نزدیکی فضایی و مکمل بودن در تجارت دانش ضمنی

We model knowledge-trading coalitions in which the transfer of tacit knowledge is unverifiable and requires face-to-face contact, making spatial proximity important. When there are sufficient “complementarities” in knowledge exchange, successful exchange is facilitated if firms can meet in a central location, thereby economizing on travel costs. When complementarities are small, however, a central location may be undesirable because it is more vulnerable to cheating than is a structure involving bilateral travel between firms. We believe that our framework may help explain the structure and stability of multimember technology trading coalitions, such as Sematech and Silicon Valley.

It is widely recognized that the creation and dissemination of knowledge are central to modern economic growth, particularly in high-technology sectors, such as computing, biotechnology, and telecommunications. How best to organize firms and industries to facilitate this process is a topic of ongoing research interest. In many industries, it is impractical for each firm to generate all relevant knowledge within its own vertically integrated structure, and the exchange of knowledge is central to industry success. This fact poses a serious organizational problem, because knowledge is a difficult good on which to contract. It may be virtually impossible to specify in advance the nature of the knowledge to be exchanged or to verify ex post whether the promised knowledge has in fact been delivered.1 Contracting difficulties are especially severe for tacit knowledge, i.e., know-how or skills that are embodied in human capital and are difficult to codify. 2 Tacit knowledge takes a variety of forms. In a manufacturing setting, learning-by-doing is critical in many industries. For example, the fabrication of silicon wafers is central to modern semiconductors and is a delicate art that is only gradually learned on the job. Managerial processes, more generally, also involve tacit knowledge. While much has been written about total quality management, Womack (1991) points out that American automobile manufacturers took years to learn the process from the Japanese and only began to develop mastery through joint ventures with Toyota and Honda. Critical to these and other examples is that sharing tacit knowledge requires face-to-face contact; reading about the skills involved is not sufficient.3 When meetings are essential to knowledge exchange, spatial proximity plays a natural role in determining the cost of sharing knowledge. Marshall (1895) famously stressed that knowledge spillovers are a driving force for the agglomeration of industries. More recently, Saxenian (1994) and Porter (1998) have provided engaging accounts of the role of spatial clustering in creating regional economic advantages.4 There is also a growing empirical literature documenting the importance of spatial proximity for knowledge spillovers between firms. For example, Jaffe et al. (1993) find that patent citations are significantly more likely to come from within the same country, state, and even metropolitan area than would be predicted by the geographical dispersion of similar research.5 The foregoing work, while intriguing, has not developed formal models of the role of spatial proximity in knowledge-based industry clusters. Our goal is to build a simple dynamic model in which competing firms trade tacit knowledge, the transfer of which is possible only when individuals meet face-to-face.6 As a result, geographical location becomes essential to the analysis. We consider two possible organizational structures for exchange, a centralized meeting location and bilateral travel. The “central location” structure is possible only if a given firm's knowledge can be conveyed without being in the presence of that firm's own facilities. This setting corresponds to the presence of a joint facility that can be shared by all firms, akin to the “foundry” model for semiconductor production.7 This setting also applies to an industry in which tacit knowledge is entirely independent of any physical facilities, and hence meetings can be held at a convenient centrally located hotel or conference center. The “bilateral travel” structure is relevant when a firm's tacit knowledge is intimately tied to its actual physical facilities. This was the case, for example, in von Hippel's (1988, chapter 6) classic account of informal trading of proprietary process know-how between U.S. steel minimill producers, and is likely to be the case for benchmarking of any complex manufacturing processes, e.g., total quality management (TQM), in which plant visits were necessary for Americans to truly comprehend the Japanese management approach. The impact of knowledge exchange on costs depends on the extent to which the knowledge of the two parties is complementary. In strictly “independent” knowledge exchange, one firm can passively absorb the knowledge presented by another without revealing his own knowledge, and there are no joint gains from mutual exchange. In “complementary” knowledge exchange, there is an interaction that generates new insights and joint benefits not recognized by either party prior to the encounter, but only if both parties actively exchange their knowledge. In this type of exchange, both parties gain from a mutual revelation of information, and the whole is greater than the sum of the parts. We show that the balance between these two forms of knowledge has important implications for the sustainability of knowledge trading. In general, greater complementarities facilitate the exchange of knowledge across greater distances, thereby supporting the formation of successful clusters. Moreover, the advantages of particular organizational structures are related to the extent of complementarities in knowledge exchange. When complementarities are large, knowledge exchange is facilitated when firms have the ability to meet in a central location, thereby economizing on travel costs. When complementarities are small, however, a tradeoff emerges in the use of a central location. While the central location reduces travel costs, it is also more vulnerable to cheating than is a structure involving bilateral travel between pairs of firms. With a central location, a firm can opportunistically cheat all other firms in the industry by traveling to the center, passively absorbing knowledge from all its rivals, and withholding its own knowledge. In the bilateral travel structure, however, a firm can only cheat a subset of the other firms in its industry before its cheating behavior is identified and punished. This makes cheating less profitable than in the central location structure. We are aware of only two other papers that attempt to formalize the role of spatial proximity in knowledge exchange. Cooper (2001) models information transmission via job mobility and finds that contractual clauses restricting mobility are generally welfare-decreasing. Berliant et al. (2000) develop a model in which individuals search for others with complementary knowledge; they derive equilibria in which the extent of agglomeration is endogenously determined.8 In the following section, we present our basic model of knowledge exchange in an oligopoly, analyze the stage game involving travel to meetings, knowledge exchange, and output choice, and lay out the structure of the repeated game. In Section 3, we study the knowledge-sharing equilibria that can be sustained when all firms travel to a central location. Section 4 studies the case where pairs of firms travel to one another's facilities to exchange knowledge; in both 3 and 4, we emphasize the relationship between knowledge complementarity and the sustainability of knowledge sharing. Section 5 concludes. All proofs are relegated to Appendix A.

Existing theoretical work has paid scant attention to the role of spatial proximity in facilitating knowledge exchange within clusters of technologically interlinked firms. In this paper, we have provided a simple model in which spatial proximity is important due to the need to exchange cost-reducing tacit knowledge via face-to-face contact. We believe our analysis helps to clarify the factors that contribute to the viability of innovation clusters. One factor we highlight is the importance of knowledge complementarities in the sustainability of knowledge-sharing coalitions. Because knowledge exchange is unverifiable, each firm may have incentives to cheat on the other members of its coalition. Nevertheless, we found that even in a one-shot game, knowledge exchange may be an equilibrium if there is sufficient complementarity in the exchange process, that is, if mutual sharing produces a cost reduction beyond what is possible simply through the discrete individual contributions of each party. In the case of repeated trading, firms in our model that cheat on the coalition are excluded from further cooperation, while the remaining members of the coalition continue to cooperate. We find that the presence of greater complementarities facilitates the exchange of tacit knowledge, in the sense that it allows such exchange to be sustained over greater distances in both the stage game and the repeated game. We also find that the organizational structure of the industry is an important determinant of whether knowledge exchange is viable. When complementarities are large, knowledge exchange is facilitated when firms have the ability to meet in a central location, thereby economizing on travel costs. This may be as a result of sharing a joint research or manufacturing facility, as was the case for the SEMATECH coalition in the United States or the Taiwan Semiconductor Manufacturing Company. It may also come about because the relevant knowledge is not tied to any physical facilities, in which case meetings can take place at any convenient central location, such as a hotel or conference center. When complementarities are small, however, a tradeoff emerges in the use of a central location. While the structure reduces travel costs, it is also more vulnerable to cheating than is a structure involving bilateral travel between pairs of firms. With a central location, a firm can opportunistically cheat all other firms in the industry by traveling to the center, passively absorbing knowledge from all its rivals but withholding its own knowledge. In the bilateral travel structure, however, a firm can only cheat a subset of the other firms in its industry before its cheating behavior is identified and punished. This makes cheating less attractive than in the central location structure.20 The interfirm trading practices inside geographical clusters are perhaps best documented for the Silicon Valley region. Our analytical structure helps to explain how a cluster, such as Silicon Valley, maintains interfirm collaboration among the competing firms given that such collaboration is inherently fragile. The Santa Clara Valley and its surrounding towns of Mountain View, San Jose, and Sunnyvale are home to several densely located groups of specialized firms, mainly in the semiconductor industry. For example, as is shown in Angel and Scott (1987), the geographical location of the specialized semiconductor establishments in Silicon Valley displays a close-knit functional distribution among the circuit design establishments, mask-makers, independent test facilities, device assembly houses, and other ancillary subcontractors. Such observations provide intriguing, if anecdotal, evidence on the significance of spatial proximity in linking clusters of firms with complementary products and technologies. Considerable work remains to be done incorporating spatial proximity and knowledge complementarities into economic analysis of knowledge exchange. On the theoretical side, one step would be to include explicitly in our model investments in research and development that generate the knowledge to be exchanged. Another would be to incorporate distance and complementarities in a social network approach, by modeling in detail the formation of links between firms that allow for knowledge sharing, and assessing the equilibrium structure of such networks. A third would be to blend our model of knowledge sharing within coalitions with models of information transmission via job mobility, with the aim of providing a more comprehensive picture of information transmission within clusters. On the empirical side, detailed field studies of collaboration within clusters would be valuable. If documented carefully, they could provide the foundation for econometric research on spatial proximity and knowledge complementarities, and their role in knowledge exchange.