Preferential Trade Agreements as dynamic farsighted networks

48 Pages·2012·1.41 MB·English

Preferential Trade Agreements as dynamic farsighted
networks
James Lake∗
Southern Methodist University
September 15, 2012
Abstract
In the presence of multilateral negotiations, are Preferential Trade Agreements
(PTAs) necessary for, or will they prevent, global free trade? This question is ex-
plored using a novel dynamic network theoretic model where countries are farsighted
and asymmetric in terms of market size. I develop a new equilibrium concept that
endogenizestheorderofnegotiations. WhentwocountrieshaveaPTA,onemember’s
formationofanadditionalPTAmaycreateincentivesforitsoriginalpartnertoforma
PTA with its new partner. When considering forming an additional PTA, the current
member therefore recognizes the potential for erosion of its preferential access in both
partnermarkets. Thisfearofpreferenceerosionunderminesitswillingnesstoformthe
additionalPTA.Thus,globalfreetradeisattainedviaPTAformationwhencountries
fearofpreferenceerosionissu(cid:30)cientlysmall. Looselyspeaking,PTAsarenecessaryfor
global free trade when there are two small countries and one large country but PTAs
preventglobalfreetradewhentherearetwolargecountriesandonesmallcountry. The
model provides insights into the dynamics of recent trade negotiations involving the
US and suggests ambiguities inherent in GATT Article XXIV may actually promote
global free trade.
JEL: C71, F12, F13
Keywords: PreferentialTradeAgreements,preferenceerosion,multilateralism,free
trade, networks, farsighted
∗E-mail: [email protected]. I would like to especially thank Pravin Krishna and M. Ali Khan as well as
the editor and three anonymous referees. I would also like to thank Kamal Saggi, Emanuel Ornelas, Ray
Riezman,JonFaust,HulyaEraslan,HanOzsoylev,MattJackson,MartinRichardson,ReneeBowen,Kyle
BagwellandSumitJoshiforusefulcommentsanddiscussionaswellasseminarandconferenceparticipants
atthe2011SpringMidwestEconomicTradeMeetings,2011PublicEconomicTheoryConference,2011Asia
Paci(cid:28)c Trade Seminar, 2011 International Trade, Development and Game Theory Workshop at the 22nd
Stony Brook Game Theory Festival, the 26th Congress of the European Economic Association, Southern
MethodistUniversity,CollegeofWilliamandMary,UniversityofMemphisandSAISBologna.
1
1 Introduction
Inrecentdecades,thenumberofPreferentialTradeAgreements(PTAs)hasexpandedexpo-
nentially. AlthoughsanctionedbyGATTArticleXXIV,suchagreementsarediscriminatory
by construction and stand in contrast to the central principle of non(cid:21)discrimination artic-
1
ulated in the most favored nation (MFN) principle of GATT Article I. The proliferation
of such discriminatory PTAs has stimulated a substantial academic and policy debate on
whether PTAs hinder or facilitate greater liberalization, especially given the lack of multi-
lateral liberalization since the 1994 Uruguay Round. In the phrasing of Bhagwati (1991,
1993) are PTAs (cid:16)building blocs(cid:17) or (cid:16)stumbling blocs(cid:17) on the path to global free trade?
Various approaches in the academic literature have investigated the interplay between
PTAs and non(cid:21)discriminatory multilateral liberalization. In essence, this is a dynamic
question concerning the evolution of trade agreements over time, yet much of the previous
analysis has used static three(cid:21)country models. These models ask whether an arbitrarily
chosen pair of countries want to form a bilateral agreement (BA) and, if so, how this
a(cid:27)ects the incentives for expansion of the agreement to include the third country, thus
2
achievingglobalfreetrade(see,forinstance,Levy(1997),Krishna(1998),Ornelas(2005b)).
3
Building a dynamic model to analyze the building bloc(cid:21)stumbling bloc issue faces the
importantchallengethatadynamicframeworkrequiresspecifyingtheorderofnegotiations.
That is, which country is initially left out and how, if at all, will it be included later?
Specifyinganarbitraryorderofnegotiations(asinMukunokiandTachi(2006)andAghion
et al. (2007)) creates di(cid:30)culties because the equilibrium of sequential move games is often
sensitive to the order of negotiations (Ludema (1991), Ray and Vohra (1997), Jackson
(2008)) especially since asymmetries in country characteristics are likely to endogenously
4 5
determine the order.
To alleviate this problem, this paper develops a novel dynamic network model in which
6
countriesarefarsightedandasymmetricintermsofmarketsize. Thenoveltyarisesbecause
1WhileGATTArticleIrequiresanytari(cid:27)reductionsa(cid:27)ordedtoonecountryarea(cid:27)ordedtoall,GATT
ArticleXXIVprovidesanescapeclausewherebyPTAmemberscaneliminatetari(cid:27)sbetweenthemselvesas
longastheydonotraisetari(cid:27)sorothernontari(cid:27)barriersonothercountries.
2Alternatively, Ornelas (2005a) views multilateral liberalization as tari(cid:27) reductions on non(cid:21)PTA mem-
bers. BagwellandStaiger(1999),Freund(2000),Bondetal.(2001)andSaggi(2006)alsotakethisapproach
butviewdeterminationoftari(cid:27)sonnon(cid:21)PTAmembersasaselfenforcingoutcomeofarepeatedgame. In
contrast,takingthestallednatureofMFNliberalizationasexogenous,Baldwin(1996)showsthepossibility
ofaPTA(cid:16)dominoe(cid:27)ect(cid:17) inastaticncountrymodel.
3This two(cid:21)step approach is e(cid:27)ectively static because countries do not consider that the initial BA may
createincentivesforformationoffurtherBAs.
4Thein(cid:29)uentialworkofAghionetal.(2007)assumesaleadercountrymakessequentialtakeitorleaveit
o(cid:27)erstotwofollowingcountrieswhonevernegotiatebetweenthemselves. Incontrast,MukunokiandTachi
(2006)assumeanorderinginwhicheachpairofcountrieshasanopportunitytonegotiate.
5Jackson (2008, p. 372) states that (cid:16)... the ordering of links can have a substantial impact on which
networksemerge,anditisnotclearwhatanaturalorderingis.(cid:17)
6SeeGoyalandJoshi(2006)andFurusawaandKonishi(2007)forthe(cid:28)rstapplicationsofnetworktheory
to the PTA literature. They use the Jackson and Wolinsky (1996) static network equilibrium concept of
pairwise stability which is a myopic best response concept. For alternative network theoretic approaches
2
the model embeds a coalitional simultaneous move game in each period of the dynamic
game to endogenously determine the order of negotiations. The new equilibrium concept
thatemerges,calledafarsighteddynamicnetworkequilibrium(FDNE),isintuitivelysimilar
to a subgame perfect equilibrium. However, rather than requiring a Nash equilibrium in
every subgame, an FDNE requires an Equilibrium Binding Agreement, a solution concept
introduced by Ray and Vohra (1997) and Diamantoudi (2003), in every subgame. The
7
dynamics arise because countries form agreements sequentially, at most one per period.
Countries are farsighted because they anticipate the equilibrium evolution of the global
tradenetworkconditionaluponformingandnotformingapotentialagreement,andcompare
the two discounted payo(cid:27)s. Because countries are farsighted, the presence of market size
asymmetryandanendogenousorderofnegotiationsleadstoarichenvironmentofstrategic
interaction and equilibrium dynamics.
The dynamic network model developed provides an opportunity to capture the equilib-
rium e(cid:27)ect of BAs in a three country setting. Loosely, this e(cid:27)ect translates into the idea of
whether BAs are building blocs or stumbling blocs. However, the important work of Saggi
andYildiz(2010,2011)emphasizesthatcapturingtheequilibriume(cid:27)ectrequirescomparing
the equilibrium in which only the MFN principle exists to the equilibrium in which BAs
8
also exist. In contrast, much of the earlier literature draws implications from formation
of a single BA. By comparing the di(cid:27)erent equilibria, Saggi and Yildiz (2011) de(cid:28)ne BAs
as (cid:16)strong building blocs(cid:17) if global free trade is only attained in the presence of BAs. In
contrast, this paper refers to BAs as (cid:16)strong stumbling blocs(cid:17) if global free trade is only
9 10
attained in their absence.
The farsighted and dynamic aspects of the FDNE shed new light on the strong building
bloc(cid:21)strong stumbling bloc question with the notion of preference erosion central to the
analysis. Suppose two countries have the sole BA. These countries are (cid:16)insiders(cid:17) and the
other country is the (cid:16)outsider(cid:17). If an insider forms an additional BA, it becomes the (cid:16)hub(cid:17)
while the other countries become (cid:16)spokes(cid:17). Now the hub has sole preferential access in
each spoke market. However, when contemplating such a move, the insider recognizes the
see Zhang et al. (2009) for a farsighted static framework and Zhang et al. (2011) for implementation in a
symmetricsequentialmovesetting.
7DespitetherecentdramaticaccelerationinPTAformation,individualtradeagreementsstillformslowly
overtime. Forexample,NAFTAwasnotimplementeduntil1994despitenegotiationsbeginningasearlyas
1986, andtwotothreeyearsbetweencommencementofnegotiationsandimplementationofanagreement
iscommon.
8Thisapproachwas(cid:28)rstadoptedbyRiezman(1999)andAghionetal.(2007). However,unlikeAghion
etal.(2007)whouseanextensiveformgamewherealeadermakessequentialtakeitorleaveito(cid:27)erstotwo
followercountries,SaggiandYildiz(2010,2011)allowthefollowercountriestoformanagreementbetween
themselves. UnlikeRiezman(1999),SaggiandYildiz(2010,2011)solvethemodelanalytically.
9ThenewterminologyofSaggiandYildiz(2011)re(cid:29)ectsthevariedusageofthebuildingbloc(cid:21)stumbling
bloc terminology (e.g. Bhagwati and Panagariya (1996), Saggi (2006), Aghion et al. (2007) and Furusawa
andKonishi(2007)).
10WhenglobalfreetradeisonlyattainedintheabsenceofBAs,SaggiandYildiz(2011)refertoBAsas
weak stumbling blocs if some BAs form but they refer to BAs as strong stumbling blocs if no BAs form.
Thispapermakesnosuchdistinction,referringtoBAsasstrongstumblingblocsinbothsituations.
3
spokes may form their own subsequent BA, which erodes the value of preferential access in
each spoke market. When the discount factor is su(cid:30)ciently large, the e(cid:27)ect of preference
erosion dominates the immediate hub bene(cid:28)ts and the insiders (cid:28)nd it Pareto dominant
to remain insiders. Thus, the fear of preference erosion prevents BA formation leading
11
to global free trade. Because sequential BA formation creates rents on the equilibrium
path, sequential BA formation arises in equilibrium even when countries have the option to
formMFNagreements. Moreover, thepreferenceerosionlogicappliesregardlessofwhether
MFN agreements, by themselves, lead to global free trade. Thus, BAs can be either strong
building blocs or strong stumbling blocs.
Marketsizeasymmetryandthediscountfactordrivethefearofpreferenceerosion. Even
whencountriesaresymmetric,asu(cid:30)cientlylargediscountfactormeansthefearofpreference
erosionpreventsadditionalBAformationandunderminesglobalfreetrade. Initially,greater
asymmetry between the insiders and the outsider increases insider rents by increasing the
valueofpreferentialaccessprotectedbyinsiders. Thismakespreferenceerosionmorecostly.
Inturn,sincepreferenceerosionarisesinthefuture,attainmentofglobalfreetraderequires
greater insider impatience. Thus, the extent to which BAs lead to global free trade falls. In
terms of the equilibrium when only MFN agreements exist, the largest country blocks the
move to global free trade when it is su(cid:30)ciently large relative to the medium sized country.
This has two implications for the strong building bloc(cid:21)strong stumbling bloc issue. First,
looselyspeaking,BAsarestrongbuildingblocswhenthereisone(cid:16)larger(cid:17) andtwo(cid:16)smaller(cid:17)
countries. When only MFN agreements exist, the largest country blocks a direct move to
global free trade because the medium country is su(cid:30)ciently small. But, unless the discount
factor is very high, the relatively small insider rents protected by the largest and medium
countries mean the fear of preference erosion does not prevent BA formation leading to
12
global free trade. Second, loosely speaking, BAs are strong stumbling blocs when there
is one (cid:16)smaller(cid:17) and two (cid:16)larger(cid:17) countries. When only MFN agreements exist, the largest
country does not block a direct move to global free trade because the medium country is
su(cid:30)cientlylarge. But,unlessthediscountfactorisverylow,thelargeinsiderrentsprotected
by the largest and medium countries means the fear of preference erosion prevents further
BA formation.
While greater asymmetry initially makes preference erosion more costly, the fear of
preference erosion eventually disappears for some countries. When su(cid:30)ciently large, the
largest country no longer forms the (cid:28)nal spoke(cid:21)spoke BA with the smallest country. Thus,
the medium country no longer fears preference erosion and, thus, no longer hesitates in
becoming the hub. In turn, the largest country exercises far less restraint in becoming the
11BecauseleastdevelopedcountrieshaveprivilegedaccesstotheEUmarketthroughtheEverythingBut
Arms agreement, recent work in the policy literature has investigated the cost of preference erosion they
faceiftheEUgrantslargescaleMFNtari(cid:27)reductions(seeHoekman(2006),LawrenceandRosito(2006),
LimªoandOlarreaga(2006)).
12Thedependenceonthediscountfactorwhichunderliesthe(cid:16)looselyspeaking(cid:17) quali(cid:28)cation.
4
hub. Hence, regardless of whether global free trade is attained when only MFN agreements
exist, the role of BAs becomes much more constructive. The key implication is a non
monotonic relationship between market size asymmetry and the role of BAs: greater levels
of asymmetry initially decrease (increase) the extent to which BAs are strong building
(stumbling)blocsbutcrossingthethresholdlevelofasymmetryprovidesadramaticreversal.
WhilethequestionaskedinthispaperisthesameasAghionetal.(2007)andSaggiand
Yildiz (2010, 2011), the answers are di(cid:27)erent. In addition to developing a dynamic model
that endogenizes the order of negotiations, the results di(cid:27)er from Aghion et al. (2007)
because BAs can be strong stumbling blocs even if the aggregate world payo(cid:27) is maximized
13
underglobalfreetrade. RelativetoSaggiandYildiz(2010),themostimportantdi(cid:27)erence
is that BAs can be strong stumbling blocs. The presence of dynamics and farsightedness
underlie this di(cid:27)erence. Even when all countries would willingly move to global free trade
if MFN agreements were the only form of liberalization, a su(cid:30)ciently large discount factor
meansfearsofpreferenceerosiondominatetemporaryhubrents. Inthiscase,thepresenceof
BAs prevent global free trade. However, this dynamic farsighted logic of preference erosion
is nonexistent for Saggi and Yildiz (2010). There, an insider does not contemplate that the
spokes may subsequently form their own BA if it becomes the hub. Since the spoke(cid:21)spoke
BA underlies the fear of preference erosion, Saggi and Yildiz (2010) (cid:28)nd that BAs cannot
be strong stumbling blocs.
An obvious corollary is that the rationale behind BAs being strong building blocs, i.e.
necessary for global free trade, is di(cid:27)erent to Saggi and Yildiz (2010, 2011). There, the
discrimination faced by an outsider when insiders form a BA can induce the outsider’s
participation in an MFN agreement leading directly to global free trade. Here, in contrast,
insider incentives drive the strong building bloc result. When the fear of preference erosion
is su(cid:30)ciently small, BAs lead to global free trade because an insider willingly forms a BA
with the outsider to become the hub. Moreover, for Saggi and Yildiz (2010, footnote 24),
the outsider’s discrimination fear is general enough that analogous results hold under the
caseofonelargerandtwosmallercountriesinadditiontothecasetheypresentwhichisone
smaller and two larger countries. However, in this paper, these two cases deliver di(cid:27)erent
results in terms of the strong building bloc(cid:21)strong stumbling bloc dichotomy because the
value of insider rents, and thus the fear of preference erosion, depend on the joint size of
insider markets.
The dynamic role of preference erosion underlying the results of this paper is identi(cid:28)ed
14
byMukunokiandTachi(2006). TheirmainresultshowsaconstructiveroleforBAs: when
insiders have a BA, sequential BA formation can yield global free trade when a Customs
13More speci(cid:28)cally, given government payo(cid:27) functions, BAs can be strong stumbling blocs if the world
payo(cid:27)ismaximizedunderglobalfreetrade. Themaintextconsiders(cid:28)rmpro(cid:28)tsasthegovernmentpayo(cid:27)
functionbutAppendixDshowsthemainresultsarerobusttousingnationalwelfareinstead.
14Indeed, Proposition 1 closely resembles the equilibrium characterization described by Mukunoki and
Tachi(2006).
5
Union (CU) would not. Thus, they do not focus on the destructive impact that preference
erosion can have on BA formation which is the focus of this paper. Moreover, since their
focus is the relative merits of BAs versus CUs, they do not consider MFN agreements
and thus they do not consider the question of this paper: the strong building bloc(cid:21)strong
stumbling bloc question. Additionally, they do not endogenize the order of negotiations or
consider country asymmetries which are important features of this paper.
In a related strand of the literature, Krueger (1999) describes how the MFN principle
emerged in the 1800s and early 1900s as a mechanism to protect the value of preexisting
trade concessions. Indeed, Schwartz and Sykes (1997) argue this is the main bene(cid:28)t of the
MFN principle. This may appear to contrast with the result that, despite the presence of
the MFN principle, preference erosion allows a destructive role for BAs as strong stumbling
blocs. However, this result merely emphasizes a key point of Bagwell and Staiger (2005):
whiletheMFNprinciplecanhelpprotectpreexistingMFNconcessions,itcannot,ingeneral,
protect preexisting discriminatory concessions (i.e those won via PTAs).
Insummary,thispaperdevelopsadynamicfarsightednetworkmodelthatendogenously
determines the order in which countries negotiate. The dynamic and farsighted behavior of
countriesimplythat,unlikeearlierwork,BAscanbestrongstumblingblocs,thuspreventing
global free trade, even if the world payo(cid:27) is maximized under global free trade. Moreover,
asymmetry and an endogenous order of negotiations lead to rich equilibrium dynamics that
haveobservableimplicationsforPTAnegotiations. Indeed,theseimplicationsareconsistent
with actual PTA negotiations.
The model predicts a relationship between the order that negotiations commence and
theordertheyconclude: thesmallerinsiderbeginsnegotiationswiththeoutsiderbeforethe
larger insider but, in equilibrium, this induces the larger insider to become the hub. Recent
BAnegotiationsbetweentheUS,CanadaandColombiaaswellastheUS,CanadaandKorea
15
and,toalesserextent,theUS,AustraliaandKoreasupportthissequenceofevents. While
sequential negotiations like these are the most common type of equilibrium that leads to
global free trade, the model does predict that NAFTA style negotiations, where a single
BA expands into a three country PTA, can occur. The model also suggests that preference
erosion underlies why BAs do not form. While the reason behind BA non(cid:21)formation is
inherently unobservable, spoke(cid:21)spoke BAs do not su(cid:27)er from the fear of preference erosion
that insider(cid:21)outsider BAs su(cid:27)er. Indeed, the observable implication that spoke(cid:21)spoke BAs
should have a higher probability of formation than insider(cid:21)outsider BAs receives empirical
16
support from Chen and Joshi (2010).
While the theoretical literature abstracts away from the ambiguities inherent in GATT
ArticleXXIV,theseambiguitiesaregenerallyseenasproblematic. Theambiguitieslieinthe
15TheexacttimingoftheseeventsisdiscussedinSection5.3.
16Speci(cid:28)cally,they(cid:28)ndthattheconditionalprobabilityofaspoke(cid:21)spokeBAexceedsthatofaninsider(cid:21)
outsiderBAbyafactoroffour.
6
realitythatGATTArticleXXIVonlyrequiresPTAmembersremovetari(cid:27)son(cid:16)substantially
alltrade(cid:17) andallowsremovaltobephasedoutovertime. However,themodelsuggeststhese
ambiguities may actually promote achievement of global free trade. Taking advantage of
these ambiguities increases hub bene(cid:28)ts. Indeed, they may rise su(cid:30)ciently that the fear of
preference erosion no longer prevents the insider from becoming the hub. In this sense, the
ambiguities are productive in promoting global free trade.
The rest of the paper proceeds as follows. Section 2 develops the network terminol-
ogy and equilibrium concepts. Section 3 presents the underlying trade model. Section 4
begins by analyzing the equilibrium when symmetric countries choose between BAs and
MFN agreements. It then compares the resulting equilibrium with that when only MFN
agreements exist, which underlies the strong building bloc(cid:21)strong stumbling bloc question.
Sections 5 and 6 perform similar exercises under asymmetric market size, (cid:28)rst assuming
all countries fear preference erosion and then relaxing this assumption. Finally, Section 7
concludes. Appendix B collects proofs not given in the text.
2 Network formation games and equilibrium
2.1 Overview
Following Saggi and Yildiz (2010, 2011), this paper considers two three(cid:21)player games: a
multilateralism game where only MFN agreements exist and a bilateralism game where
countries choose between MFN agreements and BAs. However, unlike Saggi and Yildiz
(2010, 2011), each game is a farsighted dynamic in(cid:28)nite horizon game where at most one
agreement can form per period. Figure 1 depicts the possible networks where the countries
are generically labeled i, j and k. An edge between two countries represents a BA. The free
trade network can arise because of the three country MFN agreement or three individual
BAs. Three features of the model warrant explicit discussion.
First, the assumption of one agreement per period is not crucial to the strong building
bloc(cid:21)strong stumbling bloc results. Because a direct move to global free trade is always
an option, the assumption only rules out a direct move from the empty network to a hub(cid:21)
spoke network. BAs can be strong stumbling blocs when the insiders prefer to remain
insiders rather than become the hub on the path to free trade. But then, by construction,
they prefer a permanent move to the insider(cid:21)outsider network rather than jumping to the
hub(cid:21)spoke network from the empty network. Conversely, when BAs are strong building
blocs, global free trade arises because the spokes bene(cid:28)t from forming their own BA. But,
this does not depend on how the hub(cid:21)spoke network emerged. Despite the non(cid:21)essential
nature of the assumption, it increases analytical tractability of the model. Indeed, de(cid:28)ning
a period as the time required to complete a PTA is not inconsistent with history in that
PTA formation takes a number of years (see footnote 7).
7
Figure 1: Network positions
Second, BAs formed in previous periods are assumed binding. Nevertheless, naturally,
when checking whether an agreement formed in the current period is an equilibrium, de-
viations that involve severing this agreement are considered. Imagining networks as nodes
of a game tree, binding agreements mean players cannot move backwards in the game tree.
Together with an assumption of Markov behavior, this implies the status quo remains for-
17
ever once global free trade is reached or no BA forms in a given period. Since there are
onlythreepossibleBAs, thenetworkremainsunchangedafter, atmost, threeperiods. This
property preserves analytical tractability.
Ornelas (2008) explains that the implicit or explicit assumption of binding PTAs is
very common in the literature (see, for example, Bagwell and Staiger (1997), Bond and
Syropoulos (1996), Maggi and Rodriguez-Clare (1998), Bond et al. (2001), Mitra (2002),
MukunokiandTachi(2006),Ornelas(2007)andOrnelas(2008))andconsistentwithhistory.
Indeed, Ornelas and Liu (2012) note that the the only PTA violating the assumption is
the 2005 Venezuelan withdrawal from the Andean Pact. McLaren (2002) provides strong
theoretic justi(cid:28)cation for the assumption. In his model, initial expenditure on sunk costs
ensureaPTAremainsinplaceeventhough,absentsunkcostexpenditures,countrieswould
prefer an MFN agreement. The sunk costs justi(cid:28)cation also has empirical support (e.g.
RobertsandTybout(1997),EichengreenandIrwin(1998)andFreundandMcLaren(1999)).
Additionally, Baldwin(2008)explainsthatthecostsofseveringBAsfarexceedlostexports
18
because tari(cid:27)s are merely one element of a large and varied set of retaliation instruments.
Third,backwardinductioncanbeusedtosolvetheequilibrium. Tobegin,considereach
hub(cid:21)spoke network and solve for the Equilibrium Binding Agreement (EBA; explained in
Section 2.2.3), given global free trade remains forever once attained. Then, consider each
insider(cid:21)outsider network and solve for the EBA given how the network evolves from any
hub(cid:21)spoke network. Finally, consider the empty network and solve for the EBA given how
the network evolves from any insider(cid:21)outsider network. The sequence of networks on the
17Suppose no link forms in the current period. Markov behavior then rules out the possibility that a
playerwouldformalinkinthefollowingperiodgivenrefusaltoformthislinkinthecurrentperiod.
18Retaliation instruments include the whole host of non tari(cid:27) trade barriers as well as development aid,
military aid and political support in various international political issues. A breakdown in international
cooperation could imply costs via less progress in issues such as climate change, human rights, money
launderingorillegaldrugs.
8
equilibrium path is the farsighted dynamic network equilibrium (FDNE). Thus, an FDNE
is intuitively similar to a subgame perfect equilibrium. However, it requires an Equilibrium
Binding Agreement, rather than a Nash equilibrium, in every subgame.
2.2 Network formation games
2.2.1 Networks and payo(cid:27)s
ThesetofplayersisN ={s,m,l};thesmall,mediumandlargecountries. Generically,they
aredenotedi,j andk. Thegameisanin(cid:28)nitehorizongamewhereanetworklinkrepresents
a trade agreement. Agreements formed in previous periods cannot be severed and, at most,
one agreement can form per period. Thus, denoting the trade agreement formed in period
t by (cid:96) , the network in existence at the end of period t is g =((cid:96) ,(cid:96) ,...,(cid:96) ).
t t 1 2 t
Given a network g, the one period payo(cid:27) to player i is π (g). Given a path of networks
i
(Fgotr0,agnt0y+1c,o.a..l)itiforonmSp⊆erioNd,t(0gon,wgards,,..p.)la(cid:31)yer i(cid:0)’gs(cid:48)c,ogn(cid:48)tinu,a.t..i(cid:1)ondpenaoytoe(cid:27)sitsh(cid:80)at∞t=tht0eβcto−atl0iπtiio(ngtS).
t0 t0+1 S t0 t0+1
prefers the former path over the latter. When the context makes clear the network path
following from g and g(cid:48) then g (cid:31) g(cid:48) and (g ,g ,...) (cid:31) (cid:0)g(cid:48) ,g(cid:48) ,...(cid:1) are used
t0 t0 t0 S t0 t0 t0+1 S t0 t0+1
interchangeably.
2.2.2 Actions, strategies and equilibrium
Given a network g, A (g) and a (g) ∈ A (g) denote, respectively, the action space and an
i i i
(cid:81)
action for player i. Similarly, A (g) = A (g) and a (g) ∈ A (g) denote the action
S i∈S i S S
space and an action for a coalition S ⊆ N. A (g) is the set of announcements i can make
i
given the network at the beginning of the period is g. When i does not have BAs with j
and k in the bilateralism game, i can make the following announcements: i) it wants to
form no agreement, denoted φ, ii) it wants to move to free trade, denoted FT, or iii) the
country name (j or k) with whom it wants to form a BA but has not yet done so. Table
1 summarizes the action space for each player and network type where (cid:216) and FT denote,
respectively, the empty and free trade networks. A proposed agreement forms when all
members of the proposed agreement announce in favor.
In the multilateralism game, only MFN consistent agreements are allowed meaning any
tari(cid:27) concessions must be given to all countries. This requirement rules out BAs. In this
paper, subject to members WTO commitment of not raising tari(cid:27)s, the two country jointly
19
optimal MFN tari(cid:27) is the initial common tari(cid:27). Thus, only the three country MFN
agreement is considered. Moreover, since the three country joint optimal tari(cid:27) is zero, this
20
agreement is equivalent to a direct move to free trade. Hence, the only possible networks
19Saggi and Yildiz (2010) allow two country MFN agreements. There, the jointly optimal tari(cid:27) di(cid:27)ers
fromtheinitialtari(cid:27).
20Seefootnote31
9
Player action space
Network
A (g) A (g) A (g)
i j k
(cid:216) {φ,j,k,FT} {φ,i,k,FT} {φ,i,j,FT}
(ij) {φ,k,FT} {φ,k,FT} {φ,i,j,FT}
(ij,ik) Empty {φ,k} {φ,j}
FT Empty Empty Empty
Table 1: Action space for the bilateralism game
inthemultilateralismgamearetheemptynetwork,withA ((cid:216))={φ,FT}foreachcountry
i
i, and the free trade network.
Given the action space for each network, a Markov strategy for player i is a function σ
i
that assigns an action a (g) for every network g. Since a strategy pro(cid:28)le σ = (σ ,σ ,σ )
i i j k
induces a unique network path (g ,g ,...) from any initial network g , σ induces the
t0 t0+1 t0
continuation payo(cid:27) for player i of (cid:80)∞t=t0βt−t0πi(gt). A farsighted dynamic network equi-
librium (FDNE) is simply de(cid:28)ned as the equilibrium path of networks that emerges by
using backward induction to solve for a strategy pro(cid:28)le σ such that the action pro(cid:28)le
a(g) = (a (g),a (g),a (g)) is an EBA for every network g or, equivalently, is an EBA
i j k
21 22
in every subgame.
2.2.3 Equilibrium Binding Agreements
RayandVohra(1997)introducedtheequilibriumconceptofanEquilibriumBindingAgree-
ment (EBA). This paper uses a slight variation introduced by Diamantoudi (2003) and
discusses this variation below.
AnEBAissimilartoacoalitionproofNashequilibrium(CPNE),recentlyusedbySaggi
and Yildiz (2010, 2011) and Saggi et al. (2011). Each concept begins by only considering
Pareto optimal action pro(cid:28)les and restricts attention to pro(cid:28)table deviations that are (cid:16)self
enforcing(cid:17). A deviation is self enforcing if the deviation results in an action pro(cid:28)le that is
itself an equilibrium. Thus, both concepts require coalition deviations be robust to subse-
quentdeviationbycoalitionmembers. Hence,bothconceptsare,tosomeextent,farsighted.
However, the key di(cid:27)erence is that deviating players in a CPNE assume other players ac-
tionsremain(cid:28)xedfollowingtheirdeviationwhiledeviatingplayersinanEBAassumeother
players actions adjust in response to their own deviation.
CentraltoanEBAistheideaofacoalitionstructure. Acoalitionstructure, denotedP,
21An FDNE can be seen as an extension of the Dutta et al. (2005) dynamic network formation model.
Unlikehere,theDuttaetal.(2005)notionofanequilibriumprocessofnetworkformation(EPNF)assumes
the pair of players who negotiate in any given period, the (cid:16)active pair(cid:17), is exogenous. However, unlike
an FDNE, an EPNF allows each player in the active pair to sever any of its agreements. Nevertheless,
unfortunately from the perspective of BAs, an EPNF does not allow players other than the active pair to
severexistingagreements.
22Indeed,Bernheimetal.(1987)notonlyintroducecoalitionproofNashequilibrium(CPNE)tothegame
theoreticliteraturetheyalsointroduceperfectlyCPNEwhichsolvesforaCPNEineachsubgame.
10