms an FTA each with countries j and k, we call this F T AHub(i), then both tariffs of country i are set to zero by nature of its trade relation with both partner countries. Each of the other two countries operates as before: Note that in terms of decision problem, it does not matter for a country whether its partner also forms a trade agreement with the other country. Finally, if all three countries form an FTA, denoted by FTAGFT, the optimization problem is identical to the case of CUGFT, but differs in terms of structure and network position (cf. Section 2.2).
We turn finally to the case where countries i and j form a multilateral trade agreement M T A(i, j). In this case, they jointly change their tariffs vis-à-vis each other, and also for the third country. The corresponding and analogously for T j . As before, the optimization problem of country k is identical to that of the outsider 14 Note that the upper bound is uniform across trading partners by the very nature of MFN.
Electronic copy available at: https://ssrn.com/abstract=3910302 country in the case of a CU. When all three countries enter a single MTA together, which we denote by MTAGFT, the optimization problem is identical to the case of CUGFT and FTAGFT, but the regime differs in terms of network position (cf. Section 2.2).
2.2. Transition Graphs. We now consider transition possibilities from one global trade policy constellation to another. Countries can implement trade policy arrangements, or leave an existing arrangement, depending on whether they act individually or in a coalition with other countries. We represent these possibilities by means of directed graphs, with trade agreements as vertices and the transition between them as directed edges.
To start with, consider the case of a single country i ∈ N (this being a coaltion of one), with j, k ∈ N \ {i}, j = k denoting the other two countries. The digraph for this case is provided in Figure 1, leaving aside loops at every vertix for illustrative clarity. As we can see from the diagram, the baseline MFN regime is reachable from a number of different global trade policy regimes, which country i can decide to quit, but not from the trinity of GFT, i.e. CUGFT, FTAGFT and MTAGFT, because quitting those would leave a two-country arrangement between j and k in place (or possibly a FTA hub-structure, if i were to quit only one FTA).
The three variants of GFT thus form separate groups of connected trade agreements, and hence the overall transition graph (in Figure 1, abstracting from loops), consists of four sub-graphs. Next, consider the transition graph for a coalition of two countries i, j ∈ N , where i = j and k ∈ N \ {i, j} denotes the other country. The transition graph for this case is provided in Figure 2, again leaving aside loops.
As we see here, the four regimes MFN, CU(i,j), FTA(i,j), and MTA(i,j) are all interconnected. This is because the coaltion of i and j can move from and to any two-country agreement between themselves and MFN at will. In addition, any regime connected to one of the four is automatically connected to all four of them. This Electronic copy available at: https://ssrn.com/abstract=3910302 group of four represents a complete directed sub-graph, which we illustrate as a dotted (super) node in the figure. In contrast to the previous case (compare Figure 1), the coalition of i and j can move from GFT to MFN or any two-country arrangement between themselves (the super node). They can also transition from any form of GFT to a corresponding two-country arrangement between one of them and the outside country, if only of of them decides to quit, plus from FTAGFT to any FTA hub-and-spoke structure.
Finally, consider the coalition of (all) three countries. Together, these three can implement any trade policy constellation. Therefore, the corresponding directed graph for the case of the grand coalition is a complete directed graph with loops (for short, a complete loop-digraph).

Stability Concept.
In terms of stability concept, we use the approach of Chwe (1994), as he combines far-sightedness with deviations by a wider, more realistic set of coalitions. 15 Consider the tuple Γ = N, X, {≺ i } i∈N , {→ S } S⊆N,S =∅ that lists the set of countries or players, the set of global trade policy constellations, the preferences of players over these regimes, and the effectiveness relation of possible transition paths. To understand the meaning of the latter, let x ∈ X be the status quo trade agreement at the start. Next, each coalition S ⊆ N , S = ∅ (including one-country coalitions) is able to make y ∈ X the new status quo as long as x → S y. Continue with y as the new status quo. If a status quo z ∈ X is reached without any coalition moving away, then the state is actually realised and each country receives their corresponding welfare. 16 By consequence, any coalition only favors following through on their ability to move from x → S y, if it prefers the final welfare over the current one, x ≺ S z. Formally, this comparison of states by (chains of) coalitions is captured in the definition of direct and indirect dominance: 15 Consult the paper of Chwe (1994) for proofs of the propositions that are presented here. 16 Technically, the model is without any true sense of time. Any start (or end) as well as any sequence of actions should be interpreted as a thought-experiment. Furthermore, a path created in this fashion is generally not unique.
Note, that direct dominance implies indirect dominance, i.e. if x 1 < x 2 for some x 1 , x 2 ∈ X, then automat- Using this definition, we introduce the concept of the 'consistent set', a (sub-)set that exhibits internal stability in the sense of a lack of incentives to deviate: and only if for all x ∈ X and all S ⊆ N , In general, a consistent set need not be unique, but the following proposition allows us to focus on the unique 'largest consistent set', i.e. the (consistent) set that contains all consistent sets: The set Y is called the largest consistent set or simply LCS.
Similar to the internal stability captured by the definition of consistent sets, external stability is captured by an incentive to gravitate towards the consistent set: Definition 3 (External Stability). Let Y ⊆ be the largest consistent set. Then, it satisfies the external stability condition if for all x ∈ X \ Y there exists y ∈ Y such that x y.
The following result characterises one setting of relevance in which this condition is satisfied: Let X be finite and the underlying preferences irreflexive. Then, the LCS is non-empty and satisfies the external stability property.
Importantly, this result applies to our setting, so the (unique) LCS is non-empty and satisfies external (as well as internal) stability. 17 17 First of all, applying Proposition 1 to our model is trivial, because it is stated without any (additional) requirements on the involved objects. Furthermore, the application of Proposition 2 is straight forward as well: First, the set of outcomes X is clearly finite in our setting as we are only considering a finite number of different trade agreements. Second, any strict preference is automatically irreflexive and our preferences are induced by strict welfare comparisons. Thus, while the definition of the (largest) consistent set in general only guarantees internal stability, our setting actually implies external stability as well.
The largest consistent set is going to be the focus of our analysis. Any trade agreement is considered to be '(potentially) stable' if it is in the LCS, and 'unstable' otherwise. Note that the nomenclature is a tribute to the fact that the LCS as a stability concept is 'weak: not so good at picking out, but ruling out with confidence', because ultimately it 'does not try to say what will happen but what can possibly happen' (Chwe (1994)). Recall that N = {a, b, c} denotes the set of countries. We denote by G = {A, B, C} three non-numéraire goods, so that each country i is endowed with zero units of good I (the corresponding capital letter), and e i units of the other two goods. Country i will end up importing good I and exporting goods J and K, with J, K = I. Each good will thus be exported by two countries, e.g. good I will be exported by countries j and k, which has given the model its name, 'competing exporters model'. In order to guarantee the 'competing exporters'-structure, we need to impose a condition on the degree of asymmetry in terms of the respective endowments: This condition is sufficient to ensure that exports remain non-negative.
On the demand side, let preferences of individuals in each country be identical. The demand for any nonnuméraire good L ∈ G in country i ∈ N is given by d(p L i ) = α − p L i with p L i the price of good L in country i and α the (universal) reservation price. 18 As pointed out before, each country can impose tariffs on imports.
Let t ij denote the tariff imposed by country i on the import of good I from country j. The prices and tariffs of good I ∈ G across countries are linked via the following no-arbitrage condition: where i, j, k ∈ N are pairwise distinct.
In the model at hand, prices together with the corresponding endowments are the only determinants of imports and exports. In particular, the level of imports m I i of good I into country i is completely determined by the above demand function (depending on the price): In turn, the exports x I j of good I from country j are the combination of the demand function (or prices) and the corresponding endowment, x I j = e j − d(p I j ) = e j + p I j − α. Market-clearing for any good I requires that country i's imports equal the exports of countries j and k (again i, j, k ∈ N pairwise distinct) combined: Ultimately, the objective function of the benevolent policymaker in country i is its national welfare 19 , denoted W i , which includes consumer surplus (CS), producer surplus (PS), and tariff revenue (TR): Using the no-arbitrage (1) and market-clearing (2) conditions, we can compute the equilibrium prices: Given equilibrium prices, we can deduce imports, exports, and the welfare of each country up to the value of the tariffs (Appendix B.1). The maximisation of welfare with respect to tariffs will then be constrained by the trade agreement under consideration (see Section 2.1). The full equilibrium of our model is then computed as follows: Fix a trade agreement and thereby the restrictions on tariffs. Compute the best-response functions for each country (with respect to the tarifs) and determine the optimal choices. While Section 2.1 contains all information on the trade agreements that is necessary to compute the equilibria, the actual results are presented in Appendix B.
2. An overview of the (resulting) overall welfare is provided in Appendix B.3.

2.5.
Algorithm and Parameters. The contribution in this paper of considering an extensive set of trade agreements and unlimited farsightedness comes at the cost of a relatively complex computational problem. We solve this problem numerically by means of an algorithm, the pseudocode of which we provide in Appendix A. 20 To solve the model numerically by means of the alogorithm, we need to specify and discretize the parameter space.
Recall that the endowments have to satisfy 3 5 max{e j , e k } ≤ e i ≤ 5 3 min{e j , e k } for all i, j, k ∈ N in order to guarantee the 'competing exporters'-structure (cf. Section 2.4). Without loss of generality, let us normalize one endowment to one, namely e b = 1. Consequently, for i, j ∈ N \ {b}: e min ≡ 3 5 ≤ 3 5 max{1, e j } ≤ e i and e i ≤ 5 3 min{1, e j } ≤ 5 3 ≡ e max . The resulting parameter space is depicted by the hexagon in Figure 3. Given that the three countries are interchangeable, we can split the hexagon into six right-angled triangles, which 19 Depending on the type of trade agreement entered, the (joint) objective function may include the welfare of other countries as well. See Section 2.1 for the details. 20 The authors are grateful to Michael Chwe for the provision of an exemplary algorithm.
are mirror images of one another (in terms of relative endowments). Without loss of generality, we focus on one of them, namely the triangle depicted as shaded in the figure. We cover this triangle of the parameter space with a fine grid for the actual computation. 21 e c e a In addition to endowments, we also need to specify the choke price alpha in the demand function. To obtain plausible results -that is, positive prices -the parameter α needs to be chosen above a minimal value for each tuple of endowments, α min (e a , e b , e c ). Above this minimal value, results remain unchanged. 22 Taking the maximum over all these minimal values, α max min = max ea,e b ,ec {α min (e a , e b , e c )}, adding an epsilon, α = α max min + , and using it for all endowments combinations ensures that the results are plausible and comparable. 23

Analysis
We now turn to the analysis of stable outcomes among the global trade policy regimes that we consider.
That is, for every endowment vector, we determine which regimes make up the largest consistent set. Figure   4 depicts the parameter space of endowments under consideration -it is the (marked) triangle from before.
Note that different endowment vectors represent varying size combinations of countries.
For expositional purposes, we start by studying the three corners of the triangle, then turn to the connecting intervals or edges, and finally consider the entire triangle by studying the full interior. Clearly, the corners are the extrema of the edges, and the edges in turn the bounds of the interior. So the second and third step contain the preceding results as special cases, and we can think of each subsequent step as a linear combination of the endowment combinations considered previously. 21 The distance is set to 0.0013360053440215, resulting in 500 points per dimension. 22 The parameter α enters the welfare of country i as 2αe i (see Appendix B.1). Any changes above the minimal value leave the relative welfare levels and therefore the rankings unaffected. 23 In our computation is fixed at 0.01, which yields α = 1.3988888888888888.
Electronic copy available at: https://ssrn.com/abstract=3910302 For all allowable endowment combinations, we will analyse two scenarios: The first scenario corresponds to the current institutional setup of the WTO. The constitutional status-quo includes PTA regimes, as article XXIV provides for. The second scenario that we study is a hypothetical alternative constitutional arrangement In the symmetric corner, denoted by Sym in Figure 4, all three countries have identical endowments: e a = e b = e c = 1 = e min . As the countries do not differ from one another in this case, the only thing that matters for welfare is whether a country is an insider or an outsider in a specific trade agreement. In the following, we present the ranking of preferences from the perspective of country a (which represents the preferences of the other countries as well). For fixed i, j ∈ N \ {a} with i = j, we obtain the following preference ranking: The case where the two other countries i and j form a customs union is the least favourable trade constellation for country a. As an outsider to the CU (i, j), country a faces the second-highest tariffs (with MFN-tariffs the highest), while the CU members i and j abolish the tariffs between themselves. The exports of country a to the other countries, i and j, are the lowest under CU(i,j) compared to all alternative trade agreements.
The same applies to total imports. In other words, the 'trade diversion' effect is strongest for country a when we have CU(i,j).
In general, the MFN regime favours country a as compared to CU(i,j). The tariff revenue remains the same, while the consumer surplus is lower and the producer surplus higher -the increase in the latter offsetting the decrease of the former. The MFN regime mitigates the 'trade diversion' effect present in the case of CU(i,j) due to increased export values of country a.
Within the set of bilateral trade agreements where country a is an insider, the MTAs result in the lowest welfare (for country a). MTA(a,i) generates a higher welfare for country a in comparison to the MFN regime due to increased consumer and producer surplus. The FTAHub(i) constellations result in further gains in welfare for country a through higher export values and producer surplus, even though tariff revenue and consumer surplus are lower under FTAHub(i) compared to MTA(a,i).
However, country a does not have an incentive to remain in this constellation. The unilateral deviation from FTAHub(i) to FTA(i,j) -that is, if a quits its FTA with the hub country -comes with a decrease in consumer and producer surplus, but enough of an increase in tariff revenue to ultimately ensure higher welfare under FTA(i,j). Yet among (single) FTAs, being an outsider is less desirable than being an insider for any of the three countries, as the drop in tariff revenue is offset by an expansion of consumer and producer surplus, resulting in higher welfare for country a in the case of FTA(a,i) compared to FTA(i,j). As an insider, country a prefers CU(a,i) over FTA(a,i), though. Despite the decline in the consumer surplus, welfare goes up due to an expansion of tariff revenue and producer surplus.
The formation of MTA(i,j) guarantees the highest welfare for country a compared to any other bilateral trade agreement. The driving factor is the MFN-principle, which implies that in case of MTA(i,j) the insiders need to apply the same tariff to their fellow member and to the outsider. Country a free-rides on this characteristic of the MTA regime, and in addition attains the highest possible tariff revenue in this case.
Each country obtains the second-highest welfare level when the world reaches global free trade (that is, the trinity of MTA-, FTA-, and CU-GFT). Under full trade liberalisation, the producer surplus is at its second-highest among all trade agreements (effectively driving the ranking). It is only surpassed by that of FTAHub(a). This constellation brings about the highest possible welfare for country a. Notice, however, that this hub-n-spoke trade agreement disproportionally favours the hub country over the other two.
The countries' preference rankings, which we have just derived for one particular endowment combination, provide the basis for computing the largest consistent set (LCS). In the case at hand, the trinity of global free trade regimes are ranked second-best by each country, while the respective first-best options, hub-n-spoke FTA structures, are ranked considerably lower by spoke countries. The trinity of global free trade thus seems the likely equilibrium outcome. The following proposition and its proof confirm this: Electronic copy available at: https://ssrn.com/abstract=3910302 Proof. Based on the definition of indirect dominance and the transition graphs (cf. Sections 2.3 and 2.2), the preference rankings from above allow us to derive the indirect dominance matrix. If the entry in the matrix is equal to one (resp. zero), then the trade arrangement corresponding to the row of the entry is (respectively is not) indirectly dominated by the one corresponding to the column of the entry. For example, F T AHub(a) is indirectly dominated by CU GF T as there exists a (finite) sequence of outcomes and coalitions such that all coalitions in the sequence prefer the final outcome over the current one: Checking for all possible sequences yields the following indirect dominance matrix: 25 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 M F N 0 1 1 1 1 1 1 1 1 1 Note that intuitively any outcome is stable if all deviations from it are deterred. Also, a deviation from the outcome is hindered if there is a stable outcome which might be reached and some member of the deviating coalition does not prefer it over the initial outcome. In the following procedure, start with the full set and then keep removing elements that are unstable until the remaining ones are stable cannot be deterred and therefore no such x can be part of the stable set. 25 Appendix A contains the pseudocode for this procedure.
Using F T AHub(i) ≺ {j,k} F T AGF T together with the logic from before eliminates F T AHub(i) for each Focus on the set of remaining elements Y = {CU GF T, F T AGF T, M T AGF T }. Start with any element y in Y . If there is a deviation to any element x ∈ X \ Y , then there always exists an indirect dominance path (see indirect dominance matrix) x y coming back to an element y ∈ Y . In addition, for any y 1 , y 2 ∈ Y , of the representative country a over the reduced set of policy regimes then looks as follows: Proof. The indirect dominance matrix is derived as before:  We now proceed to the analysis of the other two extreme cases, which correspond to points LSS and LSL of the triangle, cf. Figure 4. The acronyms stand for country a being large, country b small (always), and country c either small or large.
We consider first the case of two small and one large country, i.e. point LSS. In this scenario, e a = e max and e b = e c = e min . We obtain the following ranking of preferences for country a and for the small countries i ∈ {b, c} and j ∈ N \ {a, i}): One immediately notices that small and large countries have different rankings. A large country profoundly dislikes the scenarios where it is an outsider; while the small countries, by contrast, dislike any trade arrangements with the large country. Note that in certain cases countries actually do not differentiate between different trade constellations. 26 For example, CU(i,j) and FTA(i,j) result in the same welfare for all countries.
In this case, under the given pattern of endowments, the optimal tariffs of the small countries for CU and FTA are above the MFN-tariff. However, the sub-paragraphs of article XXIV paragraph 5 rule this out, and therefore we cap the tariffs at their MFN-level. A similar argument applies to the case of FTAHub(a). Here, the optimal tariffs of the small countries would be negative. Restricting tariffs to be non-negative implies that FTAHub(a) corresponds to GFT, or rather a pseudo-GFT (as external tariffs between spoke countries are zero). Finally, the MTA between the small countries actually coincides with the MFN regime because of identical optimal tariffs for both cases.
Using the above preference rankings to derive the largest consistent set yields the following proposition: 26 Additional details on this can be found in Appendix B.2. Even though global free trade is the most desirable regime for the large country, the two small countries do not have an incentive to agree to such a constellation, and the large country cannot enforce it. By consequence, country a ends up with the worst arrangement (from its perspective). So in this scenario, the size advantage of the large country does not translate into a favourable outcome. Moreover, the case at hand demonstrates the relevance of restrictions on PTAs (remember that insiders are not allowed to raise tariffs on outsiders).
The constraint renders the small countries indifferent between the two forms of PTAs.
We now turn to the hypothetical scenario without article XXIV paragraph 5. The preference rankings for the large country a and the small countries b and c (indexed by i and j) are as follows: As a result, the best outcome for a small country i is the M T A(a, j) regime, i.e. an MTA between the large country and the other small country, as the PTAs are not available anymore. The next proposition presents the LCS for the reduced set of regimes: countries a/c: Electronic copy available at: https://ssrn.com/abstract=3910302 Under this pattern of endowments, the preference rankings of the countries are considerably different from previous cases. For the small country, the MFN regime generates higher welfare than any other trade agreement of which it is part. As for a large country, being an outsider is at the lower end of its ranking, while being an insider in a PTA with a small country is on the top end.
We determine the LCS under these preference rankings in the following proposition: Proposition 7. With the endowments given by e b = e min and e a = e c = e max , and under the current institutional arrangement of the WTO, the stable constellation is the CU between the two large countries, that is CU(c,a).
The small country b manages to block many desirable outcomes for large countries. Country b can unilaterally deviate from any trade agreement with higher welfare than CU(i,j) for the large countries. Thus, the two large countries, despite being a majority, cannot impose their will on the single small country. All the large countries can achieve is the best trade agreement that they can reach without the participation of the small country, which is CU(a,c), a customs union among themselves.
A similar story unfolds in the scenario without article XXIV paragraph 5. Under the reduced choice set, the countries' preference rankings are as follows: countries a/c: As the logic of the respective preference rankings for the countries is similar to before, let us directly present the proposition: Our analyses of each edge will be summarized by graphs that depict the composition of the stable set as we vary the endowment of one country (or of two in unison in the case of VSV), and we provide accompanying descriptions that explore the underlying forces at play. The exact numerical values for the (sub-)intervals of each edge are provided in Section C.3. In order to gain an intuitive understanding of the results, we identify specific trade agreements that switch from stable to unstable (or vice versa) at particular endowment tuples, and explore the underlying mechanics to understand the reason for these switches.  Electronic copy available at: https://ssrn.com/abstract=3910302 countries (b/c) or between the two smaller countries b and c appear. Towards the upper end, where e a tends to one and we reach the LSS corner, only the PTAs between the small countries b and c are still stable.
First, the spike in the number of stable constellations close to symmetry actually follows from a change in the preferences of the varying country with respect to CU(b,c) vs. the trinity of GFT regimes -it starts preferring the former over the latter as it grows larger. Furthermore, FTA(a,b) and FTA(c,a) become unstable because the small countries start to like the MFN regime more than the GFT trinity (or rather these are only stable for as long as this is not the case). When country a becomes sufficiently large, country b prefers  Figure 6. Characterisation of varying, small, and small country Close to symmetry, MTAGFT is the only element in the stable set. As soon as the small countries start to prefer MTAs with country a over MTAGFT, all three MTAs appear in the LCS. As the size of country a increases, the MTAs drop out from the LCS, because the small countries rank the MTA with the large country as the worst trade agreements (switching last place with the MFN regime), which actually also influences the 28 As before, in addition to the above mentioned trade agreements, the graphic also has MFN as a single point, see the dot, at ea = 5/3 (point LSS).
Electronic copy available at: https://ssrn.com/abstract=3910302 stability of the MTA among themselves. Furthermore, the GFT regime becomes unstable when the small countries start to prefer their joint MTA over MTAGFT.
To conclude, the effect of the PTAs on the stability of the GFT regime is significant: the abolishment of Article XXIV Paragraph 5 would facilitate the formation of GFT as long as there are two small countries and the third country is not substantially larger.  Close to the symmetric corner (Sym), the trinity of GFT regimes is stable, and remains the unique element(s) of the stable set for longer (compared to the previous case, VSS). In addition, a collection of different trade agreements is stable relatively close to symmetry. Towards the other side, as e a = e c tends to 5/3 (corner LSL), the CU between the two (varying) countries a and c is the unique stable outcome. Furthermore, the MFN regime is also an element of the LCS in two small (one tiny), separated regions.
Again, the peak in stability near symmetry stems from a shift in the preferences of the varying countries (a and c) with respect to the CUs. At the point of the shift, both these countries start to prefer a respective CU with the small country over the trinity of GFT. The occurrence of the MFN regime follows from a preference of the small country (b) of MFN over the trinity of GFT (the first region), and then over FTAHub(a) and FTAHub(c) respectively (the second, tiny region). As countries a and c grow larger, first MTA(a,b) and Electronic copy available at: https://ssrn.com/abstract=3910302 MTA(b,c) drop out from the LCS as they rank lowest according to the preferences of country b, and then MTA(a,c) follows »> CHECK «< The trinity of GFT becomes unstable once the small country b starts to prefer CU(c,a). Next, CU(a,b) and CU(b,c) follow in dropping out from the LCS as the small country starts to prefer the MFN regime over a CU with any of the larger two countries. As soon as CU(c,a) becomes   In conclusion, for the endowment constellations along this edge, the GFT regime never appears as part of the stable set, independent of the scenario (with/without PTAs). However, the constitutional setup does determine whether partial trade liberalisation may take place or not. The possibility of forming PTAs reduces the incentive of the small(est) country to free ride. Otherwise, without PTAs, the MFN regime is the unique stable outcome when there is one small, one large, and one rather small country, and it is the worst outcome 29 In addition, to the aforementioned elements, it also depicts MTA(b,c) as a single point, see the dot, but this appears only for the sake of completeness because that point corresponds to the corner LSS discussed earlier. 30 Note that MTA(b,c) is stable in the LSS corner, that is, at the lower bound of the interval.
in terms of over-all welfare. Prohibiting PTAs has this important and negative implication only along this edge.
3.3. The interior of the triangle. We now focus on the interior of the triangle in Figure 4. That is, we now consider the full parameter space of endowment allocations. For expositional clarity, we group both CUs and FTAs (incl. FTA-Hubs) together under the label of PTA in figures 11-13. 31 For the same reason, we also surpress the exact member countries of specific trade agreements, i.e. who is an insider and who stays out.
As before, we start by considering the existing institutional set-up, where PTAs are options countries can choose. Figure 11 depicts regions of the parameter space and their stable sets (or rather a simplified view of these). In a small region close to symmetry, labelled as region 1, the (trinity of) GFT regime(s) is the unique stable element. In an adjacent and a slightly more distant area, both labelled as region 2, PTAs become stable as well. The region connecting those two, which we denote as region 3, adds MTAs as another element of the stable set. In a tiny area along the diagonal, indicated as region 4, no form of trade agreement can be excluded from the stable set. 32 Towards the asymmetric corners LSS and LSL, we find two regions, both labelled as 5, where PTAs are the only stable trade policy constellation. In between those two lies region 6, where MTAs are also found to be stable. Finally, in another tiny area along the diagonal, indicated as region 7, MFN enters the stable set as well. In general, with a certain degree of asymmetry between countries' endowments, at most partial trade liberalisation can be expected, as (the trinity of) GFT is an element of the stable set only in regions 1 through 4 which are all characterized by relatively symmetric endowment allocations.
Next, we consider the alternative institutional set-up, where PTAs are not allowed. Figure 12 depicts regions of the parameter space and their corresponding stable sets. In a small area near symmetry as well as in a sizeable area away from it, both denoted as region 1, GFT (that is, MTAGFT here) is again the unique stable element. Adjacent to these are two areas, both denoted as region 2, where MTAs become stable as well.
Moving towards the asymmetric corners, two regions denoted by 3, feature MTAs as the only stable element.
In between those, in region 4, only the MFN is the unique element of the stable set.
The comparison of the two graphs allows us to deduce two compelling statements. The first noteworthy result is the extent of MFN under each scenario. In the alternative institutional setup without PTAs, the area where MFN is an element of the stable set (in fact the unique element in this scenario) is substantially larger than under the status-quo institutional rules. Note that this effect is at work sufficiently away from symmetry towards the corner LSS. Under (significant) asymmetry then, it seems that PTAs allow countries to move towards their international efficiency frontier by forming such agreements (cf. ). 31 However, graphs of this analysis that distinguish between the two types of PTAs can be found in Appendix C.2. 32 Note that this does not imply that every CU, every FTA or FTA-Hub combination of countries is stable.  The reason for this is that PTAs allow countries to discriminate against the outsider, whereas an MTA does not allow for this.
The second interesting result is the difference in the extent of stability of GFT (trinity thereof and MTAGFT respectively) across the two regulatory scenarios. First, recall that once the degree of asymmetry exceeds a certain threshold, none of the GFT regimes remain in the stable set, irrespective of the institutional set-up.
Electronic copy available at: https://ssrn.com/abstract=3910302 Around symmetry by contrast, the opposite holds in that the GFT regimes are always stable (under both scenarios). In between, the effect of PTAs on the stability of GFT depends on the structure of asymmetry. Figure 13 depicts the different areas of stability of the GFT regimes, depending on the regulatory scenario -with or without PTAs. Note that region 1, close to symmetry, indicates the stability of GFT under both regulatory scenarios, as described above. Away from symmetry, in case two countries are relatively larger (but not too large), the abolishment of PTAs results in reducing the area where GFT is stable, corresponding to region 2 in the diagram. In this region, PTAs act as 'building blocks' on the road to GFT, as they generate sufficient costs for the small country in the case of leaving the a GFT arrangement (either CUGFT or FTAGFT here). So punishment in the form of a discriminatory external tariff of a PTA between the relaltively large countries overcomes the free-riding incentive of the small country. By contrast, if two countries are relatively smaller (but not too small), the same regulatory difference yields the exact opposite effect, see region 3. Here, PTAs act as 'stumbling blocks'. When two countries are relatively smaller, a PTA arrangement between them increases their incentive to exclude the single large country. If they form an MTA (when PTAs are not allowed), they would not have such an exclusion incentive, as the non-discriminatory principle applies. The comparison of the two different forms of asymmetry thus yield an important insight: whether PTAs turn out to be 'building blocks' or 'stumbling blocks' for intermediate levels of asymmetry depends on the relative size of two countries versus country three. Figure 13. Stability of GFT regimes with (I) and without (II) PTAs We now go one step further and ask: whenever PTAs are conducive to global free trade, which form of PTA is responsible for the result? In other words, we want to find out which form of PTA, a CU or an FTA, contributes to the stability of GFT when PTAs are available (regions 1 and 2 of Figure 13). The subsequent figure is meant to shed light on this question. From Figure 14 one can see that the stability for GFT (due to the option of forming PTAs) in region 2 stems from the possibility to form a CU among the relatively larger countries. For endowment combinations with somewhat larger countries as in region 2 of Figure 14, an  Electronic copy available at: https://ssrn.com/abstract=3910302 3.4. Hypothetical scenarios with only FTAs or CUs. Figure 13 showed that the availability of PTAs can increase the stability of GFT (region 2). Figure 14 then indicated that this finding is primarily due to customs unions. We obtained this insight in a scenario where both forms of PTAs are available to decision-makers.
Taking this one step further to gain a better understanding, we now extend the space of constitutional setups by considering two additional hypothetical scenarios: In the first scenario, FTAs are ruled out, so countries can form MTAs and CUs only, while in the second scenario, CUs are ruled out, so countries can create MTAs and FTAs only. So we now have four scenarios: status-quo, no-FTA, no-CU, and no-PTA  Figure 15 shows the results for the hypothetical scenario where FTAs are not available. In Figure 16 we represent the regions of the parameter space and their corresponding stable sets for the hypothetical scenario when we rule out CUs.
A few points are worth noting. First, across both scenarios, there is no endowment configuration for which MFN is a stable outcome. Second, even though the area where GFT is uniquely stable is more extensive in a scenario without FTAs compared to the one without CUs (region 1 in Figure 15 vs. region 1 in Figure 16, the latter consisting only of the point of symmetry), the total area where stability of GFT cannot be ruled out is larger without CUs (regions 1 and 2 in Figure 15 vs. regions 1, 2 and 3 in Figure 16). Once we move further away from the point of symmetry, the scenarios considered here do not generate qualitatively different results compared to the scenario with both types of PTA available (cf. Figure 11): towards the asymmetric right-hand-side of the triangle, only partial liberalisation is attainable.
x x x 4 x x 5 x 6 x  Our main conclusion is that the fundamental trade-off between the stability of GFT regimes with and without PTAs (regions 2 and 3 in Figure 13) is also present in the scenarios without CUs. When we switch off the possibility of forming CUs, even though there is a slight gain in the area where GFT is stable (region 3 in Figure 13), we lose regions 5 and 6 where the GFT regime is no longer stable. When we switch off only FTAs, by contrast, there is no gain in stability for GFT, we simply loose stability of GFT in areas 2 and 6.
Next, when discussing region 2 of Figure 13 in the previous subsection (corresponding to regions 5 and 6 in Figure 17), we concluded that CUs were essential in extending stability of the GFT regime to region 2.
We can now provide a more nuanced view: The stability of GFT is ensured solely by the availability of CUs (region 5 in Figure 17). In region 6 of Figure 17, however, the availability of FTAs is required for CUs to play their role. This final result demonstrates the importance of considering a comprehensive set of possible trade policy arrangements when studying their stability.
Electronic copy available at: https://ssrn.com/abstract=3910302 x 5 x x 6 x , is always greater than zero but not always less than the MFN-tariff (and the one towards country j, t * ij , is always zero): i) Lower Bound. By assumption on the endowments e k ≥ 3 5 e j and thus e k > 1 2 e j , which guarantees t * ik > 0.
ii) Upper Bound. By assumption on the endowments e k ≤ 5 3 e j however t * ik ≤ t M F N i requires e k ≤ 13 11 e j , which leaves the interval 13 11 e j < e k ≤ 5 3 e j to require capping. For this interval, the (maximal) MFN-tariff is optimal as the derivative of the joint welfare with respect to t ik is always greater than zero on the interval [0, t M F N i ]: Consider the scenario FTA(i,j), then the optimal tariff of country i towards country k, given by t * ik = 1 11 (5e k − 4e j ), is neither always greater than zero nor always less than the MFN-tariff (but the one towards country j, t * ij , is zero): i) Lower Bound. By assumption on the endowments e k ≥ 3 5 e j however t * ik ≥ 0 requires e k ≥ 4 5 e j , which leaves the interval 3 5 e j ≤ e k < 4 5 e j to require capping. For this interval, the (minmal) zero-tariff is optimal as the derivative of the welfare with respect to t ik is always lesser than zero on the interval [0, t M F N i ]: ii) Upper Bound. By assumption on the endowments e k ≤ 5 3 e j however t * ik ≤ t M F N i requires e k ≤ 43 29 e j , which leaves the interval 43 29 e j < e k ≤ 5 3 e j to require capping. For this interval, the (maximal) MFN-tariff is optimal as the derivative of the welfare with respect to t ik is always greater than zero on the interval [0, t M F N i ]: Electronic copy available at: https://ssrn.com/abstract=3910302 Consider the scenario MTA(i,j), then the optimal tariff of country i, given by t * i = 1 7 (2e k − e j ), is greater than zero and less or equal to the MFN-tariff as per assumption on the endowments 3 5 e j ≤ e k ≤ 5 3 e j .
B.2.5. Notes. The analysis considered country i and an agreement with country j, but it naturally extends to all other combinations. Also, the perspective of the third country needs no further analysis as it always chooses the MFN-tariff. Furthermore, the case of FTAHub(i) is simply a combination of FTA(i,j) and FTA(i,k).
Finally, the three variants of GFT require no additional analysis as every country always chooses the zerotariff.
B.3. Overall Welfare. The following table lists the overall welfare for each (representative) trade agreement, depending purely on endowments, computed modulo 2α n∈N e n , which is the common term associated with the factor α. Also, the notation l c and l c is used to indicate that country l is capped in terms of tariffs from below or above respectively.

Trade
Overall Agreement Welfare   Proof. Let us start by giving the indirect dominance matrix: Recall that X denotes the full set and let Y = {CU (b, c), F T A(b, c)} be the candidate for the LCS. Take any element x from the set X \ Y and consider the deviation x → {b,c} CU (b, c). Note that CU (b, c) is not indirectly dominated by any other element from X and furthermore x ≺ {b,c} CU (b, c) for all x ∈ X \ Y . Thus, the deviation x → {b,c} CU (b, c) can not be deterred for all x ∈ X \ Y . Therefore, no such x can be part of the stable set. 34 As each outcome in X \ Y is indirectly dominated by y ∈ Y (see the matrix), for any coalition and any deviation away from y ∈ Y there always exists a path of indirect dominance back to Y . Moreover, no coalition is actually better off when coming back to Y , as x ≺ S y for all x, y ∈ Y , x = y, and S ⊆ N , S = ∅. Therefore, the set Y satisfies the (internal) stability condition while being maximal, i.e. Y = LCS.
Proof. The indirect dominance matrix is given as follows: 34 It might appear that this proof deviates from the general approach of eliminating element by element from the full set until the remainder forms the stable set. However, in this proof it is purely a coincidence that in one step all elements but the stable ones can be eliminated with one argument (or rather deviation). Proof. The indirect dominance matrix is given as follows:  Electronic copy available at: https://ssrn.com/abstract=3910302