DRUID Working Paper No Market Formation: Examining the Coordination of Heterogeneous Contributions. Jeroen Struben and Brandon Lee

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1 DRUID Working Paper No Market Formation: Examining the Coordination of Heterogeneous Contributions By Jeroen Struben and Brandon Lee

2 Market Formation: Examining the Coordination of Heterogeneous Contributions Jeroen Struben Desautels Faculty of Management, McGill University 1001 sherbrooke Street West Montréal H3A1G5 QC Brandon Lee London Business School Regent s Park London NW1 4SA April 2012 Abstract: While extant literature recognizes the central role of collective action in market formation, it undertheorizes the existence of collective action dilemmas and their impact on successful market emergence. We redress this gap by examining the central mechanisms governing the existence and resolution of collective action dilemmas in market formation. We use a computational model that centers on actors collective development of a market infrastructure to explore the impact of different degrees of collaboration on market formation. In particular, consistent with market settings where actors tend to perform entirely distinct roles, we allow actors resource contributions to be imperfectly substitutable. We find that while heterogeneity in growth strategies strongly reduces market emergence thresholds under perfect substitution, this effect is strongly suppressed under imperfect substitutability. Most important, our analyses point to a market emergence conundrum: market success depends mostly on collaboration precisely where the foundation for its existence is lowest. We develop a set of propositions and a grounded typology of idealtypical instances of market formation. We discuss the implications of our findings for connecting collective action and market formation research. Keywords: Market formation; Collective action; Substitutability; Path-dependence; Simulation Jel codes: ISBN

3 Market Formation: Examining the Coordination of Heterogeneous Contributions ABSTRACT While extant literature recognizes the central role of collective action in market formation, it undertheorizes the existence of collective action dilemmas and their impact on successful market emergence. We redress this gap by examining the central mechanisms governing the existence and resolution of collective action dilemmas in market formation. We use a computational model that centers on actors collective development of a market infrastructure to explore the impact of different degrees of collaboration on market formation. In particular, consistent with market settings where actors tend to perform entirely distinct roles, we allow actors resource contributions to be imperfectly substitutable. We find that while heterogeneity in growth strategies strongly reduces market emergence thresholds under perfect substitution, this effect is strongly suppressed under imperfect substitutability. Most important, our analyses point to a market emergence conundrum: market success depends mostly on collaboration precisely where the foundation for its existence is lowest. We develop a set of propositions and a grounded typology of idealtypical instances of market formation. We discuss the implications of our findings for connecting collective action and market formation research. Keywords: Market formation, Collective action, Substitutability, Path-dependence, Simulation INTRODUCTION Over the past two decades, scholars have advanced theories regarding the creation of new organizational forms, markets, and industries (Aldrich and Fiol, 1994; Rao, Morrill, and Zald, 2000; Hargrave and Van de Ven, 2006) and have empirically sought to identify the mechanisms and processes associated with their origins and trajectories (Van de Ven and Garud, 1993; Lounsbury, Ventresca, and Hirsch, 2003; Haveman, Rao, and Parachuri, 2007; Schneiberg, King, and Smith, 2008; Weber, Heinze, and DeSoucey, 2008; Sine and Lee, 2009; Hiatt, Sine, and Tolbert, 2009). Much of this work is grounded in the premise that collective action is central to the successful formation of new markets and industries. Given the collective and purposive nature of how actors seek to achieve joint interests in market formation, some have proposed that such behavior resembles that of social movements (Davis and McAdam, 2000; Rao Morrill and Zald, 2000; Fligstein, 1996). While it is understood that market formation processes require collective action, most existing literature in this domain has either taken for granted the existence of a shared collective rationale for action, examining producer markets where a clear rationale for collective 2

4 action based on a shared identity exists (e.g., Carroll and Swaminathan, 2000; Lounsbury, Ventresca, and Hirsch, 2003; Greve, Pozner, and Rao, 2006), or has focused on the role of existing social movements in facilitating market formation (e.g., Hiatt, Sine, and Tolbert, 2009; Sine and Lee, 2009). As a result, the literature has been largely silent regarding how market actors overcome collective action dilemmas and thresholds related to market formation and to the development of a social and material market infrastructure (but see Van de Ven, 1993; Van de Ven and Garud, 1993; Schneiberg, 2007). Consequently, questions of how and under what conditions markets succeed or fail to form are under-analyzed in this literature. By contrast, a stream of sociological literature has developed in parallel that provides important rationales for why collective action may be difficult despite common interests (Granovetter, 1978; Oliver, Marwell, and Teixeira, 1985; Macy 1991; Heckathorn, 1996). Highlighting the importance of interdependent actors pursuing a common cause, these studies challenge the assumption that a common interest necessarily equates to successful resource mobilization and identify the impediments to collective action and the mechanisms employed to overcome them. In particular, startup problems exist when interdependent but self-directed actors produce sufficiently strong positive externalities on each other, with each benefitting from the others commitment to a common cause (Marwell and Oliver, 2001). However, by demonstrating that under heterogeneous preferences collective action may occur as participating actors sequentially reduce others impediments to action, this stream points to how actors collectively influence the propensity to engage in collective action and the timing of that engagement (Oliver, Marwell, and Teixeira, 1985). Despite these insights, this literature makes a number of assumptions that limit its generalizability and relevance to market formation processes. First, the formal models developed in this literature assume that actor contributions to a collective effort are fully interchangeable. While this assumption may be reasonable in such collective action contexts as riots and strikes (Granovetter, 1978), it is less appropriate for market settings where actors tend to play more specialized roles. In such instances, actor interdependency is more appropriately characterized as involving imperfectly substitutable contributions. Second, these collective action models tend to portray actors as acting independently of one another, with 3

5 little need or expectation to collaborate (Macy, 1991). By contrast, resource mobilization and the joint development of institutions in nascent markets often necessitate some form of collaboration, whether formal or informal, between market actors (Powell, 1990; Van de Ven and Garud, 1994). However, achieving and sustaining such collaboration is challenging, and anticipating others future actions is difficult. Taken together, the complementary gaps in the literatures on market formation and formal collective action models suggest significant theoretical advance for clarifying the nature of collective action under different types of market formation conditions. In this paper, we extend theory regarding the conditions for, existence of, and level of market formation thresholds as interdependent market actors independently make distinct resource contributions. We do this by developing and analyzing a computational model that builds on, but alters, foundational assumptions of the collective action literature. Specifically, we highlight the fundamental difference between collective action dynamics associated with perfectly and imperfectly substitutable contributions. Most generally, the computational analysis provides insights into how similar mechanisms and processes associated with market formation may lead to entirely different outcomes, conditional on the form of interdependency and degree of collaboration between actors. This has important implications, because despite a wealth of empirical analyses of a wide range of market types, little progress has been made in abstracting away from specific markets to develop a more general view of market formation dynamics (Fligstein, 2001). Thus, we develop a theory of market formation that, while generalizable, also corresponds to empirical realities of market formation dynamics. From our analysis, we derive a set of propositions and an accompanying typology of ideal-typical instances of market formation to classify a broad range of market formation dynamics and the role and nature of collective action needed for successful market formation. The typology accommodates multiple new market forms, ranging from radical to more incremental markets, and unifies empirical and theoretical work by identifying common processes at work across these market forms. 4

6 In the next section, we distill key conceptual elements and assumptions from the literatures on market formation and collective action that underlie our formal model. We then provide the basic structure of the model, report the results from our computational analysis, and develop a typology of market formation and the accompanying set of propositions. We conclude with a discussion of the implications of this model and areas of future research. COLLECTIVE ACTION AND MARKET FORMATION While markets can be seen simply as locations where buyers meet sellers, scholars have recognized the importance of an underlying structure that enables ongoing transactions between repeated market actors (White, 1981; Sewell, 1992; Swedberg, 1994; Fligstein, 2001). Fligstein defines markets as social arenas that exist for the production and sale of some good or service characterized by structured exchange (2001: 30). Structured exchange means that because market actors desire repeated exchange, some set of rules, norms, or social structures must exist to guide and organize these exchanges. Such structure stabilizes exchange and enables ongoing investment (Fligstein, 2001: 23). It is through the establishment of such conditions that a stable market can emerge a situation of self reproducing role structures, wherein recognition and legitimacy for the product is established among buyers, a status hierarchy emerges within sellers, and the sellers 1 are relatively stable and established on a period-to-period basis (White, 1981). Based on conceptual foundations from White and Fligstein, we define markets as structured and patterned exchanges that exhibit a high degree of regularity in terms of product/service offering, the actor roles played in the exchange, and the institutions (whether cognitive, normative, or regulative, or a mix) that govern the exchange. This definition is flexible enough to include infrequent or arm s-length exchanges, but generally implies that the formation of a market requires mobilization of resources by, and investment from, interested actors (Van de Ven, 1993). In line with this, our analysis centers on the collective development of market infrastructure, which we conceptualize as comprising both social and material structure. Examples of market infrastructure include, but are not limited to, standards, legitimation, 1 Although the particular set of firms that are sellers may change, the role of seller is relatively stable and self-sustaining. 5

7 agreed-upon role structures and skills, codes, product categories, and regulations. We consider such market infrastructure a semi-public or collective good because investments in its development by market participants enhance their own value of performing exchanges while at the same time contributing to the market in the aggregate (Garud, Jain, and Kumaraswamy, 2002). By extension, while a single market actor may occasionally seek to create a market, it is generally the case that multiple actors, working in concert, are engaged in this process. For example, new product categories may require that some market actors engage in sensegiving and others in sensemaking to render the new category understandable and appealing (Weber, Heinze, and DeSoucey, 2008; Navis and Glynn, 2010). Similarly, the successful development of industry standards generally requires contributions from multiple market actors (Garud, Jain, and Kumaraswamy, 2002). Even when multiple actors have a strong interest in successful market formation, the requisite market infrastructure may not develop. For example, failure to collaborate can make it difficult for actors to mobilize the resources needed to develop viable infrastructure (Dowell, Swaminathan, and Wade, 2002). The challenges for entrepreneurs of identifying opportunities, assembling resources, and recruiting and training employees are severely compounded in nascent markets by the lack of requisite market infrastructure (Aldrich and Fiol, 1994). Consequently, the presence of coordination externalities is a major challenge in market formation (David and Bunn, 1988; David, 1995). Yet, most studies of market formation are of markets that have formed and not of those that failed to form. This serious form of selection bias (i.e., studying only markets that survived long enough to leave sufficient data to study) has long been noted (Aldrich and Fiol, 1994) and severely limits the ability to generate accurate scope conditions associated with success or failure. Using comparative case studies, Rao and Giorgi (2006) underscore the importance of considering both successful and unsuccessful attempts at change. For instance, they found that access to mobilization channels enabled successful framing efforts in some cases, but hindered them in others. Also inhering in this vein of selection bias is the tendency to take for granted a shared rationale for action. Although not explicitly speaking about collective action in creating a market, DiMaggio stated, 6

8 new institutions arise when organized actors with sufficient resources see in them an opportunity to realize interests that they value highly (1988: 14). Such language suggests that actors are already organized, possess adequate resources, and have shared interests. This sort of statement, perhaps inadvertently, tends to create an a priori assumption that a shared rationale for collective action is present. As a result of these shortcomings, thorny questions regarding collective action thresholds have not been adequately addressed in market formation settings. We redress this by conceptualizing critical market infrastructure as a public good and identifying scope conditions under which barriers to collective action and market formation thresholds are overcome. We conceptualize market formation as a process inextricably bound up in resource allocation, whether material resources (i.e., capital, labor, inputs) or more cultural, cognitive, or social resources such as managerial attention and sensegiving. To formalize the concept of market formation and to assess the degree to which particular factors influence successful formation, we define market formation thresholds as the initial resources across distinct actors necessary to set in motion a self-fulfilling process of market formation. We focus on four explanatory factors that are central to collective action dilemmas and modify them to make them relevant for market formation dynamics. Market-Level Returns-to-Scale The first factor captures how the actual development of the market infrastructure relates to the mobilization of resources. The collective action literature demonstrates that differences in the returns from cumulative collective resources dedicated to a cause dramatically alter the existence, type, and extent of collective action dilemmas (Oliver, Marwell, and Teixeira, 1985). When returns-to-scale (RtS) in resources are sufficiently strong, actors tend to face a startup problem: early resource commitment is costly and, given the uncertainty of the realization of the collective cause, also risky. However, once sufficient resources have been provided, other actors are increasingly able to overcome their startup costs, resulting in the achievement of the collective cause. On the other hand, when RtS are decreasing, the collective action problem may shift to free-riding, because only a relatively small subset of contributions is necessary for the 7

9 cause to be established, after which contributions make less of an impact. In this case, only the most interested actors contribute (Oliver, Marwell, and Teixeira, 1985; Heckathorn, 1996). Thus, RtS are important not only because they affect one s interest to commit directly, but also because they have an indirect effect by influencing others resource commitments. In market settings, the RtS that actors experience depend on the nature of a market formation problem. In the case of very new industries or radical innovations, market actors face high RtS because of an institutional vacuum, difficulty attracting necessary resources, and an overall lack of legitimacy (Aldrich and Fiol, 1994). Consequently, investment in developing market infrastructure early on yields few benefits, while contributing actors incur high costs. However, once these challenges are overcome, actors might extract large gains from their activities. In the case of a more incremental innovation or a less novel product market, market actors can leverage (to varying degrees) the resources and infrastructures of existing markets such as favorable regulation, established distribution channels, cognitively proximate product categories, and existing standards (Rao, Morill and Zald, 2000). Under these conditions, RtS tend to be low because small investments in the market infrastructure allow the reaping of value. 2 Interdependency Between Actors The second factor relates to interdependency between actors within a market. Collective action dilemmas rest on the notion that actors resource contributions are interdependent. Interdependence in this context refers to the fact that an actor s contribution to a collective cause generates benefits both for herself and for others. In the archetypal collective action situation, an individual actor faces a one-off decision to participate in a cause based on her individual interest and on the cumulative collective participation at the point of decision (Marwell and Oliver, 2001). By contrast, the nature of interdependencies is markedly different in new market settings. First, market actors make ongoing, rather than one-off decisions regarding their contributions to market 2 This conceptualization of RtS is also consistent with economics and management literatures that focus on the emergence of technology dominance via lock-in (Arthur, 1989). Further, strong RtS are associated with both supply- and demand-side factors (e.g. Suarez 2004). 8

10 infrastructure over time. Second, the relevant actors extend beyond a focal type of actor to include not only the buyer and seller but also market intermediaries, government agencies, educational organizations, the media, producers of complementary goods, and so on. Finally, the implicit assumption of formal collective action models that resource contributions are easily interchangeable (i.e., perfect substitutability of resource contributions) is generally not valid in new market formation settings. Market formation generally occurs through the alignment of resource contributions from a variety of actors that perform distinct roles. As such, their resource contributions to developing new market infrastructure are seen as imperfectly substitutable. The contrast of two stylized examples illustrates how imperfect substitutability of contributions affects the process and direction of market formation. Consider first the following situation in which small retailers in a village located in the developing world are contemplating the development of a market for contraceptives as part of a government initiative. At the outset, this new product is taboo and its use is seen as morally illegitimate. Retailers, while hoping that the sale of condoms may eventually be a profitable market, face a major startup problem. First, while sustained marketing and education efforts may improve acceptance at an accelerating pace, initial efforts have little impact. Further, there are positive externalities for legitimacy across retailers as each makes efforts to promote and market the product. Finally, individual retailers may not be sure whether even after sufficient education and marketing from their side, contraceptives will be seen as legitimate. For this stylized example, assumptions of substitutable contributions across retailers are appropriate. Consider a single retailer, denoted as ego, and her motivation to participate in the development of the market for this product (Figure 1). Ego s gains are negative at low commitments and become positive only after sufficiently large efforts. More important for market formation are the strong decreasing, or negative marginal gains for early commitments, combined with uncertainty about eventual acceptance. At this point, ego is not likely to contribute resources because either she herself considers the risk too large, or it is too difficult for her to obtain access to additional resources. Graph A in Figure 1 shows this in line 1 (no 9

11 resources by alii 3 ) with a downward arrow (point a). Only after threshold point r 1 * will continued contributions on the part of ego lead to improvements in her gains (point b). The existence and location of such an individual threshold point is not observed by ego. One way for ego s threshold to shift may be through resource commitments by alii. First, commitments by alii that expand the product s market infrastructure (legitimacy in this case) always improve ego s gains (line 2 shifts upwards compared to line 1). More importantly, given that RtS is increasing, the further investments in the market infrastructure, ego s gain function now also curves sharper upward, improving the current marginal gains she experiences (point a line 2) and reducing the threshold point (r 2 *). Thus, an improved market infrastructure, through commitments by alii, increases not only ego s profits but also the likelihood that she commits beyond her own threshold. These dynamics are central in the collective action research (Granovetter, 1978; Oliver, Marwell, and Teixeira, 1985). The influence of alii will be different, however, if we assume moderate RtS. In this case, commitments by alii, while still improving ego s gains, actually move ego s threshold point to the right. This is because ego s gains, while still following a U-shape, do not increase as sharply when more resources are allocated. By extension, when RtS are even weaker, ego may not have a threshold point at all. In that case, her gains increase up to a critical point, after which they begin to decline. Consider now a different stylized example, the development of a market for locally grown agricultural products in a metropolitan area. Multiple actors engage in a distinct component of this market: Farmers provide the fruits and vegetables, local food activists promote the overall health and sustainability benefits, and some existing retailers free up shelf space for this new food category. While not necessarily knowing each other, actors are aware of the related components needed for the market. Thus, like the contraceptive example, actors are interdependent because their efforts with respect to the market infrastructure improve benefits for all who operate in the nascent market. However, unlike the contraceptive example, each actor now provides distinct contributions to the formation of the market. For instance, when 3 When taking the perspective of a single actor, throughout the paper we use the terms ego and alii. We use alii rather than alter to reflect the notion that resources for market infrastructure derive from multiple, rather than a single other actor. 10

12 retailers do not offer them shelf space, farmers cannot easily compensate for this by investing greater effort in producing more food. Thus, contributions are imperfectly substitutable. Now consider ego s perspective as a farmer seeking to develop this market for local food. Absent any commitments by alii (i.e., retail stores, distribution, consumer awareness), increasing commitments by ego will always increase her losses (Figure 1, Graph B, line 1). Likewise, limited commitments by alii may not help much (line 2). Yet, when the relevant market infrastructure is well developed, ego is easily motivated to invest as well (line 3). Thus, in situations of imperfect substitutability of contributions, the existence and location of ego s threshold is very sensitive to commitments by alii. ************* Insert Figure 1 about here ********** Heterogeneity The third factor concerns heterogeneity across actor contributions. The collective action literature highlights how variation in actor interest and in resources across actors is critical in facilitating collective action (Olson, 1965; Granovetter, 1978; Burt, 1982; Oliver, Marwell, and Teixeira, 1985; Marwell and Oliver, 1993). For example, commitments by a few with sufficient initial interest may reduce the risk of participation for others, lowering individual thresholds for all. As more individuals begin to participate, a self-reinforcing cycle of participation is set in motion. Heterogeneity across actors in terms of resources and strategies is prevalent in new markets and industries (Kraatz and Zajac, 2001). Organizations vary in terms of initial resource endowments (e.g., Shane and Stuart 2002), in strategies and growth orientations (Eggers and Kaplan, 2009), and in the accumulation of firm-specific capabilities (Teece, Pisano, and Shuen, 1997). Likewise, organizational forms differ by an idiosyncratic subset of dominant competencies and routines (Pentland and Feldman, 2005). Building on these distinctions, we consider two types of heterogeneity critical to new market formation: variation in initial resource endowments and variation in growth strategies. Initial resource endowments refer to ex-ante generic and fungible inputs that firms possess which are then transformed into various outputs, particularly those used to develop market infrastructure. In our stylized contraceptive 11

13 legitimation example, one retailer may have an abundance of cash that it can allocate to promotion and education efforts, whereas other retailers in the community may not. We define growth strategies as those hard-to-imitate unique capabilities that enable firms to extract ongoing, greater returns from the market infrastructure. In the contraceptive legitimation example, variation in growth strategies could derive from some retailers focusing on a particular demographic segment, cultivating their loyalty through personal connections, while the other retailers focus on the market as a whole. In the local food example, variation in growth strategies comes naturally because each actor plays a distinct role in the market, performing entirely different tasks. Collaborative Coordination Given the importance of interdependence to market formation, it is vital to consider the rationale for, and nature of, collaboration between market actors. Achieving resource commitments through collaboration is an important strategy for market actors during market formation (Fligstein and McAdam, 2011). The extent of collaboration between actors is driven by diverse motivations and manifest in a variety of formal and informal ways (Powell, 1990). Collaboration may be pursued for economically rational reasons since commitments beyond what seems marginally favorable in the short run may be expected to yield benefits in the long run through an altered market formation path. Collaboration may also be facilitated by market roles and the way they are organized at the outset. For example, the vertical integration of market roles and the existence of industry associations can direct and control cooperation between firms to foster market development. Conversely, actors may contribute to growing a market and collaborate with others out of a commitment to prosocial norms, motivated by political, environmental, philosophical, or spiritual values. For example, enthusiasts or activists may commit significant resources to developing market infrastructure because they fundamentally believe it is the right thing to do, even if this provides them with little or no direct economic benefit (e.g. Weber, Heinze, and DeSoucey, 2008). Regardless of actors motives, the extent to which commitments to continued collaboration persist is 12

14 ultimately conditional on the actions of others and on subsequent market development under such collaborative commitments. A central driver of collaboration is the norm of reciprocity the societal rule that obligates individuals to repay services that have been performed for them (Emerson, 1976). Actors may be willing to collaborate to the extent that they have confidence that others will reciprocate and repeat such actions on similar principles (Ostrom, 1998). Actors confidence may manifest in myriad ways, including familiarity and norms that increase predictability (Adler, 2001). 4 In addition, actors propensities to collaborate are finite. Once a market is established, collaboration tends to give way to competition (Brandenburger and Nalebuff, 1996; Fligstein, 2001). However, no natural transition moment to non-collaboration exists. Instead, actors must reconcile their expectations of longer-run benefits from collaboration with reality. Thus, maintaining effective collaboration is difficult, and premature deviation from collaborative action may occur for various reasons, some of which are idiosyncratic to the actor and some of which are related to market/structural conditions such as competitive pressures (Kollock, 1998; Azoulay, Repenning, and Zuckerman, 2010). While collaboration clearly facilitates market formation, it is not obvious how collaboration (and the challenge of sustaining it) depends on the presence of the various market formation factors marketlevel RtS, interdependency, and heterogeneity. We conceptualize collaboration in market formation settings as actors taking a market growth perspective, which means that actors commit resources based on how they expect the market as a whole to benefit from their commitments and will therefore commit more resources than they would under an individual-based viewpoint. MODELING COLLECTIVE ACTION AND MARKET FORMATION We developed a simulation model to examine how market formation is affected by imperfectly substitutable contributions and how this interacts with variation in growth strategies, initial resource 4 Others focus on building trust through mechanisms such as interpersonal contact, reputation, and within established institutional contacts (Coleman, 1990). However, in novel market settings actors, often from distinct backgrounds, cannot rely on established institutions to provide such trust. Hence, in generalizing, it is perhaps more useful to think in terms of confidence rather than trust. 13

15 endowments, and collaborative forms. Based on these conceptualizations, the base model consists of three structures: actor gains and production functions, resource allocation, and heterogeneity. We briefly describe each below. 5 To explore the role of collaboration, we modify the resource allocation formulation in a later section. Actor Gains and Production Functions The market consists of N actors, each reaping a (subjective) value V i, i [1,N] from her business activities depending on the state of the market infrastructure R i relevant to her. For example, if R i represents the cumulative advertising and education efforts and availability of a product in retail stores, then the value V i captures sales permissible by the resulting legitimation (positive media coverage, evaluations and critiques, and a pool of consumers who actually consider the product). To develop and maintain the market infrastructure, actors allocate resources at cost C i. Thus, actors achieve gains g i =V i (R i )-C i (r i ) from their commitments to the market infrastructure. The relation between reaped value and the relevant market infrastructure is specified by the production function V i v i R i! i, with η i >0 representing the value-related RtS exponent and v i the unit value generated when R i =1. The value-related RtS exponent comprises a market-level component η as well as actor-specific variation (discussed later). When η=1, each additional resource generates the same unit value, while smaller (larger) values provide diminishing (increasing) RtS. For example, a value larger than 1 corresponds with market situations in which it becomes easier to achieve legitimation once collective efforts overcome high initial resistance. Costs of achieving and maintaining infrastructure is formulated in the same way as the value derived, except that they depend on one s own commitments r i only: C i =r γι i, with γ ι the cost-related RtS exponent. γ is naturally bounded between 0 (representing situations of pure fixed cost) and 1 (pure and constant variable costs), while values in between represent diminishing costs. Because 5 Model equations omitted in the text are provided in the appendix. An additional technical compendium that includes the full model, experiments developed in the software, numerical illustrations of its behavior, and relevant proofs behind the propositions is available from the authors. 14

16 actors typically achieve some degree of cost-related scale economies and since the importance for market dynamics is the difference between value- and cost-related RtS, we hold the market-level-related RtS constant at the intermediate γ=0.5. Market Infrastructure and Interdependency of Contributions An actor s market infrastructure R i =f(r 1,,r i,,r j,,r N ) comprises resource contributions by all actors. When these contributions are imperfectly substitutable, the summation is non-linearly based on the distribution of contributions. To capture this, we employ the constant elasticity-to-scale (CES) production function (McFadden, 1973) specifically designed to represent degrees of substitutability among various factor inputs in our case, resource contributions. The CES function relies on two parameters the crossproducer factor share parameter κ ji and the substitution parameter ρ, which respectively capture the interdependency and the degree of substitutability between actor contributions. Specifically: " R i = (! j! ji r j ) 1 " (1) The interdependency κ ji indicates the importance of actor j s contributions to the market infrastructure of actor i. Letting Σ j κ ij =1 ensures that the market infrastructure is scale invariant to parameter variations for r i =1 i, including to the number of actors N. Further, setting the importance of cross-actor contributions equal for all, then κ κ ij /k ii and κ 0 (N-1) κ, each bound by 0, define respectively the relative importance of individual and total cross-actor contributions. Alternatively, when κ 0 exceeds 1, actors influence on building the market infrastructure becomes small. In such cases market formation challenges tend to be dominated by actor apathy or free-riding (Olson, 1965; Fireman and Gamson, 1977). We assume moderate interdependency throughout. The substitution parameter ρ [,1] measures the ease with which the resource contributions can be substituted for one another. When ρ=1, resources are perfectly substitutable across contributions. In this case, the market infrastructure increases proportionally with each contribution, irrespective of their current 15

17 mix. While we treat this situation as an extreme case for market situations (our contraceptives example), it is a common assumption in collective action models (Granovetter, 1978; Burt, 1987; Macy, 1991; Marwell and Oliver, 1993). On the other extreme, when ρ, resources are non-substitutable, or perfect complements. In this case, the market infrastructure improves only when the most under-committed actor increases resource contributions. When ρ equals 0, a moderate case, resource contributions are unit substitutable. In that case, the actors market infrastructure benefits from resource contributions across actors being distributed according to their relative importance. The local food example may be considered such a case. In our analysis, we examine ρ [-1,1]. Resource Allocation We assume that actors alter the market infrastructure through gradual resource expansion or contraction, rather than in lump sums. Thus, actors continually adjust the flow of their resource allocations, or efforts, ε i. They do this in proportion to current resource commitments r i : ε i =f(. )r i, consistent with principles of anchoring and adjustment (Tversky and Kahneman, 1974). The expression f(.) captures how efforts change as a function of expected (subjective) gains from changing the market infrastructure, and is positive (negative) when those are above (below) zero. Under uncertainty of others actions or of the consequences from large-scale changes to the market infrastructure, actors resort to simple heuristics, evaluating expected gains from altering the current market infrastructure. Thus, actors assess the marginal gains of additional resource commitments given the state of the market at the moment of the evaluation (Burt, 1982; Marwell and Oliver, 1993). Later we consider actors having different motivations; for now, we assume that actors seek to advance their own direct gains only. Thus, an actor s efforts are proportional to his or her direct marginal gain from allocating additional resources, dg i /dr i : ε i dg i /dr i (2) The commitment of resources based on marginal gains corresponds with the behavior in earlier examples in Figure 1, indicated by the slope of the arrow at each point of the gain curve. The above 16

18 relations imply that ego understands her own production and cost functions at the point of the current resource allocation and that she is able to effectively evaluate the extent to which contributions to the market infrastructure by alii help her. 6 However, we do not assume that she can observe profit functions of alii. Taken together, actors resource allocation decision heuristics conform to bounded rationality assumptions (Simon, 1957; Cyert and March, 1963). 7 Heterogeneity In our model, we represent variation in growth strategies (the hard-to-imitate unique capabilities that enable firms to extract their ongoing returns from the market infrastructure) by allowing the individuallevel realizations of RtS, η i and γ i, to deviate from the market-level RtS exponents. We manipulate variation in growth strategies by changing the normalized standard deviation σ i of actors normally distributed RtS (η i, γ i ), truncated at zero. The second source of heterogeneity derives from actors initial resource endowments r 0i (the ex-ante generic and fungible inputs that firms possess which are then transformed into various outputs). Non-zero initial resources represent a pre-existing stock of generic resources that actors are endowed with at the beginning of the simulation and that are deployed to develop the market infrastructure. We manipulate variation in actors initial resource endowments, like the RtS, by adjusting the normalized standard deviation σ r of their normally distributed r 0i, also truncated at zero. ANALYSIS We used the model described above to analyze how the form of actor interdependency affects market formation. The outcome of interest is the existence and extent of market formation thresholds. Our analysis comprises three computational experiments. In experiment 1, we developed baseline results, examining how heterogeneity affected the collective market formation threshold, assuming that actors coordinate solely through non-collaboration. We performed this analysis for a representative market-level 6 For the complete equations concerning resource allocation, see Appendix I. 7 We ignore here the role of actors uncertainty about the value of current resources provided to the market infrastructure, whether it concerns their own contributions or those by alii (e.g. Podolny, 2001). 17

19 RtS that yields sufficiently high individual thresholds absent heterogeneity. In the next pair of experiments, we introduced collaboration. In experiment 2, we examined not only the threshold level but also the critical market-level RtS at which thresholds begin to occur. We examined how this is affected, jointly and individually, by heterogeneity, substitutability across contributions, and collaboration. In experiment 3, actors were allowed to defect from collaborative modes. From the experiments, we derived a series of propositions that we developed into a market formation typology. We ran simulations over 30 continuous time periods. A single period may be interpreted as ranging from months to years, depending on the type of market. The duration has been chosen such that the dynamics settle into a pattern of growth, stability, or decline. We defined the collective market formation threshold as the ease of market formation, measured by the critical collective resources r * 0 necessary to overcome the threshold. The critical collective resources r * 0 is the ensemble average from 40 simulations with outcomes r * 0e with e=[1,40] 8. Each ensemble simulation involves different realizations of actors individual growth strategies and initial resources, through random draws from the two independent distributions with standard deviations σ ι and σ r. Thus, in each ensemble simulation, when actors are endowed on average (since the distribution is σ r ) with initial resources beyond the critical r * 0e, the market will form. Then, r * 0 = means that the market will always stabilize at a single equilibrium. In such a case, results are not dependent on the initial conditions for the particular parameter combination, and therefore no threshold exists. The other extreme, r * 0 =0, means that the market will always form and grows indefinitely (since, focusing on early-stage market formation, we omitted any market saturation effects). Finally, a finite * value of r 0 indicates the presence of a market formation threshold. The analysis focused on variation of market-level RtS (η), the degree of substitutability between actor contributions (ρ) and heterogeneity (σ r, σ i ) (Table 1). While each of the remaining parameters, interdependencyκ, unit value v i, and number of actors N, affects collective action thresholds, their dynamics have been extensively examined by collective action scholars (e.g., Marwell and Oliver, 1993) 8 The choice of 40 simulations resulted from experimentation. Outcomes are robust to greater numbers of simulations. 18

20 and are therefore not our focus. We fix these parameters on values that permit a representative environment and controlled experimentation. First, we set the normal unit value of market infrastructure v i =1, guaranteeing that a viable market exists exactly when all resources are equal to 1, irrespective of other parameter choices. We do this to ensure that market success results from market formation dynamics rather than from variation in the difficulty of a market to exist. Further, for reasons discussed before, we perform simulations at an intermediate level of interdependency, and set κ 0 =0.5. Finally, the number of actors should be large enough that the variance in growth strategies and initial resource endowments across actors is meaningful. We used N=8. Experiment 1: Substitutability of Resource Contributions and Heterogeneity The first set of findings relates to situations with perfectly substitutable contributions and reveals that heterogeneity (in both initial resource endowments and growth strategies) significantly reduces market formation thresholds. Market formation thresholds under complete uniformity rather than heterogeneity (σ r =σ i =0) can be analytically derived with intuitive results. 9 First, the existence of a threshold generally requires that value-related market-level RtS η are sufficiently large compared with cost-related RtS γ. This is intuitive, because in such situations, certainly when market infrastructure is sufficiently developed, ego s value from allocating more resources increases faster than her cost. Under complete uniformity, a market formation threshold exists strictly when η >γ. Situations of complete uniformity tend to exhibit a relatively high market formation threshold because they instill overcrowding which hinders the buildup of market infrastructure (Podolny, Stuart, and Hannan, 1996). When, more reasonably, some actors are endowed with above-normal resources (and others below), σ r >0 Ι, the market formation threshold is strongly reduced. Figure 2, Graph A, illustrates this effect, showing the critical average initial resources r * 0 necessary to overcome a market formation threshold (vertical axis) as a function of variation in growth strategies (σ i, horizontal axis), under perfectly 9 See Appendix II for derivations. 19

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