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Autonomy vs. Equivalence Within Market Network Sh lecture? Harrison White --Notes, November 2002 Results from three authorsBurt, PodoIny, and White- wil1 be melded, yielding surpns~ng answers to this htle question. PART I. SET: P Structural Holes proposes formulae for direct and ~nd;irect consonants, and back~ons~nts, upon dickering of ego with all alters in ego's observed network. With dodar volume of transaction as tie sirens, Ron Burt adapts these punapled formulae for log regression fining Gross Be 500 or so four- dig~t SIC markets In Be 1970s American economy. The constraints are ~,a~ered~nto an over measure of struck autonomy~aut and en~epreneunal success is measured by net income to ego market. His Figure 2.8 iDus~ates the worst, nightmare context for ego. Podoiny Peonies the conditions In which single producers fin a finance market) win seek status ~ this market of Weirs versus when instead they will dicker a la Burt around Weir alters' anxiety of being consigner! versus ego's uncertainty in choosing a right over. Figure P is his 2x2. Markets frown Networks predicts emergence of a ranked set of producers as a market to subdue their Knighuan uncertainty of sales downstream, when Heir cost schedules stack in the same order as buyers' valuations of their qualities. The producers must offer equally ;~,ood tradeoffs of their quality status versus He volume committed to, and then each can find a unique optimum niche along He observed schedule of producer revenue by volume across Hat market So ~ cannot apply Burt s fo~Tnulas for Straut, s~nce~fold~nto a cost schedule Al the charges for procurements Tom diverse markets upstream to the volume y delivered across all buyers Townsmen by a producer, in return for revenues, can Hem wordy). Whereas Burt aggregated He producers as a market, even though he can keep He flows Tom markets upstream separate Tom flows to markets downshwn. On He other hand ~ predict, ~ don't assume as given, the sizes of He Yes to ego once these are aggregated into total inflow and outflow to that producer. And ~ predict, not just observe, He profitability to each producer. Both my predictions draw simultaneously on measures from upstream, from downstream, and from the producer set in between, not just from buyer and seller as two "sides." In Structural Holes, Burt (his Chapter 6) applies an approximate, aggregate version of this White model. alongside his Straut measures, to the industry data and concludes that they fit 78 DYNAMIC SOCIAL NETWORK HODEL~G kD ANALYSIS

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together, partially. ~ offered a very crude version of Burt's entrepreneur (my Chapter 5), with the same conclusion. But the phenomenologies remain unreconciled: the joining is ad hoc. PodoIny provides the insight to meld them: That is the goal of this paper. PART II. COMBINING INSIGHTS PodoIny like Burt deals with just two sides and invokes complementary uncertainties of egos and alters. Crucial groundwork comes from the earlier Burt book (1983), where he still troubles to keep procurement ties and sales ties distinct instead of symmetrizing the ties as he does in Structural Holes. From his fittings there (Table 2.5) to the national data: ~ ~ ~ The contribution to Straut from market procurement ties with upstream is much less so that Podoiny's looking only at alters downstream is a reasonable fit. (~) The backlash, against ego Strait, from alters exploiting weak binding among the firms within ego market is as substantial as the exploiting of structural holes downstream by ego market. So this market is shown to be a distinct operative level of actor albeit untheorized, merely ad hoc insertion, in Burt. This justifies calling on Potloiny's framing, Figure P. Markets from Networks lays out varieties of market not as a 2x2 table but as a two- dimensional MAP: see the diagram, where the vertical axis parameter, call it v, scales valuation of volume y by downstream over against valuation of y by ego as cost from upstream for volume produced. The horizontal axis parameter, call it u. analogously is ratio of valuation downstream of distinctive quality of product versus cost upstream required for that level of quality. The market mechanism runs off a profile of worth W by volume y committed to as choice set by producers. Feedback from observations by producers and others is He fuel. The mechanism is sited win appropriately simple descnpnons of cost and anon schedules. Producers engage in a self-consistent search for optimal niche on a viable schedule. Predictions of robustness of He profile vain win location in MAP, as do the volumes and profitabilites predicted across arty Macular set of qualities for producers. (~) The outcome profile, being an equilibrating between competing variabilities each local, necessarily is path dependent, which fits weL with He Burt vision of dickenng a la Smut The paw index, k, is a single number, which may be plus or minus. DYNAMIC SOCIAL NT:TWORK MODELING AND ANALYSIS 79

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(2) Only for one median pad, indexed by k = 0, can closed formulae replace messy numerical al=~onthms, gliiding qualitative exploration. (3) in this special case k = 0, each producer has Me same Drofitabilitv Percentage (tholl~sh not ~ _x _ 1_~_~_ _1__ ~ r ~ ~ A rim -it- ~~ ~,,,^~,_ 1-CVt;~lU~J, wruen also manes ror easy comparison wad Burt's treatment only of aggregate markets. Four regions of MAP are demarcated by the line at v = 1 together with the diagonal for v = u. So just these two parameters, v and u, ten much about outcomes even without knowing the producers particular locations on quality, effected Trough different investments for facilities. Descnptors for Me genes. sort of market found in each region are entered in MAP. Now we can apply to Podolny for ~dance. Alter unce~ai'v~that is downstream uneasiness about their deal-making, is surely going to increase win the extent of their being more eager for given quality than producers are to supply it at that volume. Thus the diagonal should be the split line with alter uncertainty high on the lower diagonal region. So PodoIny would have (Hypothesis I) a rank based market form such as W(y) activated down and nght *om the diagonal. Ego uncertainty that is producers' concerns about how best to handle their lousiness Surely wid be exacerbated when v is greater Dean unity which means that downstream eagerness for volume is not conveniently kept in check by cost-based reluctance of producers. So Podoiny would have (Hypothesis 2) ad hoc Burt maneuvering take over markets in contexts in He region above the horizon Iine v = ~ . Presto, we replicate the topology of Poldoiny's insightful 2x2, but with changed interpretation of cells: see the second MAP. The Low-Low eel] PodoIny has as pure competition, say wheat markets without much structuring by either rank or maneuver. But the W(y) feedback rank mode] has it as the basic ordinary sort of production marketand yet exposed arson for path indexed b negative value of k. to dissolution into chaotic maneuver a la Burt. The lower right cell, High-Low, PodoIny argues is premier context for rank market, such as his house roofin ,. But White locates regional road haulage as prototype there and shows a contradiction between context, which indeed favors rank market, and feedback mechanism, which is prey to cheating by low-quaTity aspirants for producer slots and thus induces some Burt dickering. The upper left cell, Low-High, PodoIny has as premier context for Burt maneuver. The W(y) feedback mode! agrees, but with the proviso that for a limited class of paths, a rank market can establish itself, disciplining producers. These insights can refine results from Burt, too. Note the huge scatter of market outcomes versus Straut. 80 DYNAAlIC SOCIAL NETWORK MODELING AND ANALYSIS in Burt's graphs

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According to Burt's results, constraint on alters is heavily increased by perceived extent of joint action by the producer set that they confront Burt uses the conventional Four Leading Firms' share of market as measure. And Markets from Networks derives how such concentration (using the more general Gini index) will vary with location in MAP. It is opposite in the bottom half front the top half!: the sort of result one can expect from non-linear feedback. More basic still, Burt has the profitability of ego and its four-firm concentration going up together. Whereas the W(y) mode] says they vary oppositely, though with opposite polarity for v>] and vat. suggest that if markets that do go primarily with W(y) are separated from those that are '~catch as catch can" entrepreneurial, the scatter in Burt's results will lessen because these opposite predictions are segregated out of overall results. PART III. A THIRD DIMENSION However, the deepest results concern the remaining cell: The High-High upper right box maps into the upper right triangle labeled CROWDED: This is in W(y) terms a viable stable market, and yet also a super- market in outcomes. rather than the unstable market intuited by Podoiny with High- Risk Debt as example. PodoIny's two hypotheses clash for this cell, whereas the W(y) feedback mode! shows that the two tendencies can reinforce but only in terms of a further, third dimension to MAP not mentioned earlier. This third dimension both explicates the CROWDED triangle of MAP and thus the High-High cell for Podolny. And at the same time it rescues a contribution of Burt's from his own discard pile. The third dimension, labeled x, measures aggregate impacts on valuations by buyers downstream of the ego market from their awareness of other markets Tying cross-stream. Both the markets upstream from a given market and the markets downstream are reflected in the MAP dimensions u and v. There are, besides, maybe hundreds of markets with no discernible influence, direct or indirect, on the given one. But there usually are a number of others which are to some extent structurally equivalent to the given one: that is have a somewhat similar pattern of what producers and/or markets they buy from and sell to call them "cross-stream." Cross-stream markets are a weakened form of the structural equivalence exhibited by the set of producer firms being ranked by quality within the given market. So it makes sense to call x a measure of generalized substitutability. DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS 81

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Now comes my claim: This x substitutability has impact upon W(y) market size analogous to the impact of secondary structural holes upon Straut in Burt's theory of markets. Burt is ingenious and persistent in formulating this leveraging upon dickering through - intermediary ties: see Figure 2.S and associated formulae. Yet Burt largely discards such impacts on several grounds: It is hard to trace networks completely enough to permit measurement, except for government generated censuses of ties: in the chapters where Burt treats individual mana;,ers rather than markets of firms, Burt could not come up win arty of the needed data. It is not clear conceptually how to model impact of secondary structural holes upon his dependent variable of profitability. So prediction from W(y) of the impact of substitutability x upon market size can suggest how much Burt is missing by discarding secondary holes. After all, the really extraordinary outcome is that W(y) markets can ever be stable in the High- High cell, the CROWDED triangle In MAP. The prediction is Hat markets In this region are stabilized only through an appreciable degree of substitutability x induced by cross-stream markets. In other words, my challenge to PodoInys' characterization of High-High context comes only through effects of cross-stream markets, analogous to Burt's second-order structural holes. Once again this shows how a feedback model can deepen and enrich insights. Substitutability is being included in only a crude and approximate way, as seen by use of just one parameter as sufficient descriptor. The benefit is that explicit prediction formulae can be denved. This is a complex and multi-stage procedure, which is I~d out finely in my ISERP Working Paper 02-02, available on He Web from the Columbia site. There are two final surprising predictions. (~) For most of the context bald out as pod n the parameter space MAP, as the substitutability x from cross-stream markets grows, the aggregate size of the W(y) market (assuming it Is reachable by a viable paw and so can exist) actually increases!! But the quanhtaUve impact generally is slight, which is conformable with Burt's discard. (2) There is however an exception for much of the High-High cell, Hat is, for CROWDED markets. Figure ~ from my Working Paper 02-92 shows the two possible curves for aggregate 82 DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS

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market size (sum of revenues across producers) versus substitutability x. The upper, exceptional cube applies within MAP in and only in a central cone within High-High, CROWDED region. In this cone the aggregate market size decreases as substitutability increases, just as one might intuit from He siphoning away by He cross-stream markets. But surprise #] above shows that the intuition is not generally reliable for such complex feedback situations. Putting all this together, the larger surprise is that the most distinctive, profitable and possibly common market especially, as it turns out, for new product markets is sustainable only through the hidden support of cross-stream markets, Burt's second order holes. That is, the CROWDED markets (analyzed at length in Chapters 6 and 7 of White, 1992) exist by sufferance, predictable sufferance, of second order maneuvering. There is much else to explicate. Besides k, there is another historical descriptor (tau) built into the W(y) model, and each should impact on predictions about dickering versus market profile discipline, plus there are other extensions and generalization, including possible to Small World analyses. There are hosts of other directions to explore in Burt's writings and in a cascade of articles by Podoiny and co-workers. And each of us point to still other authors contributing to the emerging network based sociology of markets and firms. References Burt, Ronald S. ~ 992. Structural Holes: The Social Structure of Competition. Cambridge: Harvard University Press. PodoIny, Joe! M. 2001. "Networks as the Pipes and Prisms of the Markets." America Journal of Sociology. White, Harrison C. 2002. Markers from Networks. Princeton: Princeton University Press. D YNAMIC SOCIAL NETWORK MODELING kD ANAL YSIS 83

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84 - - .N are' 1. ~ J (< - - - - - - - Conditions Limiting i~s En trepren eun al Negotiation in the Relationship with j Figure 2.S The entrepreneur's nightmare DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS (1)P ij is high (2)Pjq arc high (3)()jishigh (4)0j is low

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HIGH Ego uncertainty LOW e.g.l vaccine e.g.' high-yield product) on I debt e.g., wheat e.g./ house roofing LOW Figure P. HIGH Alter uncertainty Podoiny 2x2 table DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS 85

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sensitivity to quality, upstream/down v 86 TRUST ORDINARY CROWDED UNRAVELING sensitivity to quality, upstream/down MAP with varieties of markets DYNAMIC SOCIAL fJETWORKHODE~WG ED ISIS

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v ego high ; / alter uncertainty blah MAP with Podolny gradients in uncertainty DYNAMIC SOCIAL NETWORK MODL:~G~D CYSTS 87

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w alpha/tau 1 _ 1; ~ ~1 1 V' 1 ~ if. Vc V curare for V; siphoning - - curve for V' _ Figure 8. Graphs of market revenue W versus substitutability, x, given critical size vc' for two fixed value of v. The curve for W shows backward siphoning. 88 X DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS