Synergy, learning and the changing industrial structure

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Synergy, learning and the changingindustrial structureTarun Kabiraj a & Ching Chyi Lee ba Indian Statistical Institute , Kolkata , Indiab The Chinese University of Hong KongPublished online: 12 Dec 2010.

To cite this article: Tarun Kabiraj & Ching Chyi Lee (2004) Synergy, learning and thechanging industrial structure, International Economic Journal, 18:3, 365-387, DOI:10.1080/1016873042000270018

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International Economic Journal,Vol. 18, No. 3, September 2004

Synergy, Learning and theChanging Industrial Structure

TARUN KABIRAJ* & CHING CHYI LEE**

*Indian Statistical Institute, Kolkata, India**The Chinese University of Hong Kong

ABSTRACT In a set-up of two local firms and one foreign firm, we construct a modelto capture the dynamics of local industrial structure induced by formation andbreakdown of cross-border joint ventures (JVs). There is a synergic gain to the JV,and the partners learn from each other. Firms play a repeated game. We character-ize the resulting industrial configurations under different scenarios as defined by theextent of cost saving. In particular, we show that when cost saving is moderate, analliance formed between two firms in the first period, breaks up and a new allianceis formed in the second period, but again it breaks up; thereafter the marketbecomes an oligopoly of all three firms.

JEL CLASSIFICATION: F23, L13, O33

KEY WORDS: Synergy, learning, joint venture, subsidiary, industry structure

Introduction

Since the 1980s all countries are following a policy of liberalization andopening up. Even the two erstwhile protective basins of the world –namely, China and India – have extensively liberalized their economiesduring the last two decades. As a result, foreign direct investment (FDI) isflowing smoothly into these countries. FDIs are coming either throughwholly-owned foreign subsidiaries, or through joint ventures (JVs) bymeans of equity investment. The foreign multinational companies (MNCs)are bringing with them superior technologies, input and managerial knowl-edge. With this, the domestic industry is experiencing a continuouschange. Some firms are winding up their operation; some new firms areentering into the industry; some firms are gaining strength; some firms arebecoming marginalized; some firms are forming an alliance; and someother firms are switching their alliances. In this paper we provide aschematic model that captures the dynamics of an industrial structure

Correspondence Address: Tarun Kabiraj, Economic Research Unit, Indian StatisticalInstitute, 203 B. T. Road, Kolkata – 700108, India. Email: [email protected]

1016-8737 Print/1743-517X Online/04/030365-23 © 2004 Korea International Economic Association

DOI: 10.1080/1016873042000270018

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366 Tarun Kabiraj & Ching Chyi Lee

induced by JVs of domestic and foreign firms, and study the effects of theopposing pulls of synergy and learning on the evolution of JVs.

In our analysis, two driving forces behind the changing industrialstructure are synergy and learning. Depending on the extent of synergyand learning, the incentives for forming an alliance and switching analliance change over time. It is widely accepted in the literature, andcorroborated by a number of empirical studies, that the firms can pooltheir complementary resources and gain possible synergies. Also, theforeign firms can minimize the risk and uncertainty of investing in anunknown place, and the local firms gain through learning superior tech-nologies and foreign managerial skill. In fact, synergy and learning are twoimportant factors that make JVs the most popular form of internationalbusiness.1 There can also be many other strategic reasons why jointventures may be favoured.2

At the same time, a JV as a business form is very fragile.3 This isevident from the incidence of the number of JV breakdowns.4 On the onehand, synergy and learning provide incentives for forming JVs, on theother hand these factors are mostly responsible for the break-up of thealliances.5 Learning reduces the potential gain of synergy. Then break-down occurs when partners fail to sustain their complementarity.6 Thishas resulted in the changing industrial structure.

We start with a symmetric Cournot duopoly and a potential entrant.Then, as liberalization takes place, the entrant (henceforth we call it aforeign firm) enters the local industry either through opening up a subsidi-ary (in which case the market is a symmetric triopoly), or by forming a JVwith one of the local incumbents. In the case of a JV, we assume that

1 The rate of alliance formation in the United States has been growing by over 25%annually since 1985 (Pekar & Allio, 1994). In China, out of 175,000 foreign investmentprojects approved during 1979 and 1993, about 75% took the form of a joint venturebetween a local firm and a foreign multinational (Almanac of China’s Foreign Relationsand Trade, 1994). In India most of the foreign investments have come through JVs.

2 See, for instance, Marjit (1990), Chan & Hoy (1991), Kwoka (1992), Yu & Tang (1992),Purkayastha (1993), and Das (1999).

3 For a conceptual background and understanding of the problem of JV instability andbreakdown see, in particular, Dymsza (1988), Bleake & Earnst (1995), and Miller et al(1996).

4 Killing (1982) surveyed 37 international JVs and found that 36% of them performedunsatisfactorily. In Kogut (1989), out of a sample of 92 US based JVs, about half hadterminated their relation by the sixth year. The study by Mckinsey consultancy firm ofmore than 200 alliances shows that the median life span of a venture firm is onlyseven years, and in more than 80% of the cases it ends with one partner selling itsstake to the other (Bleake & Earnst, 1995). The Miller et al. (1996) survey covers 70JVs in six developing countries and finds that at least 27% of them did not survive.

5 For empirical studies on this issue see Hamel et al. (1989), Hamel (1991), Modi(1993), Beamish & Inkpen (1995) and Pilkington (1996). It may be mentioned that inour paper there is as such no difference between JV formation and merger. Therefore,breakdown of JVs will be considered as equivalent to demergers.

6 For the theoretical literature on the break down of joint ventures see Kabiraj (1999),Roy Chowdhury & Roy Chowdhury (2001), Lin & Saggi (1998), Sinha (2001) andKabiraj et al. (2001).

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Synergy, Learning and the Changing Industrial Structure 367

there is a synergy gain due to complementarity of inputs involved in thefinal good production. This reduces unit cost of production for the JV.7 Tomake the structure simple we assume that if the MNC enters through asubsidiary, it has the same unit cost of production as that of the localfirms. Moreover, if the JV is formed, partners learn from each other duringthe first period of their operation, that is, within one period each partneracquires, through learning-by-doing, the necessary knowledge embeddedin the other partner’s complementary inputs, and this learning is possibleonly through formation of a JV. The cost saving in our paper is exoge-nous, and firms play repeated games. Hence in the second period, andalso in the future periods, the partners are free to continue their JVrelations or go their separate ways.

Then the contribution of the paper is to define, in terms of the costsaving achieved through synergy and learning, the resulting equilibriumconfigurations – monopoly, duopoly, oligopoly, whether there is JV or not,and in each period. As the cost saving increases, the equilibriumconfiguration goes from oligopoly to duopoly (and JV), and then tomonopoly if the cost advantage resulting from the JV is high enough. Inparticular, we have a scenario when an alliance formed between twopartners in the first period, breaks up and a new alliance is formed in thesecond period, but with a different composition. Again, the new alliancebreaks up at the beginning of the third period. This occurs when thesynergy gain is of the intermediate level. When the industry structure isstabilized, all firms may have low cost of production, or only a subset ofthem has low cost. Thus, synergy and learning play a crucial role to shapethe future industrial structure and market competition.

It is not difficult to explain the result. If, in an industry, two firms form analliance, market concentration goes up, and competition gets reduced tothe extent the number of effective competitors falls. This does not necess-arily mean an increase in the market power of the alliance because, dueto externalities, the outsider firms gain (Salant et al., 1983). If, therefore,the alliance formation is associated with some synergy gain or costadvantage, it becomes privately profitable (Perry & Porter, 1985). In thecontext of more than one period, alliance formation can, however, beprofitable even if it is not profitable immediately, because by means ofalliance formation partners may learn each other’s complementary knowl-edge and come up with a low cost in the future; hence, partners may forman alliance in the current period for learning and future gain. Thus, onedimension of the alliance formation is learning. But as learning occurs, tothese partners the JV may not necessarily remain a profitable institution,because the potential gain of synergy declines; as we have noted already,

7 To the extent synergy arises for forming a JV between any two firms, distinguishingfirms as domestic and local is unnecessary. However, by christening some firms asdomestic and some as foreign we presume that synergy gain in JV is possible only ifit is formed between two cross-border firms. Perry & Porter (1985) provide a modelshowing how an alliance (merger) formation might result in lowering the marginal costof production.

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if the synergy gain is not sufficient, competition at the market place maybe a more profitable option. Thus, the possibility of synergy gain andlearning results in the changing industrial structure of the economy.

To summarize the results of the paper, let the marginal cost of each firmbe denoted by c. The synergy (and learning) effect gives a cost c� � c.Then the industry can be in one of the following six states: (1) Cournotduopoly with costs (c, c) when no entry occurs; (2) Cournot 3-opoly withcosts (c, c, c) when entrant enters directly; (3) JV with cost c� and an oddfirm with cost c when it stays; (4) JV monopoly with cost c� when the oddfirm exits; (5) Cournot 3-opoly with costs (c�, c’) for the partners of thedissolved JV and cost c for the odd firm; and (6) Cournot duopoly withcosts (c�, c’) for the partners of the dissolved JV and the odd firm exiting.Then, evolution is a Markov process transiting among these states, withstate 1 as the initial state. Transitions between two adjoining periodsdepend on (i) whether a hitherto non-existent JV is formed, (ii) whether anexisting JV breaks up, and (iii) whether the odd firm, if any, exits or stays.It also depends on how the players are impatient about their futurepayoffs. Industrial evolution is also sensitive to the rules of the game andto the assumption of learning.

In the next section we provide the structure of the model. In the thirdsection we analyse the results. In the fourth section we discuss our resultsunder alternative assumptions. The last section is a conclusion.

Model

We consider a framework described by the following assumptions.

(A1) Initially, two identical local firms were competing in quantities for ahomogeneous good, and entry of both foreign goods and foreignfirms were prohibited. But at present, the local government hasliberalized its economy. As a result, one foreign-based multinational(MNC) is going to enter the local industry either through forming aJV with a local incumbent or by opening a wholly owned subsidiary.The MNC has the same Cournot conjecture.

(A2) Given the technological knowledge of input and output production,the unit cost of final goods production by each firm is c � 0.However, if a joint venture (JV) is formed between a local firm andthe foreign firm, there is a gain in synergy that reduces the JV’s unitcost of production to c�, c� � c. This cost saving is exogenous.Implicitly, therefore, we assume that production of final goodsinvolves at least two inputs,8 and synergy comes from the comple-mentary nature of the input technologies. In the case of a wholly

8 For example, suppose that the MNC supplies technologies while the local firmcontributes local knowledge.

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owned subsidiary formation by the foreign firm, we assume thatthere is no set-up cost or entry cost.9

(A3) Learning is possible only through JV, and learning is complete byone period. That is, if a JV is formed, then each partner after justone period can acquire all knowledge embedded in the comple-mentary inputs of the other partner with no additional cost. Hence,if a JV is formed in any period, both the partners will have c� as aunit cost from the next period onwards. Later we discuss if learningis possible without JV.

(A4) We consider an infinite time horizon model with a symmetricdiscounting factor, �, for all firms; 0 �� 1. We also study theconsequences if the life of the product is finite.

(A5) We make the following assumptions to simplify the JV contract.First, assume that firms will write a JV contract only for one periodat a time, although they can renegotiate or recontract every pe-riod.10 Secondly, it is only the MNC that can give a JV contract. TheMNC gives a contract (�,F), where � � [0,1] is the JV profit shareof the local firm, and F is the transfer payment from the MNC to thelocal partner. The local firms simultaneously and non-cooperativelydecide whether to accept or reject the contract. If both accept, theMNC chooses its partner randomly. Quite obviously, F � 0 impliesa transfer payment from the local partner to the MNC. The MNC willtry to extract profits as much as possible. Thus, for a period forwhich the JV contract is signed, the net payoff to the local firm willbe � �J � F � x (say), where �J is the JV profit for this period, andthe foreign firm’s net payoff for that period is (�J � x). In theremaining analysis we, therefore, examine whether such an xexists so that a JV contract can be written between the MNC anda local firm. This would necessarily imply an existence of a contract(�, F) for a JV agreement.

(A6) We also assume that the local government does not allow morethan two firms to merge or form a JV. Hence it has enacted antitrust

9 If there were entry cost or cost of opening a subsidiary by the MNC (of course, assumethat entry through a wholly-owned subsidiary would still be feasible), the incentive offorming a JV would be larger, because now, in addition to synergy gain, the JV couldsave the set-up cost. At the same time incentives to break up the JV structure woulddecline for the same reason.

10 By this assumption we do not mean that firms cannot write a long-term contract in thepresent structure. In fact, in our complete information model, a breakdown of JVs ora separation of partners is always mutually beneficial, and hence, instead of writingcontracts every period (whenever profitable), firms can write the contract also on thelength of the life of the JV. It will be evident from the later analysis that the optimal lifeof the JV will be either just one period or the whole length of the time horizon. Thatfirms cannot write a JV contract for more than one period at a time is a simplifyingassumption; it enables us to reduce a two-dimensional contract, (�, F), to a singledimension, {x}.

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laws to prevent an alliance of more than two firms.11 While, in ourstructure, by assumption there is no fourth firm to enter, but anyexisting firm can leave the industry when operation is not profitable.It is also possible that due to a large synergy gain, the JV emergesas a monopoly in the industry.

(A7) Finally, we assume that the market demand for the product islinear. The demand function in inverse form is given by:

P � a ��i

qi, a � c � a/2 (1)

where P is the product price and qi is the supply of the ith firm.12

Assumptions on demand and costs are sufficient to generate uniqueequilibrium under the different scenarios we shall describe in the followingparagraphs. Readers will understand from the analysis that the results ofthe paper do not depend as such on the linearity of the demand function;the results depend on the existence of some parameters based ondemand and cost functions. The assumption of linear demand is sufficientto ensure the existence of these parameters.

Given the assumptions stated above, we study now how the industrialstructure changes over time due to the possibility of alliance formation,learning and breakdown of the alliances. In this section we study theincentive of forming a joint venture in the context of a single period.

If the MNC enters through its subsidiary, the market structure will becharacterized by the non-cooperative Cournot–Nash competition of threesymmetric firms, with each firm’s single period payoff being �(c,c,c). If thisstructure prevails for all future periods, the present value of profits of eachfirm will be �(c,c,c)/(1 � �). However, if a JV is formed between the foreignfirm and a local firm, the JV’s single period payoff will be denoted by�e(c�,c). The corresponding outsider’s (the other local firm’s) payoff is�n(c�,c). The subscripts e and n stand for ‘efficient’ and ‘non-efficient’firms, respectively. When the operating firms will be symmetric in terms oftheir costs, we shall use no subscripts. Then, in a single period context,a joint venture formation is privately profitable if and only if13

11 One motivation of this assumption is the following. In every country there are lawspreventing or minimizing the monopolization effect on consumers’ welfare. Hence, inour structure, at most a two-firm merger may be allowed. Of course, if one firmemerges as monopolist due to its low cost of production, this is always welfareimproving. It may also be mentioned that there are situations when even if we allowall firms to merger, firms may fail to form such a grand merger because of theexternalities under Cournot competition (see Kabiraj & Lee, 2003).

12 By assuming c � a/2 we have allowed that the JV can emerge as a monopoly, that is,Pm(c�) � (a � c�)/2 � c.

13 Note that even if the inequality (2) is reversed, a bilateral JV formation may beprofitable if �e(c�, c) � �n(c�, c) � 3�(c, c, c) and bribing by the third firm is allowed.While we assume that any JV contract is legally enforceable but bribing is not, bribingin fact will not occur because it will not be subgame perfect. The reason is thefollowing. Suppose �e(c�, c) � 2�(c, c, c), and bribes are paid by one of these firms tothe other two firms for forming a joint venture. Then, these firms after receiving bribes

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�e(c�,c) � 2�(c,c,c) (2)

This simply tells that a single-period JV’s profit must be greater than thesum of the non-cooperative payoffs of its constituent members for the JVto be privately profitable. Following Salant et al.’s (1983) results,14 wehave:

�e(c,c) � 2�(c,c,c) (3)

that is, if all firms are symmetric, a bilateral alliance is never privatelyprofitable. Note that �e(c�,c) is a decreasing function of c�, and that:

∃ c|c' � c ⇔ �n(c',c) � 0, �e(c',c) � �m(c') � 2�(c,c,c)

where �m is the monopoly profit (see footnote 12). From the aboveanalysis it follows that:

∃c, c � c � c|c' � c ⇔ �e(c',c) � 2�(c,c,c) (4)

This tells that if the extent of synergy gain is above some critical level, asingle period JV formation is profitable. When synergy is too strong, theventure firm will emerge as a monopoly in the industry. With demandfunction (1), we have:

c � (2c � a) andc � [(3 � 2�2)c � (3 � 2�2)a]/4�2 � 1.03033c � 0.03033a

Now given the initial cost structure, if a JV is formed in any period, thenby assumption (A3), in the next period two firms will have low cost (c’) andthe other firm high cost (c). Under this scenario, let us see the incentiveof forming a JV between any two firms for a single period.

Two types of JV are possible, namely, a JV between two efficient firms,and a JV between one efficient firm and one inefficient firm. Now, JVformation between two efficient firms is profitable if and only if:

Ge(c') � �e(c�,c) � 2�e(c�,c’, c) � 0 (5)

and JV formation between one efficient and one inefficient firm isprofitable if and only if:

Gn(c') � �(c�,c') � �e(c�,c’, c) � �n(c', c', c) � 0 (6)

Note that in the first case the JV is facing a high cost rival, and in thesecond case the rival is a low cost firm.15 The following Lemma is mostimportant for the remaining analysis.

footnote continuedwill not be interested in forming the joint venture, since they know that the bribercannot go to the court for claiming bribes. So inequality (2) remains to be thenecessary as well as sufficient condition for a profitable JV formation.

14 See Cheung (1992) and Fauli-Oller (1997). They derive conditions for a profitablealliance (merger) formation under general demand function.

15 Note that when Ge(c�) � 0 and Gn(c�) � 0, we assume that a JV is not formed. Fromthe result of Lemma 1 it is further clear that there is no range of c� in which Ge(c�) � 0and Gn(c�) � 0.

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Lemma 1. In the context of a single period, JV formation between theefficient firms is profitable iff c� � c* � (c � (�2–1)a)/2 � �2), and thatbetween one efficient and one inefficient firm is profitable iff c� � (c,c**),where c � (3c–a)/2 and c** � (15c–a)/14.16

Proof. First, note that:

∃ c|∀e' � c, �n(c',c',c) � 0

and hence for all such c�, �e(c�,c�,c) � �e(c�,c’), that is, the inefficient firmwill cease to operate under three firms non-cooperative competition if c�� c, and in that case the market will be a duopoly of efficient firms. Quiteobviously, c � c.

Then if c� � c, the inefficient firm survives under non-cooperative com-petition, and it is easy to see that Ge � 0. When c� � c, �e(c�,c) � �m(c’) and�e(c�,c�,c) � �e(c�,c’). Hence we must have Ge � 0 for this interval of c�.Also for c � c� � c, Ge(c’) is monotonically decreasing in c�. Hence:

∃ c*|Ge(c') � 0 ⇔ c' � c*

This proves the first part of the result.The JV formation between one efficient and one inefficient firm will be

profitable iff Gn(c’) � 0. This function has the following properties: Gn(c’) isinverted U-shaped with Gn(c’) � 0 for c' � c, and Gn (c’) � 0 at c� � c. Sothere exists c� � c** � c at which Gn(c**) � 0 and Gn � 0 for c� � c**.Hence, Gn(c’) � 0 for c� � (c,c**). Also, Ge(c’) � 0 for c� � c*. This provesthe second part of the result.

Comparing all the parameters so far defined17, we get:

c � c* � c � c** � c � c � a (7)

The results of Lemma 1 are depicted in Figure 1. It is seen that Ge(c’) � 0for c� � c* and Gn(c’) � 0 for c� � (c,c**). Later, we define g(c’). We arenow in a position to analyse the results of the paper. In the next sectionwe shall see how the industrial structure changes over time following theJV formation in the first period. As we shall see in the next section, theextent of synergy gain through JV and learning, and the degree ofpatience of the players about future payoffs are some factors that play themost crucial role. Then, depending on the synergy gain, the marketstructure can be monopoly, duopoly or oligopoly, and it remains unstablefor the first few periods.

16 Kabiraj & Mukerjee (2000) come up with these parameters in the context of studyingthe relationship between R&D and merger. Hence, the proof of the proposition followstheir analysis.

17 Note that in our case c** � 1.07142c � 0.07142a (approximately).

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Figure 1. Critical cost parameters and incentives for joint ventures

Results

In this section we analyse how the structure of the local industry under-goes changing over time due to synergy and learning, and therebythrough alliance formation and break up of the alliances. Now, dependingon the extent of synergy or cost saving, given the results underlyingLemma 1, we have different scenarios, and each such scenario portraysa different path of the industrial structure. Given the critical cost parame-ters defined in the last section (see equation (7)), we have six possiblecases, namely, (i) c� � [0,c], (ii) c� � (c,c*), (iii) c� � [c*,c], (iv) c�� (c,c**), (v) c� � [c**,c) and (vi) c� � [c,c). Of these cases, the scenarioas described by case (iv), that is the case when the cost saving is of theintermediate level, appears to be most interesting. Hence, we discuss thiscase separately in the next subsection; all other cases are discussed inthe subsection after. Whenever a JV is formed in the first period, we shallcall the corresponding JV local partner L1; then the other local firm is L2.To recapitulate the structure of the game, the MNC first gives an offer {x},and the local firms simultaneously and non-cooperatively decide whetherto accept or reject. If both accept, the MNC chooses one incumbentrandomly as its partner in the JV. The MNC gives the contract in such away that it maximizes its own payoff over the whole time horizon.

Intermediate Level of Cost Saving

Consider the scenario defined by the interval of c� � (c,c**). We show thatthis case will give the possibility that the first period is JV between theMNC and L1, the second period is also JV but between the MNC and L2,

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and from the third period onwards the market structure is symmetricoligopoly of all three firms.

Let us specify the moves of the players. In the first period, the MNCgives a JV offer for one period to a local firm. Note that since at this stageboth the local firms are identical, any offer by the MNC will either beaccepted by both or be rejected by both. If the offer is rejected (or, if theMNC gives a non-acceptable offer), then the market structure will be asymmetric oligopoly of all three firms for all periods, with each firmoperating at a cost level c. When the offer is accepted, let us assume thatthe MNC forms a JV with a local firm, L1. Then the market structurebecomes a duopoly with JV operating at a cost c� (due to synergy) andthe odd local firm operating at a cost c.

When the first period is a JV between the MNC and L1, at the beginningof the second period the MNC now first gives a new JV contract to L1 forperiod 2. If it is accepted by L1, then the market structure remainsunchanged, and since there is no change of the scenario, the samesecond period contract will be offered to L1 in the next period and it willbe accepted. Hence, the same market structure will prevail for all futureperiods. On the other hand, if L1 rejects the second period contract, theMNC will give a JV contract to the other local firm, L2. If L2 rejects theoffer, there will be no further change of the scenario, and hence from thesecond period onwards the market structure is oligopoly with two efficientfirms and one inefficient firm. But if L2 accepts the contract, the secondperiod will be a JV between the MNC and L2, but such a venturemust break down at the beginning of the third period. All firms nowcome up with the same low-cost technology c�, and there is nofurther synergy and learning effect; therefore, from the third period on-wards, the market structure again becomes a triopoly, but now all firmshave low-cost technology. We solve the subgame perfect equilibrium ofthis game. In particular, we focus our attention on the equilibrium whenthe first period is a JV between the MNC and L1, the second period is aJV between the MNC and L2, but from the third period onwards it is asymmetric oligopoly of all three firms. The game is portrayed in a GameTree as shown by Figure 2. The relevant nodes are denoted bynk � 1,2 … at which the MNC gives an offer. We solve the game in abackward fashion.

Let us first consider the subgame started at node n3 that follows afterthe first period JV contract is accepted by L1 but it has rejected thesecond period JV contract. Then we have the following result.

Result 1

Given the subgame at node n3, ∃ a JV contract {y} which will necessarilybe accepted by L2, and the optimal contract is y* � �n(c�,c�,c)/(1 � �) � ��(c�,c�,c)/(1 � �).

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Figure 2. Game tree when c� � (c,c**)

Proof

If a JV is formed in the second period, then from the third period onwardsthe market structure will be a symmetric oligopoly of all three firms, witheach firm’s cost c� and payoff �(c�,c�,c’) per period, and following the logicof equation (3) there can be no further alliance between any two firms. Onthe other hand, if no JV is formed in the second period, per period payoffsof the MNC and L2 from the second to future periods will be, respectively,�e(c�,c�,c) and �n(c�,c�,c). Therefore, a JV contract {y} between the MNCand L2 will be signed in the second period iff the following conditions holdsimultaneously. For the local firm (L2),

y � � �(c',c',c')/(1 � �) � �n(c',c',c)/(1 � �)or

y � �n(c',c',c)/(1 � �) � ��(c',c',c')/(1 � �) � y (8)

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and for the MNC,

[�(c',c') � y] � ��(c',c',c')/(1 � �) � �e(c',c',c)/(1 � �)or

y � �(c',c') � � �(c',c',c')/(1 � �) � �e(c',c',c)/(1 � �) � y (9)

Then we have y � y iff

[�n(c',c',c) � �e(c',c',c) � �(c',c')] � �[2�(c',c',c') � �(c',c')]

Given the assumption on synergy, the left-hand side (LHS) is negative(see equation (6)) while the right-hand side (RHS) is positive (by the logicof equation (3)). Therefore, under the optimal contract (satisfying equation(8) with strict equality), the net payoff of L2 in the second period will be:

y* � �n(c',c',c)/(1 � �) � ��(c',c',c')/(1 � �)

Correspondingly, the payoffs of the MNC and L1 in the second period arerespectively, [�(c�,c’) � y*] and � (c�,c’). This completes the proof.

Given the result of the subgame at node n3, let us now consider theequilibrium of the subgame started at node n2. Our concern is: does thereexist a JV contract, {x�}, that is acceptable to L1, noting that if such acontract is rejected by L1, the MNC will offer y* to firm L2 and L2 willaccept it, and if L1 accepts the MNC’s JV contract, the same contract willbe repeated every future period? A JV contract between the MNC and L1from the second period onwards will be profitable if the following conditionholds: the sum of the profits of the MNC and L1 under their JV will be atleast weekly larger than the sum of their profits when a JV is formedbetween the MNC and L2 in the second period. This means:

�e(c',c)/(1 � �) � [�(c',c') � ��(c',c',c')/(1 � �) � [�(c',c') � y*]� ��(c',c',c')/(1 � �)

i.e.

� � � �2�(c',c') � �n(c',c',c) � �e(c',c)

2�(c',c') � 3�(c',c',c')

One can easily check that the denominator of the expression �; � ispositive, and also the numerator is positive ∀c� � (c,c**). Hence we havethe following result.

Result 2

Given c� � (c,c**), when ��, the subgame equilibrium at node n2 is thesecond period JV between the MNC and L2 and all future periods aresymmetric oligopoly of all three firms.

Let us now consider the subgame at node n1 (i.e. the whole game).Does there exist a JV contract in the first period? First consider the casewhen � � � so that it is a JV between the MNC and L1 from the secondperiod onwards subject to the formation of a JV between them in the firstperiod. Immediately we have the following result.

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Result 3

Given � � �, the first period must be JV between the MNC and L1, andthe subgame perfect equilibrium of the whole game is a duopoly with JV(between the MNC and L1) and firm 2 competing for all periods.

Proof

The sum of profits of the MNC and L1 when they form a JV between themis �e(c�,c)/(1 � �), whereas the sum of their profits under no JV at all is2�(c,c,c)/(1 � �). Since �e(c�,c) � 2�(c,c,c) given c� � (c,c**), the sub-game perfect equilibrium is JV between the MNC and L1. This completesthe proof.

Now consider the case when ��. Any contract {x} if it is acceptablein the first period, then L1 derives a payoff x � � �(c�,c’) � �2 �(c�,c�,c’)/(1 � �), that is, x in the first period, �(c�,c’) in the second period (becausethere will be JV between the MNC and L2 in the second period) and�(c�,c�,c’) in all the future periods (because there will be no further JV inthe future). So if L1 does not accept the contract, it expects L2 to acceptthe contract. Hence when L1 accepts, it must be:

x � ��(c',c') � �2�(c',c',c')/(1 � �) � �n(c',c) � �y* � �2�(c',c',c')/(1 � �)or

x � �n(c',c) � �y* � ��(c',c') � x (10)

Offering such a contract will be profitable to the MNC iff

[�e(c',c) � x] � �[�(c',c') � y*] � �2�(c',c',c')/(1 � �) � �(c,c,c)/(1 � �)orx � �e(c',c) � �[�(c',c') � y*] � �2�(c',c',c')/(1 � �) � �(c,c,c)/(1 � �) � x (11)

Plugging the value of y*, from equations (10) and (11) we get:

x � x ⇔ R(�) � A�2 � B� � C � 0 (12)

where:A � 3�(c',c',c') � 2�(c',c')B � 2�(c',c') � 2�n(c',c',c) � �n(c',c) � �e(c',c)C � � [�(c,c,c) � �n(c',c) � �e(c',c)]

Let:

�* � [�(c,c,c) � �n(c',c) � �e(c',c)]

To characterize the function �* we may note that �* is an increasingfunction of c�, with �*�c and �*�c** � 0. Hence:

∃c0,c � c0 � c**|c' � (or, � )c0 ⇔ �* � (or, � )0 (13)

Then given equation (13), we must have C � 0 at c� � c and C � 0 atc� � c**; also R�� 0 � C and R�1 � 0; moreover, �2R/��2 � A � 0, implyingthat R(�) is strictly concave in �. Hence, we must have R � 0 at least for

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relatively large �.18 Thus, equation (12) holds when either c� � (c�,c0) or� is large. Now that first period will really by a JV, it is necessary that thelocal firm’s payoff by accepting the contract {x} in the first period is notless than the payoff with no JV at all. By accepting the contract in the firstperiod, the firm expects a payoff:

x � ��(c',c') � �2�(c',c',c')/(1 � �) � �n(c',c) � �y* � �2�(c',c',c')/(1 � �)

whereas by rejecting the JV contract it gets just �(c,c,c)/(1 � �). Therefore,the first period will be JV (given ��) iff

�n(c',c) � �y* � �2�(c',c',c')/(1 � �) � �(c,c,c)/(1 � �)i.e.

� � � ��n(c',c) � �(c,c,c)

�n(c',c) � �n(c',c',c)

Note that the denominator is always positive, but �n (c�,c) ��(c,c,c) iff c�� ((5c–a)/4, c**) where 5(c–a)/4 � c. So if c� � (5c–a)/4, then � � 0, andthere will be no JV in the first period as well as in the future periods. Onthe other hand, if (5c–a)/4 � c� � c**, ∃�, such that 0 �� giving thepossibility of JV in the first period.

Summarizing the analysis of this section we can write the followingproposition.

Proposition 1

(a) If � � �, the JV between the MNC and L1 will occur for all periods,and the market structure will be an asymmetric duopoly.

(b) If ��, but either � � � or equation (12) does not hold, then there willbe no JV, and the market structure will be a symmetric oligopoly witheach firm operating at a cost level c.

(c) If �� min {�, �} and equation (12) holds, the first period is a JVbetween the MNC and L1, the second period is again a JV butbetween the MNC and L2; from the third period onwards the marketstructure is an oligopoly with all firms operating at a lower cost c�.

Case (c) above is most interesting as it explains how the industrialstructure changes over time. We can easily see that case (c) is not empty.For instance, consider c� � ((5c – a)/4, c0) so that equation (12) issatisfied for all �. For such a c�, we have 0 � �� 1. Moreover, we haveseen that �� 0. Hence, given c� � ((5c – a)/4, c0), if �� min {�, �}, in thesubgame perfect equilibrium the first period will be a JV between the MNCand L1; the JV breaks up in the beginning of the second period and a newJV is formed between the MNC and L2; again it breaks up at thebeginning of the third period; thereafter all firms become equally efficient,and they compete non-cooperatively for the remaining future periods.

18 If c� � (c, c0), ∀� R, is necessarily positive, because C is positive for this interval of c�.

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Other Possible Scenarios

In this subsection we shall discuss other possible scenarios based on theamount of cost saving. The mode of the analysis is same as above, buteach of these cases is distinctly different in the sense that each casegives a different industrial evolution.

Scenario 1: c� � [0,c]

Given the assumption on synergy in this case, if a JV is formed betweena local firm (L1) and the MNC, not only is JV formation profitable to thepartners, but the JV also emerges as a monopoly. So the other local firm(L2) will cease to operate. Then, in the beginning of the second period, wehave two identical efficient firms (i.e. the MNC and L1), and hence forminga JV between them for every future period will be profitable, becausemonopoly profits are larger than the symmetric industry duopoly profits.So consider the optimal contract for JV formation in the first period. Givenany contract {x} accepted by one local firm (L1), the other local firm’spayoff is reduced to zero. Because of this bidding competition betweenthe local firms, the MNC will be able to extract all payoffs. Since, from thesecond period onwards, L1’s reservation payoff is its non-cooperativeduopoly profit �(c�,c’), conditional on the first period JV formation, theMNC will give a contract {x} such that:

x � ��(c',c')/(1 � �) � 0 (14)

where x is the net payoff of the local insider in the first period, and sucha contract will be accepted by L1. The term on the right-hand side is zerobecause of bidding competition; the second term of the left-hand side isthe present value of L1’s payoffs from the second period to the future (allevaluated at the beginning of the first period) conditional on the JVformation in the first period. Such an � must satisfy the following constraintfor the MNC:

[�m(c') � x] � �[�m(c') � �(c',c')]/(1 � � � �(c,c,c)/(1 � �) (15)

Given the assumption regarding learning, if JV is not formed in the firstperiod, it will never be formed, because the scenario will remain un-changed in that case. Quite obviously, in equilibrium the inequality (14)will be satisfied with strict equality, and the optimal contract will bex* � � ��(c�, c’)/(1 � �). Each local firm will accept the contract, and theMNC will select one (L1) as its partner. Under this contract, the MNC’spayoff will be �m(c’)/(1 � �). Hence, the MNC and L1 can write a JVcontract in the first period. Once the first period is a JV, all future periodswill also be a JV. Under the synergy assumption of this case, the JV willremain as a monopoly in the industry for all periods.

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Scenario 2: c� � (c, c*)

Given Lemma 1, in this case if the JV is formed in the first period, theoutsider local firm’s payoff will be positive, because synergic gain is not sostrong compared with the previous case. Hence, if the JV is formed for thefirst period, the market structure will be a duopoly consisting of thelow-cost JV and the remaining inefficient local firm. In the next period,both the JV partners will have a low cost, implying that L1’s non-cooper-ative (or reservation) payoff in the second period (and also in every futureperiods) is �(c�,c’). Note that under the non-cooperative situation, L2cannot operate under this case, but if the MNC and L1 form a JV, L2 willcertainly operate. We also know from Lemma 1 that the formation of a JVbetween the MNC and L1 (that is, between the efficient firms) is profitable.This means, conditional on the first period JV, for every future period(starting from the second period) the MNC will give a JV contract underwhich the local insider will retain a payoff �(c�,c’), and the foreign firmretains �e(c�,c) � �(c�,c’). Taking into account these future payoffs, theMNC will design a contract {x} such that both the insider and the outsiderreceive the same payoff. The outsider’s payoff over the whole timehorizon is �n(c�,c)/(1 � �). Hence a contract {x} will be offered such that:

x � ��(c',c')/(1 � �) � �n(c',c)/(1 � �)or

x � �n(c',e)/(1 � �) � ��(c',c')/(1 � �) � x2. (16)

Such an � must also satisfy the MNC’s constraint:

[�e(c',c) � x] � �[�e(c',c) � �(c',c')/(1 � �) � �(c,c,c)/(1 � �)or

x � �e(c',c) � �[�e(c',c) � �(c',c')]/(1 � �) � �(c,c,c)/(1 � �) � x2 (17)

From (16) and (17), a contract exists iff x2 � x2, that is,

�* � �n(c',c) � �(c,c,c) � �e(c',c) � 0

The condition is necessarily satisfied19 for c� � (c,c*). Hence a mutuallyagreeable first period JV contract between the MNC and L1 exists. Theoptimal x will satisfy the inequality (16) with strict equality. Thus under thesynergy assumption of this case, for all periods, the market structure willbe a duopoly comprising the efficient JV and the inefficient L2.

Scenario 3: c� � [c*,c]

This portrays an interesting case when, in the first period, a JV will beformed between one local firm and the MNC, but from the second period

19 See equation (13). Note that �e(c�, c) � 2�(c, c, c) for c� � c and �n(c�, c) ��(c, c, c)for c� � (c1, c2), where c1 � (11c � 7a)/4 and c2 � (5c � a)/4.

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onwards there will be no further JV. The market structure will still remaina duopoly, but with a different composition. In the first period, industry willconsist of the efficient JV and the inefficient non-JV local firm. From thesecond period onwards, only the efficient firms (the MNC and L1) willcompete non-cooperatively, and the inefficient local firm (L2) will cease tooperate. Let us explain why this is so. Conditional on the first period JVformation, the scenario at the beginning of the second period is describedby two efficient firms and one inefficient firm. Then, from Lemma 1, in thisinterval of c�, the efficient partners will derive more payoffs by competingwith each other than keeping the JV structure alive and allowing theinefficient firm to operate. Thus, the first-period outsider’s payoff is just �n

(c�,c), and it thereafter derives zero profits in the future. Therefore, biddingcompetition in the first period means that the MNC, by giving an offer inthe first period, must ensure this amount of payoff at the minimum to thelocal insider. If a JV is formed in the first period, the payoffs of each of theMNC and L1 in the future periods will be � (c�,c’). Then under the optimalJV contract in the first period, the local firm’s participation constraint is:

x � ��(c',c')/(1 � �) � �n(c',c)

orx � �n(c',c) � ��(c',c')/(1 � �) � x3. (18)

and that for the MNC is

[�e(c',c) � x] � ��(c',c')/(1 � �) � �(c,c,c)/(1 � �)or

x � �e(c',c) � ��(c',c')/(1 � �) � �(c,c,c)/(1 � �) � x3 (19)

From equations (13) and (14), we shall get x3 � x3 iff

�[2�(c',c') � �e(c',c) � �n(c',c)] � �*

The LHS is positive and the RHS is negative for the synergy assumptionof this case (see equation 13)). Hence, in the first period, a JV contractcan be written between the MNC and L1. They become separated in thenext period, and in that case the inefficient L2 will cease to operate. So,under Scenario 3, the market structure is a duopoly for all the periods, butwith a different composition compared with Scenario 2. The optimal x willbe solved from equation (18) with strict equality. Note that, in this case, L2is facing a less formidable rival compared with the previous case, but itsposition is more vulnerable in the sense that it cannot operate in thefuture.

Scenario 4: c� � [c**,c)

Given the assumption about synergy as implied by the above interval, ifa JV is formed in the first period between the MNC and a local firm, thenfrom the second period onwards the market structure must be an oligo-

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poly comprising two efficient firms (the MNC and L1) and one inefficientfirm (L2), because once, after the first period, the JV partners come upwith low cost production knowledge, there is no further incentive for anyalliance formation between any two firms (see Lemma 1). Thus, con-ditional on the first period JV, each of the efficient firms’ per period futurepayoff is �e(c�,c�,c). So if x is offered by the MNC, the local firm byaccepting the contract expects a payoff x � , ��e(c�,c�,c)/(1 � �), whereasby rejecting the contract it expects �n(c�,c) � ��n(c�,c�,c)/(1 � �) if the otherlocal firm accepts the contract. Hence the contract {x} must satisfy thefollowing restriction for the local firm,

x � ��e(c�,c�,c)/(1 � �) � �n(c',c) � ��n(c',c',c)/(1 � �)or

x � �n(c',c) � �[�n(c',c',c) � �e(c',c',c)]/(1 � �) � x4 (20)

and that for the MNC:

[�e(c',c) � x] � ��e(c',c',c)/(1 � �) � �(c,c,c)/(1 � �)or

x � �e(c',c) � ��e(c',c',c)/(1 � �) � �(c,c,c)/(1 � �) � x4 (21)

Then a JV contract exists iff x4 � x4, that is,

� �[�n(c',c) � �(c,c,c) � �e(c',c)]

[2�e(c',c',c) � �e(c',c) � �n(c',c) � �n(c',c',c)]� �*

Under the assumption of synergy in this case, both the numerator and thedenominator are positive, and �* � 1. Hence, the first period marketstructure will be characterized by a duopoly and the future will beoligopoly, provided that ��*. This condition has an obvious explanation.The first-period local insider is sacrificing present profits with a view to again in the future by means of learning. This is possible only if it is patientto a critical extent.

Scenario 5: c� � [ c, c)

This is the case when JV formation is not profitable as far as a singleperiod is concerned (see the definition of in equation (4)). However, sincethrough JV formation partners can learn and come up with low cost in thefuture, JV formation may be profitable. Then, if JV is formed in the firstperiod, the local firm derives a payoff x � ��e(c�,c�,c)/(1 � �), and byrejecting the contract it should get �n(c�,c) � ��n(c�,c�,c)/(1 � �). Thus wehave the similar structure as in the previous case and hence we shall getstructurally the same condition for a profitable JV contract in the firstperiod, that is,

� � � ��n(c',c) � �(c,c,c) � �e(c',c)

2�e(c',c',c) � �e(c',c) � �n(c',c) � �n(c',c',c)(22)

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But we must note that, in this case, we have less synergy compared withthe previous case (that is, higher c’). Since the first period is not privatelyprofitable to the JV members, we should expect that the JV will be formedin the first period if and only if the partners give more weight to futureprofits. Hence we expect that ��*. This is in fact the case.20 If theplayers are very impatient (i.e. low �), the JV agreement cannot be signedin the first period, and the market structure will remain an oligopoly withhigh cost of production for all periods.

The results of this section are summarized in the following proposition.

Proposition 2

(a) If c� � c, the industry structure will be a monopoly of the venture forall periods.

(b) If c� � (c, c*), the market structure will be a duopoly comprising theJV and the inefficient non-JV local firm for all periods.

(c) If c� � [c*, c], again the industry structure will be a duopoly for all theperiods, but in the first period it is a duopoly of the JV and the non-JVlocal firm, and from the second period onwards it is a duopoly of theefficient JV partners who formed the JV in the first period; theinefficient firm will exit the industry after the first period.

(d) If c� � [c**, c), the first period is a duopoly of the JV and the non-JVfirm if ��*, but from the second period onwards the market structureis an oligopoly with two low cost firms and one high cost firm.

(e) If c� � [c, c), the first period is a duopoly iff �� , and in that case,from the second period onwards the market structure is an oligopoly;otherwise it is an oligopoly for all the periods, with each firm havinghigh cost.

In the next section we discuss the result under alternative assumptions.

Alternative Assumptions

In this section we relax assumption (A3) and (A4) and discuss very brieflythe possible consequences. First, let us relax assumption (A4), andassume a finite time horizon or life of the product. This means that thefuture is shortened. To the extent that writing a JV contract depends moreon future profits, a more stringent condition is needed to impose on thediscounting rate (i.e. �) for the first period to be a JV. In the extreme case,it is possible that under some synergy assumption, the JV contract doesnot exist even with � � 1.21

20 In the expression of �* (or �) the numerator is increasing in c� and the denominator isdecreasing when c� � c.

21 For example, consider only three periods with � � 1. Then given assumption (A5), therelevant conditions for the existence of a JV contract in the first period are: for the L1,x � �n(c�, c) � 2�n(c�, c�, c) � 2�e(c�, c�, c) and for the MNC, x � �e(c�, c) � 2�e(c�, c�,c) � 3�(c, c, c). Then it is easy to see that for c� close to c, there does not exist anyx that satisfies both the above conditions.

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Now relax assumption (A3). In most cases the local firm contributeslocal knowledge to the JV. Hence it is reasonable to assume that if theMNC enters the domestic country without any JV relation, it can acquirelocal knowledge within a definite period. Assume that the foreign firm canacquire the knowledge embedded in the local inputs by the end of the firstperiod. This means that if the first period is no-JV, in the beginning of thesecond period we have now one efficient (low cost) firm and two inefficient(high cost) firms. First consider the incentive of forming a single-period JVbetween the MNC and a local firm under this scenario. We shall get thefollowing result.

Lemma 2. Assume that three are two high cost (c) firms and one low cost(c’) firm. Then a single period JV is profitable between the efficient firmand one inefficient firm iff c� � (c,c), where c � 2c – a and c � (14c –a)/13.

Proof. In this case a JV formation is profitable if and only if:

g(c') � �e(c',c) � �e(c',c,c) � �n(c',c,c) � 0

Now, for c� � c, g(c’) � 0 because �e (c�, c) � �m (c’), �e (c�, c, c) � �m (c’),and �n (c�, c, c) � 0, and for c� � c, g(c’) � 0. Also g(c’) is an invertedU-shaped function. Hence

∃c|(c') � 0 iff c' � (c,c)

This completes the proof.For the demand function (1), we have:

c � (14c � a)/13, and c � c � c**

Note that under this situation a JV formation between two inefficient firmsis never profitable. The g(c’) function is also drawn in Figure 1. Let us nowdiscuss the possibility of the changing industrial structure in this case. Itmay be understood that if a JV is formed in the first period, then thescenario that prevails at the beginning of the second period is the sameas in the previous section. However, under the alternative assumption of‘learning’, the MNC must see whether it will go at all for a JV, becausewith no JV in the first period it gains a competitive advantage over itsrivals in the future periods through learning, but a JV formation will makeone rival competitive in the future. When a JV is formed in the first period,the changing industrial structure should follow the same path as in theprevious section. To highlight the difference of results compared to theprevious section consider the following case.

Suppose c� � c. In the previous subsection under Scenario 5, we haveshown that, depending on the value of �, there was a possibility of forminga JV in the first period, although JV formation was not profitable as far asa single period is concerned. Under the assumption of the present

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section, however, there will be no joint venture ever, because in theprevious section, by forming a JV, the MNC sacrifices some profits that itovercompensates in the future. But in the present section, given theassumption of learning, the MNC comes up with the same payoffs, as inthe previous section, from the second period onwards without a JV.Hence it will not be willing to sacrifice profits in the first period by forminga JV. In that case the market structure will remain an oligopoly of all threefirms for all periods. In the first period, all firms have high cost, and in allother periods the MNC has low cost and the local firms have high cost.But under the assumption of the previous section, if the discounting factoris high enough, the first period is a symmetric duopoly and the future isan oligopoly comprising two low cost firms and one high cost firm.

Summarizing the analysis, we can have following results.

Proposition 3. If the time horizon is finite, or the ‘alternative’ assumptionof learning holds, it is possible to have a situation where no feasible JVcontract exists, and then entry of a foreign firm will occur in the form ofopening a wholly owned subsidiary.22

Proposition 4. The dynamics of the industrial structure depend not onlyon the extent of synergy and degree of firms’ patience about futurepayoffs, but also on the assumption regarding learning and the nature ofthe JV contract.

Conclusions

This paper focuses on the changing industrial structure based on synergyand learning. In the last two decades, most of the countries have openedup their economies to foreign trade and investment. As a result, the inflowof foreign goods and investment has increased tremendously. Because ofsome strategic and other advantages, international business often takesthe form of JVs. By this, partners can pool their complementary resourcesand exploit possible synergies. This also facilitates organizational learn-ing. In particular, partners can acquire the knowledge embedded in others’complementary inputs. This changes the comparative advantages andcompetitive positions of the firms. The prospect and profitability of allianceformation and the break up of the alliances also undergo a change. Thiscontinually reshapes the local industrial structure. If the synergy gain istoo strong, the market structure becomes a monopoly, and if it is toosmall, the market is an oligopoly. The evolution of the industrial structuredepends, in our paper, on the extent of synergy and learning. In general,therefore, the market structure can be a monopoly, duopoly or oligopolyin different periods. We have shown the results in a very simple structurewith initially two local firms and one foreign firm, where JV formation

22 It may be recalled that the possibility of no JV can also arise under infinite time horizon(see Proposition 1).

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facilitates synergic gain and learning. We have also provided analysis toshow that our results are quite general in the sense that these do notdepend much on a particular assumption of the model. Hence, our papercaptures the changing pattern of the industrial structure that we observein many countries in the post-liberalization period.

One limitation of the model may be noted in this context. In our paperwe have, instead of modelling ‘learning’ properly, introduced it artificially.Hence, in an extension, one may think of a dynamic process of learningthat influences and in turn is influenced by the market structure. Also,instead of the one period threshold for revelation of information, one mayallow a gradual diffusion of knowledge in the JV. This would thendetermine endogenously the potential break-up time of the JV.

Acknowledgements

The authors are grateful to the comments and observations made by an anony-mous referee of this journal. The authors would like to thank the participants inseminars at Hong Kong University of Science and Technology (Hong Kong),Delhi School of Economics (Delhi), and Indian Institute of Management (Kolkata)for helpful suggestions.

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Synergy, learning and the changing industrial structure