Endogenous Business Networks - Oxford Academic

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Endogenous Business Networks Raja Kali University of Arkansas

Business networks are a feature of the organizational landscape of many countries, though they vary in magnitude. This article develops a theory of business networks where they are endogenous to the reliability of the legal system. Networks are a substitute for reliable institutional support that guarantees written contracts. The existence of networks exerts a negative effect on the functioning of the anonymous market. This is because the network absorbs honest individuals, raising the density of dishonest individuals engaged in anonymous market exchange. Since this lowers the payoff from market exchange, larger networks may be easier to enforce. We find that networks are economically inefficient unless they are relatively large. This is consistent with the view that informal contract enforcement institutions may be inefficient in general equilibrium even though they enhance efficiency in partial equilibrium.

1. Introduction While it is an understatement to say that the price mechanism as the coordinator of exchange occupies the principal place in economic theory, it is fair to note that a lot of economic exchange does occur in non-price-driven environments. An easy example of this is the firm. What distinguishes the firm from the market is the fact that within a firm most, if not all transactions, are not guided by a system of prices. Instead, firms usually coordinate their internal activities using a combination of centralized, and often hierarchical, command and convention.1

I am grateful to Larry Ausubel, Indranil Chakraborty, Javier Chavez-Ruiz, Maitreesh Ghatak, Bengt Holmstrom, Tridib Sharma, and Jean Tirole for helpful discussions. Comments by Oliver Williamson and an anonymous referree also improved the article. I thank seminar participants at the University of Maryland, ITAM, El Colegio de Mexico, and the 1998 North American Summer Meeting of the Econometric Society for their comments. All errors are my own. 1. Kreps (1990) compares corporate culture to a convention, in that corporate culture in a firm is meant to convey to its employees the (focal) behavior they are expected to follow. Milgrom and Roberts (1992) also talk about the role of corporate culture as a partial solution to the problems that arise because contracts are incomplete. c 1999 Oxford University Press °

616 The Journal of Law, Economics, & Organization, V15 N3

This issue has been of interest to economists since the seminal insight of Ronald Coase (1937). Using the market mechanism is itself not a costless activity and it may be possible to organize activity in a different way that is more efficient. This “different way” is sometimes called the firm. In many emerging economies we also observe a “different way” of organizing exchanges. Networks of informal relationships dominate business activity throughout east Asia. These networks usually involve an exchange of favors which make doing business easier for those within the network.2 Though exchange within these networks does not rely on explicit written contracts, relationships between the members are highly formalized, through what could be called norms.3 Recent empirical studies in the organizational behavior literature suggest that these networks are a response to inadequate institutional support (Boisot and Child, 1996; Xin and Pearce, 1996), essentially in terms of the legal infrastructure that guarantees written contracts and private property.4 Managers often cultivate personal relationships to substitute for a stable legal and regulatory environment that allows for impersonal business dealings. This article has two objectives. First, to understand how nonmarket institutions such as business networks are endogenous to an inadequacy of reliable legal institutions. Second, with the first objective as the leitmotiv, to study the efficiency implications of such networks as informal contract enforcement institutions. We therefore examine the interplay between network size, the functioning of the economy, and economic efficiency. An understanding of personalized exchange and impersonal markets is a central theme in the institutional approach to the study of economic development and growth (North, 1991). In the absence of well-developed legal systems people rely on self-enforcing contractual arrangements. An important question with these arrangements is whether they improve overall economic efficiency. A survey of the literature yields mixed results on this issue. In pioneering research, Greif (1993) presents one such informal institution, a coalition of Mediterranean traders from the 11th century known as the Maghribi.5 The commitment problem intrinsic in the relation between the merchants and their overseas agents is surmounted by a multilateral reputation mechanism whereby an agent refrained from cheating a trader because then all other traders would refuse to hire him. In the absence of an effective formal contracting mechanism—on account of the complexity and uncertainty of long-distance commerce—the fact that there are only a handful of documents containing allegations of misconduct shows that the informal enforce-

2. The Chinese word for this type of activity is guanxi. 3. We use the word norm in the way that it has been used in the economics literature following Kandori (1992), as a specification of desirable behavior together with sanction rules in a community. 4. The article “And never the twain shall meet . . .” in The Economist, March 29, 1997, pp. 67–68 also makes this point. 5. See also Clay (1997) for a similar analysis in the context of Mexican California.

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ment mechanism worked well. Greif therefore concludes that the coalition of traders enhanced economic efficiency by reducing transaction costs.6 However, Greif’s framework is partial equilibrium. A number of articles (briefly discussed below) suggest that the partial equilibrium result—of informal contract enforcement institutions enhancing economic efficiency—is not robust to a general equilibrium extension. Arnott and Stiglitz (1991) study one aspect of the interaction between traditional or informal institutions with modern ones. In their model, because of the presence of moral hazard, individuals are partially insured. This creates demand for informal insurance which is provided by friends and family. The availability of such insurance leads individuals to take less care and insurance firms respond with less insurance: that is, informal insurance crowds out formal insurance. Since the former has lower risk-pooling capability, this causes welfare to go down. A recent article by Kranton (1996) develops an explanation of reciprocal exchange as a self-sustaining system. She develops a model in which some agents engage in reciprocal exchange and the remainder in anonymous market exchange. Agents who use the market have access to a variety of goods, but they must search for trading partners. In reciprocal exchange, agents economize on search costs but obtain only the commodity produced by their trading partner. When more people engage in reciprocal exchange, market search costs increase, reciprocity is easier to enforce and yields higher utility. Thus personalized exchange can persist even when it is inefficient for the economy.7 This article contributes to the general equilibrium perspective on informal contract enforcement institutions. We consider an economy in which there are two institutions for exchange: the anonymous market and the personalized business network. The economy is populated by three possible types: honest, dishonest, and opportunistic. The price at which the buyer and seller trade is fixed, but delivery of the goods takes place after the contract has been signed and so the seller has the opportunity to default on the terms of the contract. The remedy for this is, of course, contract law. But courts may be inadequate, leading to imperfections in rulings and enforcement of the law. This happens because of unreliable or underdeveloped institutions, perhaps coming from a lack of resources and training. A business network is modeled as a group of people who trade with each other. The spot price at which trade takes place within the network is the same as in the market, but the penalty for cheating on a trade is expulsion. The accumulation of social capital within the network takes time and this is embedded in the increasing structure of returns from intra-network exchange. We focus on the enforceability of honesty within the 6. In another article, Greif (1994) notes that in the long-run the collectivist nature of the Maghribis probably retarded development and led to their eventual disappearance as a trading community in competition with the Genoese, who had an individualistic system. 7. Banerjee and Newman (1998) present a related result on partial versus general equilibrium effects of informal institutions while studying the interaction of economic growth and institutional transformation through the process of migration.


network. The norms governing exchange within the business network enable it to function as a self-selection device for individuals. This depends on their proclivity for and gains from dishonesty. We find that while the enforceability of a business network depends on the reliability of the legal system, the existence of the network exerts a negative influence on the level of honesty in the anonymous market. This is because the network absorbs honest individuals, increasing the density of dishonest individuals involved in anonymous market exchange. This in turn makes network exchange easier to enforce. Members of the network are better off at the expense of individuals engaged in anonymous market exchange. Consequently, we find that networks are economically inefficient unless they are relatively large. The mechanism through which the personalized business network leads to inefficiency is the “cream skimming” of “good” types by the network that worsens the pool of agents remaining in the anonymous market. The article most closely related is the one by Curtis Taylor (1996) (see also Ghosh and Ray, 1996). He develops a model of an exclusive group whose membership is governed by personal contact. Members of this network attempt to shield themselves from being cheated by interacting only infrequently with unproven nonmembers. Of importance, the absorption of honest individuals into the network is endogenized in his article. Differently however, because in his model people are either cheaters or not, we explicitly consider the temptation to cheat that opportunistic agents face. The trade-off between the anonymous market and the personalized network is a central theme here. The remainder of the article is organized as follows. Section 2 provides some background on business networks in emerging economies and briefly surveys some related literature. This section is the primary empirical motivation for the article. Section 3 describes the assumptions characterizing the economy. This model serves as the vehicle for subsequent analysis. Section 4.1 analyzes the anonymous market economy in the absence of any other exchange institution. Depending on whether opportunists in the economy behave honestly or not, the economy operates in a low-dishonesty or high-dishonesty regime. This decision depends on the parameters of the economy, especially the reliability of the legal system. Section 4.2 shows how the business network functions and focuses on its enforceability. Inside the business network individuals play a repeated matching game.8 If court reliability is high, networks are not enforceable as institutions for governing exchange. As formal contract enforcement begins to deteriorate, networks become enforceable and may emerge as a substitute exchange institution. Section 4.3 grafts the business network analysis of Section 3.2 on the anonymous market and considers the economy with both.

8. Enforceability of honesty is a simple application of the notion of community enforcement under public observability as in Kandori (1992). With less information dissemination, more complicated strategies such as the contagion strategy can sustain cooperation with local information transmission and some other restrictions. See Kandori (1992) for more details. We wish to keep this aspect of the model as simple as possible.


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Section 5 studies how the efficient functioning of the economy is affected by the presence of business networks. Section 6 discusses implications of and caveats to the analysis. This section considers the idea of path dependence and the role that culture may play in the emergence of these networks. 2. Business Networks While the initial motivation for this article comes from Chinese guanxi practices, similar business networks are found in several parts of the world. Economies in Latin America (e.g., Mexico), eastern Europe (e.g., Russia), and south Asia (e.g., India) are in the process of dismantling interventionist methods of economic organization and attempting to make the transition to more marketoriented systems. These economies are still deficient in reliable legal institutions for the resolution of contractual disputes. In many cases, the legal system, though not theoretically dissimilar from those in advanced countries, is capricious in practice as well as being overburdened and slow. Scholars of organizational behavior (Woolsey-Biggart and Hamilton, 1992; Ambler, 1991) have noted that networks of relationships between businesses play an important role in these economies. In some of these countries, such as Mexico and India, networks are formalized as business groups. Indeed, business networks are a feature of the organizational landscape of many countries, though there is variation in their magnitude and importance. Business networks are more than just the platitudinous “life is about relationships.” These relationships are highly commercial and structured, even though contracts are not formally written. Trading relationships within the network are governed by clear and well-understood norms. Transactions occur within a relatively permanent group which reduces the potential gains from opportunistic behavior. Even when partners do not know one another, they understand the rules or norms of interaction, and it is important to adopt these norms in order to become a member. The giving of gifts is often a prerequisite to becoming a member of a business group. These gifts are viewed as investments in the relationship. Developing trust within the group takes time. Trading privileges rise with seniority in the group. An advantage of the group is the assurance that the terms of the contract will be honored, but a disadvantage is the investment in time that is required to establish significant trading privileges in such a system. The commercial legal system that is associated with advanced market economies can be viewed as a substitute to these business networks: the presence of one reduces the need for the other. Well-developed contract enforcement institutions give traders assurance that deals will be honored. In fact, formal contract law originated in 18th-century Europe because relationships were weak and legal sanctions were viewed as necessary to ensure obligations were met. In a market economy there are no restraints to trade of the type described above. But because of the anonymous nature of the trading, if legal institutions are inadequate, there is the possibility that the terms of the contract will not be honored. The modeling approach used in this article is supported by a number of recent empirical studies. Using data collected in seven African countries (Burundi,


Cameroon, Ghana, Ivory Coast, Kenya, Zambia, and Zimbabwe) Bigsten et al. (1998) demonstrate that long-term relational contracting is the norm between manufacturers, their suppliers, and clients. These relationships are a guard against contract nonperformance and are especially important when the transaction costs of using the formal legal infrastructure are high. On the basis of data on agricultural traders in Madagascar, Fafchamps and Minten (1998) find that social network capital enables traders to deal more efficiently with each other in the presence of costly courts and lawyers. In a couple of recent articles that deal with Vietnam’s emerging private sector, Haggard, McMillan, and Woodruff (1998) and McMillan and Woodruff (1999) seek to understand how firms cope with undeveloped legal and market institutions. Using descriptive data and regression results they show that reputational mechanisms and business networks that allow for collective sanctioning of dishonest trading partners work well. 3. The Model 3.1 Matching

Consider a large and stationary economy in which individuals are infinitely lived. Time proceeds in discrete periods and individuals have the discount factor δ > 0. In each period an individual is either a buyer or a seller with equal probability. Agents are randomly matched. A buyer contracts with a seller for the supply of a product whose quality can be high or low. The payoff to the buyer is 1 if the product is of good quality and 0 if it is bad. Providing the highquality product costs the seller c (1 ≥ c > 0), while the low-quality product costs the seller zero.9 The buyer prefers the high-quality product and so always contracts for high quality. The buyer pays the seller a price of p for a unit of the product. There is a lag between contracting and supply. After contracting and payment the seller can cheat and provide low quality. The product is an experience good. Quality is verifiable only after delivery. This is therefore a situation of postcontractual private information, that is, moral hazard. As will become clear, the exact value of p is unimportant for our analysis. The role of p is simply to divide the surplus between the seller and buyer. 3.2 Agent Preferences

The economy consists of N agents. There are three types of agents in the economy: “honest,” in proportion α, “dishonest,” in proportion β, and “opportunistic,” in proportion γ (α + β + γ = 1). Honest agents have a strong distaste for, and never engage in, corrupt activities. Dishonest agents always cheat. Opportunistic agents have no aversion to being corrupt, but trade off the costs and benefits from cheating.10 A buyer is cheated if he is matched with 9. The upper bound on c ensures that the prices in the market and the business network are less than unity and is an artifact of the assumption that the gross surplus to a buyer for the high quality is unity. Generalizing that would permit this to be relaxed. 10. This formulation of preferences is standard in reputation models (see, e.g., Tirole, 1997). The presence of honest agents creates an incentive for opportunists to build a reputation. The presence


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a seller who is a dishonest type or an opportunist behaving dishonestly. Also, a buyer who is a dishonest type or an opportunist behaving dishonestly claims that he has been cheated even when he has in fact been provided high quality by the seller. While honest and dishonest agents behave mechanistically with regard to cheating they are not precluded from being strategic in other respects, such as network formation. Reservation payoffs are zero for all. 3.3 Courts

Courts can enforce contracts, but they do so imperfectly. With exogenous probability θ (1 ≥ θ ≥ 0) the court rules correctly in any dispute. This will be used as the index for the reliability of the legal system. When the court rules in favor of the buyer it forces the seller to pay damages to the buyer equal to the difference between the buyers ex ante contracted-for surplus (1 − p) and the ex post surplus (− p) that the buyer receives if the seller had cheated. That is, the court forces the seller to make the buyer “whole” by paying 1− p−(− p) = 1. When the court rules against the buyer, the seller pays nothing but the buyer pays a fine of d (1 ≥ d > 0) as a punitive penalty for what the court considers a frivolous lawsuit.11,12 Court reliability can be thought of as less than unity because of capriciousness on the part of the judiciary or because of insufficient resources, reasons which can be summarized as the inadequacy of legal institutions. 3.4 Information

Agents know their own preferences (i.e., their types), but not what the preferences of other agents are. One period is defined as the time it takes for the entire sequence of the previous events to play out. All of this is common knowledge. 4. Analysis 4.1 The Anonymous Market

We first analyze the economy when the anonymous market is the sole institution for economic exchange. The seller promises to provide high quality at the time of contracting and therefore this is the price that the buyer pays. Ex post, the seller does not honor the terms of the agreement and provides the buyer with a low-quality product with probability π. We refer to π as the “cheating probability.” This is also the probability with which an honest seller meets a dishonest buyer and is falsely accused of providing bad quality. This is, respectively, β or β +γ depending on whether the opportunists decide to behave

of dishonest agents eliminates a spurious multiplicity of equilibria associated with an indeterminacy of off-the-equilibrium path beliefs. Diamond (1991) was the first to use this formulation. 11. We have in mind here that the court imposes a small penalty for what it considers a false lawsuit or perjury. The fine is not so large that an opportunistic agent will never cheat regardless of court reliability. 12. Allowing courts to err in the damage dimension rather than on liability would only change the expected payoffs. None of the results would change in nature.


honestly or dishonestly.13 If the opportunists decide to behave honestly the economy experiences what we call a “low-dishonesty regime” or Regime (a). If they decide to behave dishonestly the cheating probability in the market increases to β + γ . We refer to this as a “high dishonesty regime” or Regime (b). We consider them in turn and derive the conditions under which each prevails. 4.1.1 Low dishonesty: Regime (a). Suppose that all the opportunists always behave honestly. Then πa = β. The expected payoffs of buyers and sellers depend on whether they are behaving honestly or dishonestly. The expected payoff of a buyer behaving dishonestly in any period is

U BD = (1−πa )(1− p)+(1−πa )[(1−θ )−θ d]+πa [− p+θ − (1−θ )d] = (1 − πa )(1 − p) − πa p + (1 − θ − θ d) + πa (2θ − 1)(1 + d). where the relevant superscripts stand for whether the agent is honest or dishonest and the subscripts represent whether the agent is a buyer or seller. The first term is the probability of not being cheated times the net surplus. However, the dishonest agent will claim to have been cheated even when he has not, and the second term represents the expected gain from this behavior. The last term is the probability that the agent has been cheated times the expected gain (loss). The expected payoff of a buyer behaving honestly in any period is U BH = (1 − πa )(1 − p) + πa [− p + θ − (1 − θ )d] = (1 − πa )(1 − p) − πa p + πa [θ − d(1 − θ )]. The expected payoff of a seller who is behaving honestly in any period is U SH = p − c − πa (1 − θ ). The expected payoff of a seller who is behaving dishonestly in any period is U SD = p − θ. The expected payoff for a dishonest agent in any period is ¤ 1 1£ D U + U SD = [2(1 − θ ) − πa − θ d + πa (2θ − 1)(1 + d)]. 2 B 2 The expected lifetime discounted utility from market exchange for a dishonest agent is then, VMDa =

1 [2(1 − θ) − πa − θ d + πa (2θ − 1)(1 + d)] + δVMDa , 2

13. We will subsequently find conditions such that all opportunists prefer to behave in only one way, that is, either honestly or dishonestly. That is, for the moment we will not consider mixed strategy equilibria.


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yielding VMDa =

2(1 − θ) − πa − θ d + πa (2θ − 1)(1 + d) . 2(1 − δ)

(1)

The expected payoff for an honest agent in any period is ¤ 1 1£ H U B + U SH = [1 − πa − c + πa (2θ − 1 − d(1 − θ ))]. 2 2 The expected lifetime discounted utility from market exchange for an honest agent is then, VMH a =

1 [1 − πa − c + πa (2θ − 1 − d(1 − θ ))] + δVMH a , 2

yielding VMH a =

1 − πa − c + πa (2θ − 1 − d(1 − θ )) . 2(1 − δ)

(2)

4.1.2 High dishonesty: Regime (b). Suppose now that opportunists are always corrupt. That is, πb = β + γ . Then 2(1 − θ) − πb − θ d + πb (2θ − 1)(1 + d) (3) VMDb = 2(1 − δ)

and VMH b =

1 − πb − c + πb (2θ − 1 − d(1 − θ )) . 2(1 − δ)

(4)

4.1.3 Regime Choice. Whether the economy is in Regime (a) or Regime (b) depends on whether the opportunistic agents choose to behave honestly or not. A “low-dishonesty” equilibrium prevails if an opportunist prefers to behave honestly given that all other opportunists act honestly. That is, VMH a ≥ VMDa . Similarly, a “high-dishonesty” equilibrium prevails if an opportunist prefers to behave dishonestly given that all other opportunists act dishonestly, that is, VMDb ≥ VMH b . Define R a ≡ VMDa − VMH a and R b ≡ VMDb − VMH b . Then, if R a ≤ 0, we have Regime (a) and if R b ≥ 0 we have Regime (b). We can write,

1 [2(1 − θ ) − πa − θ d + πa (2θ − 1)(1 + d) 2(1 − δ) − (1 − πa − c + πa (2θ − 1 − d(1 − θ )))] 1 [1 − c − 2θ − θ d + πa θ d] = 2(1 − δ)

Ra =

and Rb =

1 [1 − c − 2θ − θ d + πb θ d]. 2(1 − δ)


Proposition 1. If the legal system is perfectly reliable, then the economy will be in the low-dishonesty regime: If θ = 1 then R a < 0 and R b < 0. Proof. See the appendix. This result provides us with a useful benchmark. But it should not be difficult to appreciate that it is more likely to be the case that courts are less than perfect. For the remaining discussion we therefore focus on situations of imperfect reliability, that is, θ < 1. Given a situation of less than perfect court reliability, we now turn our attention to the effects of increasing reliability. As court reliability increases, the marginal gain for an honest agent is positive. This is driven by the cheating probability in the economy and the penalty that the court may incorrectly impose, which decreases with increasing court reliability. Given that the honest agent is cheated, an increase in court reliability reduces the likelihood of a false penalty. But for an opportunist behaving dishonestly, an increase in court reliability is a mixed blessing. There are two effects that work in opposite directions for such an individual. The marginal payoff has a negative term that is due to the increase in the expected penalty for lying to the court, and a positive part that is due to the increased reliability of the court when the agent is cheated. It is, however, unambiguously less attractive for an opportunist to behave dishonestly as court reliability improves. Proposition 2. Increasing court reliability improves incentives for honest i behavior: ∂∂θR < 0, i = a, b. Proof. See the appendix. It is clear that when court reliability is very high, R i < 0, i = a, b, and Regime (a) prevails, while if court reliability is very low R i > 0, i = a, b, and Regime (b) prevails. But for an intermediate range of court reliability it is possible that both R a < 0 and R b > 0. It is logical that in this region an opportunist will choose based on a comparison of the size of the incentives to behave one way versus the other, that is, the magnitude of R a versus R b . At some value of court reliability these magnitudes will be equal. That is, if we 2(1−c) . Call this value of court reliability set −R a = R b , then θ = 2(2+d)−d(π a +πb ) ˆθ. If prevailing court reliability is ≤ θˆ opportunists prefer to be dishonest. Together with Propositions 1 and 2, this implies that as court reliability falls, there is a critical value of court reliability at which opportunists will switch from being honest to dishonest, causing the economy to leap from a low- to a high-dishonesty regime. Figure 1 demonstrates this situation graphically. It is commonly perceived that the risk of being cheated in economic exchange is higher in some countries than others. In keeping with the flavor of the preceding analysis, one could say that the difference between a high- and lowdishonesty country is that in a high-dishonesty country opportunists choose to behave dishonestly, while in a low-dishonesty country they choose to behave


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Figure 1.

honestly. This decision depends on several economic parameters, the reliability of the legal system being among them. 4.2 Network Exchange

This section introduces the functioning of the business network. A business network is a finite set G = {1, 2, . . . , 2k} of agents who trade within this set. Inside the business network individuals play a repeated matching game. Each period the set is partitioned into two subsets of equal size, S and B, corresponding to sellers and buyers. In any period a member has an equal chance of belonging to either set. Individuals from each set are randomly matched in a uniform manner. Matching in each stage is independent. Let µ(i, t) be player i’s match at time t. Then, 1 for all i ∈ S and j ∈ B and for all t. k Exchanges within the network are governed by the following norms. In order to be admitted into the network an agent makes a one-time payment Pr ob{µ(i, t) = j} =


of H. This can be interpreted as a “gift” that a prospective member pays. The gift depreciates completely after it has been given.14 The price within the group is the same as the market price. Within the network contracts are perfectly honored. An individual is expelled from the group if he cheats another member.15 Expulsions are immediately replaced with new members, keeping network size constant. Since networks are formed to avoid the cheating problem in the market, we focus on the enforceability of honesty within the network. Because of the lump-sum entrance fee, we can say that the net revenue from network membership for an individual increases with the passage of time. This could be thought of as representing the idea that the returns from trust or social capital accrue after honest behavior has been observed over time. The network is composed of honest agents and/or opportunist agents choosing to behave honestly as members of the network. Let V g be the expected lifetime discounted utility from network exchange. Let U S be the per-period payoff from being a seller in the network and U B be the per-period payoff from being a buyer in the network. Then, 1 δ δ2 V g = −H + [U S + U B ] + [U S + U B ] + [U S + U B ] + · · · 2 2 2 δ δ2 1 = −H + [1 − c] + [1 − c] + [1 − c] + · · · 2 2 2 1−c = −H + 2(1 − δ) That is, V g = −H +

1−c . 2(1 − δ)

(5)

Network exchange relationships are enforceable, that is, constitute a perfect equilibrium, if and only if a member does not have the incentive to cheat another. Since dishonest agents always cheat, a network will never be enforceable if dishonest types are members. Therefore a necessary condition for the sustainability of a network is that dishonest agents should not want to join it. A member who cheats once is expelled from the group and trades henceforth in the market. A dishonest type will not want to participate in a network if the first period gain from trading within it plus the discounted value of trading in the market from the next period on is less than the expected payoff from always trading in the market. The one-period gain from being dishonest in the group 14. See Carmichael and Macleod (1997) for a model in which this result is derived endogenously. They develop an evolutionary explanation for how the social custom of giving gifts at the beginning of a relationship can lead to trust and cooperation. Their approach makes predictions about the character of goods that can be used as gifts. It is important for gifts to be privately inefficient and nonrecyclable or depreciable. The seminal article on economic explanations of gift giving is by Camerer (1988). 15. The article by Biggs and Raturi (1998) emphasizes that transaction costs of doing business within the network of firms in their study is minimized because of almost perfect information transmission. This could be considered an example of what we have in mind.


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is the expected gain from being a buyer or a seller within it and cheating, 1 F = −H + [(1 − p + (1 − θ ) − θ d) + p] 2 2 − θ(1 + d) . = −H + 2 The first term within the brackets in the above expression is the gain from being a dishonest buyer. Such a buyer goes to court and makes a false accusation. The last term is the gain from being a dishonest seller. A dishonest seller who is subsequently expelled has no reason to go to court since the network is free to exclude who it wants. The enforceability of network exchange depends on the payoff from market exchange, which in turn depends on whether opportunists in the market choose to behave honestly or dishonestly. We consider these two possibilities in turn. 4.2.1 Low dishonesty: Regime (a). Suppose that opportunists in the market choose to behave honestly. In order to keep dishonest agents out it is sufficient that F + δVMDa ≤ VMDa . This condition can be written as,

−H +

2(1 − θ ) − πa − θ d + πa (2θ − 1)(1 + d) 2 − θ(1 + d) ≤ 2 2

or 2 − θ(1 + d) 2(1 − θ ) − πa − θ d + πa (2θ − 1)(1 + d) − . (6) 2 2 Let H0 be the value of the lump-sum entrance fee for which the above holds as an equality. Then, H0 ≡ 12 [θ + πa d + 2πa (1 − θ (1 + d))]. This value of the entrance fee is a necessary condition for the existence of a business network. But it is not sufficient. The next logical question is whether it is worthwhile for honest individuals to be part of the network. Honest and opportunist agents in this regime would prefer to trade in the network if V g ≥ VMH a . This condition can be stated as H≥

−H +

1 − πa − c + πa (2θ − 1 − d(1 − θ )) 1−c ≥ 2(1 − δ) 2(1 − δ)

or 1 − πa − c + πa (2θ − 1 − d(1 − θ )) 1−c − ≥H 2(1 − δ) 2(1 − δ) Let H1 be the value of the lump-sum entrance fee for which the above holds −1−d(1−θ )] . Honest agents will want to join as an equality. Then, H1 ≡ πa −πa [2θ 2(1−δ) a network only if H0 ≤ H1 . If this is true then the value of H0 also becomes a sufficient condition for the network. We will assume that the lump-sum entrance fee will not be larger than is necessary. Hence, for the remainder of the analysis the entrance fee will be equal to H0 .


Proposition 3. If the legal system is perfectly reliable then business networks are not enforceable: If θ = 1, then H0 > H1 . Proof. See the appendix. This is because if courts are perfectly reliable the payoff from trading in the anonymous market is higher than that in the network, on account of the nonlinear returns from joining a network. The entrance fee to the network is a pure loss in such a situation. θ (1−πa d) .16 Let δ ∗ be the value Setting H1 − H0 ≥ 0, yields δ ≥ θ +πa d+2π a (1−θ (1+d)) of the discount factor at which this is an equality. Networks are enforceable when the prevailing discount factor in the economy is greater than or equal to this critical value δ ∗ . We can then obtain the following result. Proposition 4. If court reliability decreases, the critical value of the discount factor at which business networks are enforceable decreases, that is, networks ∗ > 0. become easier to enforce: ∂δ ∂θ Proof. See the appendix. The intuition is that if court reliability falls, the payoff from exchange in the anonymous market decreases. Consequently, the alternative exchange institution, the business network, becomes relatively more attractive. It therefore becomes easier to enforce. An implication of this result is the following. Consider a situation where the prevailing discount factor δ is smaller than the critical value δ ∗ . Then, given the parameters of the economy, business networks are not enforceable. However, if we reduce court reliability, then by Proposition 4, δ ∗ falls. Eventually, at some value of court reliability, say θ ∗ , the critical value of the discount factor will equal the prevailing value, that is, δ ∗ = δ. Networks will then be enforceable. Consequently, we can say that networks are enforceable for court reliability in the region θ ≤ θ ∗ . Networks will be enforceable if court reliability is low enough. 4.2.2 High dishonesty: Regime (b). Suppose that opportunists in the market choose to behave dishonestly. That is, D ≥ 0. The cheating probability in the economy increases from πa to πb . The critical value of the discount factor at which a network is enforceable decreases.

Proposition 5. An increase in the cheating probability lowers the critical value of the discount factor at which business networks become enforceable: ∂δ ∗ < 0. ∂π Proof. See the appendix. 16. In the context of implicit (subjective) versus explicit performance measures, Baker, Gibbons, and Murphy (1994) have made the related point that when spot markets are sufficiently close to perfect, firms lose the ability to write implicit contracts.


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In other words, it becomes easier to sustain a business network in a highdishonesty regime. The intuition for this is similar to Proposition 4. An increase in the cheating probability lowers the payoff from trade in the anonymous market, making networks easier to enforce. A logical question at this stage is whether opportunists would ever want to be part of a network in the high-dishonesty regime. In other words, even though they choose to be dishonest in the market, would they prefer to join a business network and behave honestly within it? For opportunists to want to be part of the business network V g ≥ VMDb . This condition can be stated as 2(1 − θ ) − πb − θ d + πb (2θ − 1)(1 + d) 1−c ≥ −H + 2(1 − δ) 2(1 − δ) or H≤

1 − c − [2(1 − θ) − πb − θ d + πb (2θ − 1)(1 + d)] 2(1 − δ)

Let H2 be the lump-sum fee at which this holds as an equality. Opportunists would want to join the group if H2 − H0 ≥ 0. Simplifying this condition yields 1+c−θ (1+d) . Call the value of the discount factor for which this δ ≥ θ +πa d+2π b (1−θ (1+d)) 1+c−θ (2+d(1−πb )) . From holds as an equality e δ. Then we can obtain, e δ − δ ∗ = θ +π a d+2πb (1−θ (1+d)) 1+c ∗ e this we find that δ ≥ δ if θ ≤ 2+d(1−πb ) . One way to interpret this is to say that if court reliability is very low, opportunists behaving dishonestly in the market will prefer to join the network at higher discount factor than is needed to induce honest agents. Otherwise they would prefer to be part of the business network even though they are dishonest in the market. 4.3 The Market and the Business Network

In this section we integrate the analysis of the preceding sections and consider how the existence, size, and composition of the business network affects the functioning of the anonymous market. In the previous section we identified the critical value of court reliability at which business networks are enforceable, without considering how the relative size of the network influenced the functioning of the alternative exchange institution, the anonymous market. We now turn to this issue. Since trades within the network are honest, a business network is constituted of honest agents and opportunists choosing to behave honestly inside it. Hence, an increase in the size of the business network leads to the absorption of more honest and opportunistic individuals, raising the density of dishonest agents in the anonymous market. This increases the cheating probability in the economy, which in turn affects the critical value of court reliability at which networks are enforceable. This implies that, given values of the other parameters in the economy, it is possible to find a minimal network size that is sufficient to raise the critical value of court reliability to the prevailing level, thereby making the network enforceable.


At this point we make an important assumption. For the subsequent analysis we will assume that the size of the business network is never so large that there is excess capacity, that is, the business group is “small” relative to the size of the economy. This could be justified through out-of-model arguments relating to discoordination problems within the network that increase with its size. The members of the business network will be either honest or opportunist agents, of whom there are (α + γ )N . Hence we assume that the network size 2k < (α + γ )N . 4.3.1 Low dishonesty: Regime (a). The network is of size 2k and the value of court reliability in the economy is θ . Honest and opportunist agents have equal 2k . The fraction of honest agents in probability of being included, φ = (α+γ )N the market is then λ0 ≡ (1 − φ)α and the fraction of opportunist agents in the market is λ1 ≡ (1 − φ)γ and β + λ0 + λ1 = 1. The cheating probability is . This is greater than consequently πa (k) = 1 − (λ0 + λ1 ) = 1 − (α + γ ) + 2k N if the network did not exist. Note also that πa (k) is increasing in network size k. From Proposition 5 we know that an increase in the dishonesty probability lowers the critical value δ ∗ . This implies that given the prevailing discount factor in the economy, there exists a minimal network size that can raise the cheating probability in the anonymous market and, by induction, lower the critical value of the discount factor at which networks are enforceable, to equal the prevailing discount factor. In other words, there is a value of k at which δ ∗ = δ, where δ is the prevailing court reliability. Call this network size k ∗ .

Proposition 6. Given the prevailing discount factor in the economy there is a minimum network size that is enforceable. If δ is the prevailing discount factor then the minimal network size is implicitly determined from the equation θ (1−πa (k)d) . δ = θ +πa (k)d+2π a (k)(1−θ (1+d)) However, there is an important qualification on this result. Because the business network is “small” relative to the economy in the sense described < (α + γ ) and hence πa (k) < 1. This maximal value of πa (k), above, 2k N call it π, ¯ in turn imposes a lower bound on δ ∗ , call this δ. If the prevailing discount factor is less than δ, networks are not enforceable in the economy, that is, Proposition 6 does not hold. 4.3.2 High dishonesty: Regime (b). The analysis in this regime is similar to that in the preceding section, except for the fact that we can now find a minimal network size at which opportunists will find it attractive to seek membership even though they prefer to behave dishonestly in the market. This is the value of k at which e δ falls to the level that equals the prevailing discount factor δ. 1+c−θ (1+d) . This network size is implicitly determined from δ = θ +πa (k)d+2π b (k)(1−θ (1+d))

5. Efficiency We have seen that a business network can be rationalized as an alternative to the anonymous market when court reliability is imperfect. In this section we study the implications of this for economic efficiency. We do this by comparing social


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welfare in two situations: when the anonymous market is the only exchange institution in the economy and when business networks coexist with the anonymous market. In this section we focus on how relative efficiency is affected by changes in network size and prevailing court reliability. For the subsequent analysis we will assume a low-dishonesty regime in the economy. Results for the high-dishonesty regime will be qualitatively similar and we comment on this at the end of the section. Let welfare be defined as W yi , i = a, b and y = M, G, where M represents the market and G represents the business network. We will use simple utilitarian social welfare functions for the welfare analysis. 5.1 The Anonymous Market

In the low-dishonesty regime social welfare is a = N [(1 − β)VMH a + βVMDa ]. WM

(7)

In the high-dishonesty regime social welfare is b = N [αVMH b + (β + γ )VMDb ]. WM

(8)

We take these values as the benchmarks. 5.2 The Market and the Business Network

Now suppose that the economy possesses a business network in addition to the anonymous market. In the low-dishonesty regime social welfare is · ¸ 2k g a V + (1 − πa (k))VMH a + βVMDa . =N (9) W = WGa + W M N The first term in the brackets in Equation (10) is the welfare of members of the network and the other terms are the welfare of individuals trading in the anonymous market. The analysis in Section 3 provides us with a hint of the notion that even though the welfare of members within the group is higher, the welfare of those still in the market falls, and the welfare reduction of the second group may be to such an extent that society as a whole is worse off. We investigate this issue further. Subtracting Equation (8) from Equation (9) yields ¸ · 2k g Ha Da V +(1−πa (k))VM +βVM − N [(1−βa )VMH a +βVMDa ]. (10) Z=N N If the network is of size zero (k = 0), then Z = 0. Therefore, if Z > 0 then having a business network is more efficient than not. An increase in network size has two different welfare effects given the prevailing regime. The network absorbs honest agents and opportunistic agents choosing to behave honestly from the market. This raises the density of people behaving dishonestly in the market, causing the cheating probability to rise. This affects the welfare of the members of the network and the welfare of the agents trading in the market in different ways. The welfare of people involved in market exchange falls. But because of this it is easier to enforce honesty


Figure 2.

within the network. The lump-sum entrance fee falls. This raises the welfare of network members. In other words, as the network becomes larger, the welfare of network members rises at the expense of the people trading in the market. Unless networks are quite large, the first effect dominates the second. Business networks are inefficient for the economy. Only if the network becomes so large in size that the fraction of the population remaining in anonymous market exchange is small, does the network become an economically efficient institution. Moreover, if court reliability increases, networks remain inefficient over a larger size range. Figure 2 helps illustrate this point. We state this result in the following manner. Proposition 7. (i) Business networks are economically inefficient unless they become very large relative to the size of the economy: if k is “small” then social welfare is lower when the economy contains networks, but if k is “large” then social welfare is higher when networks are present. (ii) As court reliability increases, networks are inefficient over a larger range of size: if θ increases, k2 increases. Proof. See the appendix. In a high-corruption regime the value of the cheating probability πb (k), is greater than πa (k). The difference from the preceding analysis is therefore quantitative rather than qualitative.


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6. Discussion This article investigates the sustainability of business networks when the legal system is imperfectly reliable. We have looked first at the functioning of the anonymous market when courts are unreliable and there are no business networks. In such a situation the decision of opportunistic agents to be honest or not determines whether the level of dishonesty that an economy experiences is low or high. One could argue that what separates some countries from others is that in some, the degree of honesty in anonymous interactions is higher than in others. This depends on the reliability of the legal system, but other factors, such as the exogenous split of the population into inherently honest, dishonest, and opportunistic individuals also plays a role. We find that networks hamper the efficient functioning of the economy unless they virtually encompass the economy. The latter possibility is unlikely because of coordination problems that large networks will face. We believe that the efficiency result has implications for economies in transition. If a policymaker has the option of choosing which institutions to manipulate or the sequencing of reform, the theory developed here suggests that strengthening the legal infrastructure should take priority over supporting the role of connections and other modes of informal contract enforcement. We feel it is important to note that the theory developed here focuses on enforceability but does not guarantee that individuals will organize themselves as business networks, even though the parameters of the economy may be conducive to their sustainability. Culture and ethnic ties may play an important role in this. It would therefore be useful to study a cross section of developing countries in order to examine when networks are observed and when they are not, even though other parameter values in the economy suggest that they may be enforceable. In the same spirit, it is important to recognize that the efficacy of court enforcement varies among transactions. Some are easy to enforce and do not need support. Others, like intellectual property rights, are inherently difficult. Accordingly, we should observe networks forming for the latter but not for the former. Empirically this implies studying the prevalence of network type arrangements across classes of transactions.17 Once networks have come into existence, perhaps because of historical accident or cultural reasons, they may persist even though they are economically inefficient because they benefit the participants, and the participants have a vested interest in their preservation. Because of this kind of path dependence, some countries may be handicapped with regards to current economic performance as well as prospects for future development.18

17. See the simple contractual scheme of transaction cost economics as in the Economic Institutions of Capitalism (Willamson, 1985:32–35). 18. Regarding path dependence the reader is referred to Arthur (1988), David (1988), and Leibowitz and Margolis (1990, 1995). On path dependence and institutions, see North (1990, 1991).


We are aware that the efficiency results in Section 4 are not the final word. There are, of course, other functions that business networks perform. In situations with imperfect markets for labor and capital, networks are able to act as surrogate labor markets and venture capitalists. Further theoretical work will try to explicitly account for these functions. Another caveat to the theory developed here is that it considers the existence of only one network. An important issue that this article does not address is the nature of interaction, strategic and otherwise, when there are multiple networks in the economy. Relatedly, we do not deal with the endogeneity of network size. This is an area on which fundamental research has begun, such as Caplin and Nalebuff (1997). It is clear that empirical work on several of the issues raised here is especially warranted, given increasing international integration and the focus on emerging markets and economies in transition. In particular, it would be worthwhile to assess quantitatively the impact that large business networks have on the functioning of emerging or transition economies and the relationship of this with the efficiency of the judiciary, after adjusting for other factors such as the level of per capita income. This could perhaps be done using indexes of social and judicial efficiency in a spirit similar to the article by La Porta et al. (1997). Appendix Proof of Proposition 1. If θ = 1, then R i = 0, i = a, b. Proof of Proposition 2.

∂ Ri ∂θ

1 [−1 2(1−δ)

− c − d + πi d]
0. Hence the condition H0 ≤ H1 is violated. Proof of Proposition 4. δ ∗ ≡ Then =

∂δ ∗ ∂θ

=

[(1−πa d)(θ+πa d+2πa (1−θ (1+d))−(1−πa d)θ (1−2πa (1+d))] [θ +πa d+2πa (1−θ (1+d))]2

(1−πa d)πa (2+d) [θ +πa d+2πa (1−θ (1+d))]2

> 0.

Proof of Proposition 5. δ ∗ ≡ Then =

∂δ ∗ ∂π

=

θ (1−πa d) . θ +πa d+2πa (1−θ (1+d))

θ (1−πa d) . θ +πa d+2πa (1−θ (1+d))

−[θ d(θ +πa d+2πa (1−θ (1+d))+(1−πa d)θ (d+2(1−θ (1+d)))] [θ +πa d+2πa (1−θ (1+d))]2

−θ (2+d)(1−θ ) [θ +πa d+2πa (1−θ (1+d))]2

< 0.

Proof of Proposition 7. Set Z = 0. This is a quadratic function in network size k. Hence there are two roots. We know from Equation (11) that Z = 0 when k = 0. The two roots are then of the form k1 = 0 and k2 > 0. −1−d(1−θ )] ∂2 Z = 2[2−2(2θ > 0. So Z is a convex function. This proves the ∂k 2 N 2 (1−δ) first part.


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2 Using the implicit function theorem on Z = 0 yields ∂k = − ZZ θk , where Z θ ∂θ 2 and Z k are the relevant partial derivatives. Z k > 0 and Z θ < 0. Hence ∂k > 0. ∂θ This proves the second part.

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