Strategc Management Journal Strat. Mgmt. J., 38: 17 41 (2017) Publshed onlne EarlyVew n Wley Onlne Lbrary (wleyonlnelbrary.com).2592 Receved 30 Aprl 2014; Fnal revson receved 27 February 2016 VALUE CAPTURE THEORY: A STRATEGIC MANAGEMENT REVIEW JOSHUA GANS and MICHAEL D. RYALL* Rotman School of Management, Unversty of Toronto, Toronto, Ontaro, Canada Research summary: Ths artcle provdes the frst revew of a growng lne of scholarly work n strategy that we refer to as value capture theory. The common thread n ths work s ts use of cooperatve game theory as a general, mathematcal foundaton upon whch to buld a deep understandng of frm performance n market settngs. Our revew: (1) descrbes the prmary elements of the theory; (2) hghlghts mportant blndspots that t resolves wth respect to exstng theoretcal approaches; (3) calls attenton to several of ts novel nsghts; and (4) summarzes a myrad of applcatons and emprcal studes that have appeared n recent years usng value capture theory. Manageral summary: Tradtonally, theoretcal clams n strategc management have been supported by nformal, qualtatve reasonng. Recently, however, a new lne of theoretcal work based upon mathematcal methods, known as value capture theory, has been ganng n popularty. Ths artcle revews the recent advances n ths lne wth a partcular emphass upon a number of ts mportant nsghts, several of whch challenge longstandng propostons from the tradtonal lne. For managers, the formal nature of value capture theory s well-algned wth data-drven analyses of strategc stuatons. Copyrght 2016 John Wley & Sons, Ltd. INTRODUCTION Understandng persstent heterogenety n frm performance s, perhaps, the central objectve n the feld of strategy. 1 The semnal contrbuton of Brandenburger and Stuart (1996) ntated a unque stream of work desgned to deepen our understandng of ths phenomenon through the Keywords: value creaton; value capture; competton; cooperatve game theory *Correspondence to: Mchael D. Ryall, 105 St. George St., Toronto, ON M5S 3E6, Canada. E-mal: mke.ryall@ rotman.utoronto.ca 1 As evdence for ths asserton, we note that an adequate revew of the exstng emprcal lterature on ths topc would requre a separate artcle of ts own. For example, a partal lst of relevant emprcal analyses on the extent to whch above-average profts persst ncludes: Cubbn and Gerosk (1987), Dos, Lechevaler, and Secch (2010), Jacobsen (1988), Knott (2003), McGahan and Porter (2003), Mueller (1977, 1986), Roberts (2001), Rumelt (1991), Warng (1996), Wggns and Ruefl (2002), and Madsen and Walker (2015). development of a mathematcal theory of value creaton and capture under competton. Snce then, ths lterature has quetly and steadly grown to the pont where t now represents a substantal body of work. Due to ts mathematcal nature, the collecton of fndngs buld upon each other, thereby creatng a coherent, nterlockng set of theoretcal clams. These clams reveal subtletes of competton that were not prevously apparent, pushng strategy scholars to rethnk some fundamental deas about value capture under competton. What s more, recent advances n emprcal methods have opened the door to emprcal nvestgaton of these clams. Fnally, t s mportant to note that the theory of nterest s entrely publshed n strategc management journals. Ths has not been an exercse of locatng techncal results outsde the feld and mportng them nto strategy va renterpretaton and analogy. Rather, ths work contans novel propostons of ts own, wth Copyrght 2016 John Wley & Sons, Ltd.
18 J. Gans and M. D. Ryall mplcatons extendng well beyond the boundares of strategy. Thus, we presently fnd ourselves n a stuaton n whch a stream of lterature has developed to the pont that a general, scholarly audence s lkely to fnd the nsghts t offers of substantal nterest, yet t s early enough n the process that these nsghts are not broadly dssemnated. In other words, the tme seems just rght for a revew of ths stream amed at a general audence. The purpose of ths artcle s to provde such a revew. Our specfc goals nclude dentfyng the major ssues ths research s ntended to address, explanng the mathematcal framework upon whch t s bult, hghlghtng the central theoretcal nsghts thus far obtaned, descrbng notable applcatons (both theoretcal and emprcal), and concludng wth some thoughts about open ssues and future drectons. The scope of our revew ncludes papers (1) publshed n management journals that (2) present novel mathematcal propostons usng cooperatve game theory. By adoptng ths unfyng theme, the scope of our artcle s manageable, permts a coherent dscusson, and allows us to treat key deas wth a reasonable degree of depth. Moreover, by restrctng attenton to management publcatons, we provde a sense of the novelty and substance of the stream wthn our own feld. 2 Our ntended audence ncludes those lookng for an overvew of the central concepts and latest results assocated wth ths lne of work as well as those consderng enterng and contrbutng to t. Therefore, ths artcle s constructed to be self-contaned wthn the content constrant of a sngle journal artcle the formalsm, relevant assumptons, assocated nterpretatons, and mportant results to date are all covered, albet concsely, wth ctatons to more n-depth sources for those nterested n pursung them. Ths beng a lterature revew, t s also worth pontng out that the ssues elaborated below were the product of a dscovery process: theorsts bult models that seemed sensble; based on these models, formal propostons were proven; mathematcal clams led to nsghts about value capture under competton n the real world; these nsghts led to a grasp of the knds of ssues that the domnant 2 Unfortunately, ths scope does mply, on the one hand, passng over a number of thought-provokng, qualtatve papers n strategy that adopt deas from cooperatve game theory and, on the other hand, gnorng potentally nterestng papers publshed n other felds (most notably, economcs). Stuart (2001) provdes an early precursor to ths artcle. paradgms mssed. Ths artcle proceeds n reverse order: we summarze the (now) apparent ssues; then, we present the formalsm and trace the lne of results derved from t; ths should spark nsghts n the reader regardng value capture under competton; whch, cumulatvely, should lead to a deeper understandng not only of ths lne of work but also to new questons for future nqury. A MOTIVATING EXAMPLE To provde context for our survey, t s useful to begn not wth the lterature but wth an example that motvates value capture theory and the contrbutons t can make. The example s ntended to be llustratve rather than the model of a specfc strategc stuaton. Status quo confguraton Any formal model of an ndustry usually starts wth a benchmark or what we wll call a status quo confguraton upon whch changes can be compared. For our example, suppose there s an ndustry that conssts of value networks composed of some fnte numbers of agents. By value network we mean a collecton of agents connected to one another va chans of transactons that, taken together, ultmately result n the producton of economc value. The network ncludes all agents nvolved n the producton of value, from the most upstream resource provders all the way down through the fnal consumer. An example of a value network would be the agents engaged n the Apple moble computng ecosystem, ncludng those who provde platform elements, moble carrers who provde access to communcatons and the Internet, app developers, the content provders and the consumers and end-users themselves. The Apple value network competes wth others bult around Samsung, Google, etc. Suppose there are exactly two such networks, A and B. Further, assume that addng up the utlty enjoyed by end-users and subtractng all of the economc costs assocated wth creatng and delverng the products to those end-users (ncludng costs relatng to the transactons themselves) Network A creates economc value of $200 mllon and Network B creates economc value of $180 mllon. Ths s the stuaton depcted n the frst panel of Fgure 1 (Confguraton #1).
Survey of Value Capture Theory 19 Value Network A $200 Value Network A $150 Value Network A $150 Value Network B $180 Value Network B $180 Value Network B $210 F forms a trval value network $0 Fgure 1. Three ndustry confguratons Assume ths confguraton s actually the one observed operatng n the world and, hence, refer to t as the Status Quo. In aggregate, the ndustry produces $380 mllon n economc value. Fnally, suppose our nterest s n understandng the performance of a focal frm F, whch s presently operatng n Network A. For nstance, to contnue our moble example, F may be Adobe, whch provdes specalzed Flash software. Although ths setup s smple n the sense that t contans only two value networks, t s worth pontng out a number of smplfyng assumptons that were not mposed. We dd not lmt the number of agents (beyond beng fnte), exclude transactons costs, restrct consderaton to two-sded markets, exclude buyers, represent buyers as a lnear demand curve, mpose specal functonal forms on producton functons, exclude postve externaltes, and so on. Ths level of generalty s a feature of the mathematcal approach we descrbe n more detal below. Compettve upper bound In the second panel of Fgure 1 (Confguraton #2), we ndcate the chans of transactons that would arse were all agents n the market to forgo transactons wth F; for nstance, decdng not to support Adobe s software. In our example, the value produced by Network A drops to $150 mllon, whle Network B contnues to create $180 mllon n value. Of course, F can create no value on ts own. In ths case, the aggregate value produced n the ndustry would drop from $180 to $330 mllon, a decrease of $50 mllon. Ths dfference the ncremental value produced as a result of F s presence n the market s called ts added value (to the market as a whole), symbolcally, av F = 50. It s easy to see that, n a noncoercve market settng, whatever amount of the $380 mllon F ultmately captures, t cannot be more than $50 mllon. Why? Because were F to nsst upon a share greater than ths, the other agents n the market could mplement
20 J. Gans and M. D. Ryall Confguraton #2, whch would yeld them more value than producng $380 mllon and gvng F more than $50 mllon. By now, the noton of added-value and ts role as a lmter of value capture s well known wthn strategy (see, Brandenburger and Nalebuff, 1996; Gans, 2005). Even so, there are a few ponts worth hghlghtng. Frst, as shown n the fgure, Confguraton #2 contemplates a dfferent collecton of transactons to those at work n Confguraton #1. Computng added value goes beyond the smple removal of transactons wth a gven agent, to nclude a complete assessment of the new collecton of transactons that would actually arse n ther place. Second, t llustrates a general feature of added value. An agent s added value can be computed wth respect to any group (the quantty of value produced when the group ncludes that agent less the quantty produced wthout t. When the added value beng computed s wth respect to a status quo value network that ncludes the agent, that added value represents an upper bound on ts ablty to capture value. As we see from the fgure, F s added values to Network A and to the market as a whole concde at $50. 3 Fnally, added value provdes an mportant nsght nto the nature of competton. Competton n markets means vyng for transacton partners. To engage n the transactons that produce $380 mllon, other transactons must be forgone. In partcular, n order to ensure that the transactons depcted n Confguraton #1 actually arse, F must offer enough value to all of the agents wth whom t transacts to persuade them not to engage n the transactons depcted n Confguraton #2. The latter transactons provde F s transacton partners wth a valuable alternatve to dealng wth F an alternatve aganst whch F must, n effect, compete. Compettve lower bound Now consder the thrd panel of Fgure 1, Confguraton #3. Here, F deals wth Network B, wth a resultant ncrease n the value t produces from $180 to $210 mllon. Thus, F s added value wth respect to Network B s $30 mllon. Note the mplcaton: the agents n Network B are wllng to gve F a share of up to $30 mllon (at whch pont they are ndfferent to F s ncluson) n order to effect the transactons depcted n Confguraton #3. Ths llustrates an often-overlooked aspect of competton: F s transacton partners must offer t enough value to ensure that F remans n Network A rather than abandonng them to transact wth Network B. How much must they offer F to reman? At least $30 mllon. It s mportant to observe that the focus here s entrely on the quantty of economc value a partcular agent captures n return for the part t plays n the aggregate creaton of value wthn the ndustry. Thus, there s no dscusson of prces or margns or even a descrpton of the products that generate revenue or nduce costs. Specfyng prces, quanttes, and costs s not the goal of ths sort of analyss. 4 Rather, ths method places the productve powers of agents, the competton between them to transact wth one another, and the mplcatons for value capture front-and-center. Notce that competton operates symmetrcally. To nduce the other agents n Network A to forgo alternatve deals n favor of transactng wth t, F must offer them a suffcent share of the value created by ther jont economc actvtes. However, those very same transacton partners must, smultaneously, offer F a suffcent quantty of value to ensure that t does not act upon the alternatve transactons that t has avalable. Here we see a flp sde to added value: when the added value beng computed s wth respect to a status quo value network that does not nclude the agent, that added value represents a lower bound on the value the agent must capture. Thus, competton need not hurt an agent t may play out n ts favor. Value capture theory sorts out both sdes of competton. Thus, wthout mposng too many restrctons (and computng only four numbers), we expect that the quantty of value captured by F wll be between $30 and $50 mllon. The former s a floor mposed by competton for F, and the latter s a celng mposed by competton for F s transacton partners. The analytc work n the lterature we revew follows ths thrust. In general, there are many confguratons to consder, many ways to add nterestng structure, and many nsghts avalable by so dong. Let us consder some now. 3 The two need not be equal, though an agent s added value to the market as a whole s never greater than ts added value to a dstnct value network. 4 A feature of cooperatve game theory s consstent wth the call by Wernerfelt (1984) and noted by Lppman and Rumelt (2003).
Survey of Value Capture Theory 21 SOME BLIND SPOTS IN PREVAILING THEORY The modern era of strategy scholarshp dates to the famous collecton of papers appearng n the 1980s, all of whch offer explanatons for the phenomenon of persstent performance heterogenety among frms. These nclude Porter (1979, 1980), whch ntated the ndustry postonng stream (IP); Wernerfelt (1984), the paper that sparked the resource-based vew lne of work (RBV); and Wllamson (1981), an early paper advocatng hs transactons cost approach to organzatonal analyss (TCE). 5 In the years followng, strategy scholars expanded these orgnal deas n a number of frutful drectons, thereby formng a commonly accepted collecton of explanatons for persstent dfferences n frm performance. Our goal n ths secton s to dentfy several substantve oversghts, or blnd spots, shared by these manstream explanatons. Blnd spots are elmnated by turnng attenton toward them. By so dong, we see the ssues surroundng our extant body of theory more completely whch, n turn, opens the door to greater generalzaton and unfcaton. Of more mmedate relevance for our purposes s that the blnd spots dscussed below were revealed by the methods revewed by ths artcle. Thus, our presentaton reverses the hstorcal process of analyss-reflecton-nsght by whch these blnd spots were revealed. Instead, we begn wth the blnd spots, explaned n plan language. Our hope s that, upon reflecton, these explanatons wll trgger nsghts nto both the exstence and potental mportance of the dentfed oversghts. Then, once we do elaborate the techncal detals of the method, our further hope s that these nsghts wll carry over, allowng readers to grasp how the mathematcs of value capture reveal the dentfed blnd spots n an explct fashon. Before proceedng, we warn that any generalzaton of large, complex streams of scholarly work wll, by ts nature, blur ther fner and more subtle ponts. Our ntent s not to gloss over these subtletes. Rather, we wsh to provde a persuasve llustraton of the way n whch dfferent approaches (n 5 The rapd coalescence of these deas nto a separate feld, busness strategy, was surely facltated by the dsnterest toward ths phenomenon apparent n economcs at that tme. Economcs has snce come around; see, e.g., Syverson (2011) and Bloom et al. (2013). ths case, mathematcal) can expand our explanatory horzons. Many scholars have weghed n on both sdes of the argument regardng the effcacy of mathematcal theory n management research. Agan, our purpose here s not to engage those arguments. Rather, we smply pont out that, for better or worse (dependng upon one s phlosophcal sensbltes), a unque feature dstngushng the value capture stream from others n strategy s that ts clams are formulated usng a sngle, overarchng mathematcal framework. The result s a collecton of rgorously derved fndngs that buld upon one another to create a coherent whole, one wth the potental to unfy and refne prevalng theory. 6 The free-entry blnd spot Because strategy s about the performance of frms n free markets, competton s always a central concern. In proposng ther explanatons for frm performance heterogenety, tradtonal theores share the premse (often mplct) that wherever postve profts are to be found, compettors are attracted lke a swarm of locusts to a luscous crop of wheat. Thus, competton s typcally conceved of as an ever-present, corrosve force drected toward those enjoyng postve economc profts. 7 The entrants-as-a-swarm-of-locusts concepton s one nherted from neoclasscal economcs. As Makowsk and Ostroy (2001) explan (p. 484): Neoclasscal economsts borrowed from ther classcal predecessors the vew that, n a producton economy, perfect competton s the smple, nescapable concluson of free entry. And wth free entry comes zero profts. Ths noton of how competton works contnues to run deep, both n strategy and beyond. 8 The founders of modern strategy were nterested n explanng what seemed obvous by casual emprcsm that persstent performance dfferences wthn ndustres was more the rule than the excepton. Indeed, strategy presently sports a remarkable body of emprcal work drectly at odds wth the clam that competton nexorably drves 6 In ths sense, the work surveyed here answers the challenge posed by Oxley et al. (2010). 7 See, for example, the comments by Porter (1980: 5 and elsewhere). 8 See, e.g., any strategy textbook for frst-year MBAs or, n economcs, hstorc work such as Schumpeter (1934) to more modern peces lke Hopenhayn (1992).
22 J. Gans and M. D. Ryall ndustry profts to zero. 9 However, to supervene ths clam, one must fnd a way to escape the neoclasscal logc. One reasonable escape path s to propose a class of barrers thought to nterrupt the progresson nduced by free entry toward zero profts. Ths s precsely the approach adopted by each of the major schools: IP proposes barrers to ndustry moblty, the RBV proposes barrers to resource moblty, and TCE proposes barrers to perfect nformaton. It s mportant to note that, even though t avods the essental concluson of the standard neoclasscal model, ths barrer vew retans ts essental premse that entry s an ever-present threat whenever postve profts are present. 10 The challenge we now pose s: Why not dscard the neoclasscal premse altogether? Suppose the world s stock of economcally productve resources (raw materals, captal, human bengs, tme, etc.) s fnte. Of all the assumptons one mght entertan, the fntude of resources strkes us as supremely reasonable an mmedate, unversal feature of our shared economc experence. Yet, ths axomatc premse has serous mplcatons. In such a world, logc does not dctate that the moment some resource becomes a source postve value capture for ts owner, other agents wll reallocate ther own resources aganst t n a tsunam of competton. Rather, economc logc mples that agents allocate away from less proftable to more proftable settngs, and resource fntude mples that such settngs need not be exhausted n a fnte world, economc proft may well be the rule rather than the excepton. The mportance of ths pont cannot be overemphaszed n the context of strategy: global resource fntude mples that specal barrers to competton are nether necessary nor suffcent for the exstence of persstent economc proft. To be sure, there may be settngs n whch such barrers are a proxmate cause of proft persstence. 11 That sad, a body of theory focused only upon ths aspect of competton must, n tself, be ncomplete. Ths carres wth t the 9 To cte several compellng nstances: Cubbn and Gerosk (1987), Dos (2007), Jacobsen (1988), Knott (2003), Madsen and Leblen (2015), McGahan and Porter (1999), Mueller (1977, 1986), Roberts (2001), and Vllalonga (2004). 10 Gans, MacDonald, and Ryall (2008) elaborate on ths dea. As an anonymous revewer ponted out, the free-entry, swarm of locusts dea appears most promnently and explctly n RBV scholarshp. 11 By specal we mean explct barrers to the allocaton or reallocaton of economc resources. emprcal mplcaton that varaton n the strength of specal barrers s unlkely to be a robust predctor of varaton n frm performance. As we show below, the fnte agent/resource assumpton s explctly embedded n the value capture model, even when scalng up to global-economy-level scope. The compettve-determnsm blnd spot Theorsts have an averson to models prone to ambguous conclusons. For example, the two market models wth whch most strategy scholars are famlar are Cournot and Bertrand, the workhorse tools of ndustral organzaton economcs. No small part of the popularty of these models arses from ther tractablty, n partcular, ther ablty to provde exact, pont-estmate solutons for profts once ther parameters are fxed. In what follows, we show that the value capture model suggests that competton s properly construed as placng bounds on the amount of value an agent may capture wthout fully determnng t. Takng the premses of the model serously, ths s a feature not a bug (n the parlance of our tme). It says that, n general, competton defnes a precse nterval wthn whch an agent s value capture les; where wthn that nterval actual capture lands s due to factors other than competton. 12 As we dscuss n greater detal below, the theory ponts toward a new concepton of compettve ntensty, as well as the exstence and possble mportance of persuasve resources, the express purpose of whch s the capture of more value wthn the range permtted by competton. 13 The product-prce blnd spot Harkenng back to modern strategy s foundng corpus, Wernerfelt (1984) argues that, n order 12 On the ssue of generalty, t s worth remndng readers of Kreps and Schenkman (1983), who llustrate the sense n whch the Cournot results are consstent wth a Bertrand game wth capacty commtments. Smlarly, Stuart (2005) shows that Cournot can also be thought of as a specal case of a cooperatve game wth capacty precommtments. In other words, both Cournot and Bertrand can be thought of as specal cases of a cooperatve game. A related lne of research s pursued n Byford (2010). 13 Here, t s useful to note that emprcal research n strategy ndcates that the frm effect s sgnfcant n explanng performance heterogenety (see Dos, 2007, for a revew). The possble mportance of a persuasve category of resources opens up a new area of exploraton for emprcal scholars nterested n explanng these effects (e.g., n the sprt of Roberts and Dowlng, 2002; Vllalonga, 2004).
Survey of Value Capture Theory 23 Fgure 2. A balanced, but tangled, vew of the one force of competton to develop a deeper understandng of persstent performance heterogenety, analyss must shft from the pervasve prce-product orentaton of ndustral organzaton economcs to a more strategy-useful agent-proft perspectve. The massve, resourcebased vew lterature, whch arose from ths observaton, extends the ssue by postng that persstent performance heterogenety s due to the exstence of unprced resources (a result of market falure ). The blnd spot here s not n argung that the product-prce unt of analyss s problematc but, nstead, n not takng the agent-appropraton perspectve suffcently serously. When the agent s the unt of analyss, the quantty of value t captures s, n essence, a prce. It s the prce of engagng that agent ncludng ts resources and capabltes, themselves prced or not n the actvtes requred to produce value. Market falure at one level does not mply falure at the other. The value capture model shfts away from products and prces toward agents, the myrad value creaton opportuntes avalable to them, the value actually produced, and what t takes n terms of value capture to engage them n the assocated productve actvtes. The web-of-transactons blnd spot The central nsght of Porter (1979, 1980) s that understandng competton requres a broad vew of who counts as a compettor. In hs famous Fve Forces model, Porter (1979) argues that the set of actve market partcpants those agents whose decsons are amed at appropratng a share of the value produced wthn an ndustry must nclude buyers, supplers, rvals, even potental rvals and the producers of substtute goods outsde the ndustry. Extendng ths nsght to ts logcal concluson, Porter s (1979) model tself s ncomplete: a frm s appropraton ultmately depends upon the Fve Forces groups, as well as supplers of supplers, substtute buyers n other markets, potental entrants nto dstrbuton channels, and so on and so on. One gets a sense of the larger pcture from Fgure 2, though ths too falls short. In any gven ndustry, value s created and approprated through complex webs of transactons pursued by multple layers of actve, ntellgent agents. Returnng attenton to market models lke Cournot and Bertrand, the problem s that the only actve agents (.e., the only agents whose decsons are taken nto account)
24 J. Gans and M. D. Ryall are typcally the frm and ts drect rvals. They too are ncomplete, often makng mplct, ad hoc assumptons that leave prce-settng power n the hands of the frms, wth all other market partcpants playng a passve role. THE BIFORM MODEL The bform model of Brandenburger and Stuart (2007) s presently the state-of-the-art model for analytcal work n strategy on value capture under competton. The bform model s so-called because t syntheszes two dstnct areas of game theory noncooperatve (NGT) and cooperatve (CGT) nto a sngle model. The great strength of NGT s ts ablty to capture strategc behavor;.e., stuatons n whch agent actons nteract n the generaton of outcomes and, therefore, n whch assessng the behavor of others s mportant. The power of CGT s n ts ablty to analyze value creaton and capture n markets, especally n settngs where agents dealngs do not follow some predefned process. In a bform model, each type of theory plays a role consstent wth ts strengths, thereby creatng a complementary whole. Bform models consst of two stages. The frst stage, NGT, ncludes all the agents whose actons have a sgnfcant mpact upon the outcomes for a focal frm. In an ndustry, ths typcally ncludes drect rvals as well as, e.g., the agents n the other categores of Porter s Fve Forces framework (buyers, supplers, etc.). In the NGT stage, agents take actons desgned to prepare the compettve battlefeld to ther advantage that s, to structure ther compettve envronments n a way that permts them to capture the most value possble. Such actons nclude ntatves lke marketng projects, capacty decsons, new product or technology ntroductons, mergers, recrutng polces, market entry, and so on. The jont actons taken by the agents n the frst stage nduce a partcular market envronment n the second stage, CGT. Here, agents engage n organzng and executng the free-form deals that result n the producton and capture of value. Essentally, the value captured n second-stage competton serves as the the payoff to the strategc acton taken n the frst. We begn by elaboratng the second (cooperatve game) stage. COOPERATIVE GAME STAGE A cooperatve game conssts of a par (N, v) where N {1,, n} ndexes the n < agents partcpatng n the market, and v, referred to as the characterstc functon, s a map from each subset of agents to the quantty of economc value producble by the agents wthn t. The scope of ths setup s broad: t can be used for small nteractons (e.g., n equal two to a few, such as frms competng for an acquston or contemplatng a strategc allance for technology development), all the way up to those nvolvng large numbers of agents (e.g., the global economy). Gven a group of agents G N, v(g) denotes the amount of value the agents n G can create on ther own (.e., when the members of G lmt ther transactons to one another only). Thus, the startng pont for the CGT stage s an elaboraton of how much value each of the varous groups of agents could create n ths way were they to decde to do so. Out of all the possbltes so elaborated, some deals do occur, some value s produced, and some share of t (possbly zero) s captured by each of the agents n N. Adstrbuton of value, denoted π (π 1,, π n ), s a lst ndcatng how much each agent captures n return for ts productve actvtes (.e., agent captures π ). Agan, the central dea behnd ths setup s to show how the feasble productve opportuntes n a market shape a frm s ablty to capture value. Ths requres some lnkage between v, whch descrbes the former, and π, whch descrbes the latter. The frst step s to determne how much aggregate value s actually produced wthn the market. The answer s straghtforward: v(n) s, by defnton, the aggregate value generated by the agents n N. In strategy applcatons, v(n) represents the actual, aggregate quantty of economc value that wll be created (n the case of a theoretcal predcton) or was created (n the case of an emprcal analyss). It s a key observable assocated wth the model. The strategy lterature commonly uses the specal label V v(n) to emphasze ths dstncton. The majorty of of the v(g)s for groups other than N never actually materalze. These unrealzed possbltes are consttutve of competton and, as such, shape the dstrbuton of value. 14 14 When the value created wthn a market arses as the aggregate of productve actvtes by dstnct groups, then the economc value created by each of those partcular groups s, n fact, realzed.
Survey of Value Capture Theory 25 Note that V and the v(g)s are real numbers. The usual nterpretaton s that v(g) s the economc value created by the transactons that would actually arse were transactons restrcted to the agents n G. However, dependng upon the applcaton, they can also represent cash, expected value, net present value, etc. Frequently, authors assume that v s superaddtve: the unon of two dsjont groups produces at least as much as the sum of what the groups produce ndependently. The ratonale for ths s that the transactons assocated wth the ndependent group values are stll feasble even though new, cross-group transactons may arse under the unon of the two groups. 15 How do the value creaton opportuntes shape value capture? Typcally, two assumptons are made. The frst s a feasblty assumpton: π = V, (1) N.e., the amount of value captured equals the amount produced. The second s a compettve consstency assumpton: for every group G N, π v (G), (2) G.e., the aggregate value captured by the agents n G must be at least as large as the value they could produce on ther own. Suppose, n return for ther contrbutons to the producton of V, the agents n G face deals such that G π < v (G). Then, the agents n G could eschew those deals and, nstead, undertake to produce v(g) under terms that would make each and every one of them strctly better off. 16 In the strategy lterature, a dstrbuton of value that meets the feasblty and consstency condtons s sad to be compettve. The set of all such dstrbutons s referred to as the core. 17 15 In most strategy applcatons, ths assumpton s nnocuous although t does rule out cases n whch some subset of agents creates negatve externaltes wth others (and, addtonally, n whch economc actvtes cannot be organzed n such a way as to neutralze them). 16 Some authors refer to ths as the stablty condton; the dea beng that aggregate producton of V s assured only f ths condton s, by necessty, met. 17 Ths term s mported from economcs, whch, lke most economcs termnology assocated wth CGT, s not especally helpful or clarfyng. There are many other approaches to analyzng the solutons to cooperatve games n strategy settngs. For example, de Fontenay and Gans (2008) use the Shapley value, whch has the In what sense are dstrbutons that meet Equatons (1) and (2) compettve? The answer les n thnkng of V as the aggregate value arsng from a specfc set of actual transactons. Thnk of these transactons, the value they create, and the shares of value captured by the agents nvolved as observables (.e., as data or potental data). The v(g)s, then, are the feasble values produceable through alternatve transactons and groupngs. In ths context, v(g) should reflect the actual economc value that would be produced va some other specfc set of transactons, ncludng any costs assocated wth organzng them (e.g., swtchng costs). Then, the alternatve transactons compete wth those antcpated n the producton of V.Or,as vewed from the agent perspectve, the members of G provde competton for one another and aganst ther respectve transacton partners n the creaton of V. To nterpret compettve dstrbutons n a strategy context, brng Fgure 2 to mnd. The frm engages n specfc transactons wth a specfc network of supplers and buyers resultng n the creaton of actual economc value. At the same tme, rvals, potental entrants, and producers of substtute products offer the frm s customers and supplers productve alternatves. These agents compete aganst the frm and for ts partners. Smultaneously, rvals, potental entrants, and substtutes operate at every level of the value chan, thereby provdng competton for the frm and aganst ts partners. The characterstc functon v provdes a summary of all these compettve alternatves. Ths leads to the followng nsght. Insght 1 There s only one force of competton, not fve or some other number. Competton s mpled by a tenson between havng to neutralze all the competng alternatves n Equaton (2) usng the lmted value produced n Equaton (1). These condtons mpose value capture consequences on every agent n the market. That s, whle ts value capture mplcatons may vary from agent to agent, the set of compettve consstency condtons from whch those mplcatons arse s the same for every agent. All agents face a tenson between Equatons (2) and feature of provdng pont-estmates n place of core ntervals. As we explan below, however, the dentfcaton of ntervals s a useful feature wth respect to understandng one s strategc stuaton.
26 J. Gans and M. D. Ryall (1). From the frm s pont of vew, the effects of ths tenson run n two drectons: one n ts favor (provdng t more optons), the other aganst t (provdng others more optons). Thus, the CGT conceptualzaton treats competton as a sngle force, wth symmetrc structure and two effects, one good and one bad, on each agent. Insght 2 Competton bounds an agent s value capture possbltes. Mathematcally, Equatons (1) and (2) mply an nterval of value capture possbltes for an agent. That s, for every agent, competton determnes an nterval, wth bounds π mn π max, such that π s part of a compettve dstrbuton of value f and only f t s contaned n [ ] π mn, π max. Ths s contrary to the pont-estmate ntuton nherted from famlar models lke Cournot and Bertrand. Competton for an agent pushes up π mn, whle competton aganst t drves down π max. By way of analogy to blateral trade, π max s the market s wllngness-to-pay for agent s nvolvement n the creaton of V. Smlarly, π mn s, loosely, s wllngness-to-sell that nvolvement to the market. Both values are pnned down by competton mplct n the feasble alternatves to producng V avalable to market partcpants. Insght 3 Compettve ntensty wth respect to agent should be [ conceptualzed ] wth respect to the length of π mn, π max. At ts most ntense, π mn = π max. Whle the usual concepton of extreme compettve ntensty (.e., perfect competton ) may hold (π mn = π max = 0), so may compettve ntensty at the other end of the spectrum (π mn = π max = V), and everythng n between (Montez, Ruz-Alseda, and Ryall, 2015). Thus, extreme compettve ntensty s nether good nor bad per se. At the same tme, the model admts stuatons n whch π mn = 0 and π max = V;.e., competton plays no role n determnng what the agent captures. If these dstnctons are features of real-world ndustres, they have substantal mplcatons for strategy scholars and practtoners alke. Insght 4 Value capture depends upon two classes of resources compettve and persuasve. Whch s class s most mportant vares wth compettve ntensty. The value captured by frm s the sum of ts compettvely guaranteed mnmum plus some porton of ts feasble nterval, the latter obtaned va extra-compettve means. Formally, π = π mn + α ( π max π mn ), (3) where α [0, 1] s called s appropraton factor. The α parameter summarzes the effect of all super-compettve determnants of frm s ablty to capture value.e., factors that nduce others to part wth value beyond the mplcatons of Condton (2). 18 When compettve ntensty s slack, the control of superor persuasve resources s the key to value capture (Ryall, 2013). From a postve perspectve, the predcton here s that hgh-performng frms n low-ntensty ndustres ether control superor persuasve resources or enjoy nsttutonal advantages (e.g., bddng norms) vs-à-vs the other agents. At the other end of the spectrum, when ntensty s at ts most extreme, persuasve resources play no role. Accordngly, emprcal analyses that fal to account for varaton n ntensty/control of superor persuasve resources are unlkely to provde consstently good explanatons of frm performance heterogenety. 19 NONCOOPERATIVE GAME STAGE Ultmately, strategy scholars and practtoners alke are nterested n understandng how frm strateges affect value capture. To nvestgate ths ssue, Brandenburger and Stuart (2007) propose lnkng the compettve (CGT) stage to a precedng strategc (NGT) stage by way of a bform game. The goal s to admt a model n whch the agents ve wth one another to alter the compettve landscape (.e., the second-stage cooperatve game) to ther advantages. For example, frm strateges may nvolve nvestments n cost-reducng process technologes, capacty expanson, new market development, personnel practces, attempts to adjust corporate culture 18 When used prospectvely, the appropraton factor can be thought of as a subjectve estmate of an agent s own ablty to persuade ts transacton partners to part wth value, by all means other than pontng out the mplcatons of v. 19 We are presently unaware of any explct nvestgatons nto the competton/persuason resource dchotomy. However, the theory s consstent wth phenomena such as the nvestments n the acquston of partner nformaton pror to prce negotatons, as descrbed by Madsen and Leblen (2015).
Survey of Value Capture Theory 27 and so on. Smultaneously, dstrbutors may adopt new technologes, end users may hre negotaton experts, supplers may mplement new nformaton systems, etc. All of these actvtes, presumably the result of each agent s busness strategy, nteract to determne the actual value creaton opportuntes avalable n the marketplace. Formally, each agent N begns wth a set of feasble actons, A, wth typcal element a, an acton. Acton sets can be fnte or nfnte, scaler or multdmensonal, dependng upon the applcaton. Snce the frst stage s a noncooperatve game, t can take strategc or extensve form. The latter s approprate for nvestgatng stuatons n whch move tmng and nformaton ssues are mportant. To keep t smple, we wll descrbe the general strategc form: each agent chooses ts acton wthout knowledge of the other agents choces (.e., smultaneous-moves). The result s a lst contanng each agent s acton, referred to as an acton profle and denoted a (a 1,, a n ). The set of all such profles s denoted A. The dea s that the jont actons of the market partcpants nteract to nfluence both the characterstc functon, v, as well as each agent s appropraton factor, α [0, 1], ultmately determnng each agent s appropraton, Equaton (3). Thus, the parameters descrbng value capture n the second stage can be dentfed by acton profle superscrpts. For example, two dfferent acton profles a and a nduce cooperatve games (N, v a ) and (N, v a ) as well as appropraton factors α a and α a for agent, etc. Then, each agent s payoff n the second stage s assessed accordng to Equaton (3). Thus, the value captured n the market stage s the payoff to an agent s acton n the strategc stage, gven the effects of everyone s actons. Formally, agent s value capture gven acton profle a can be wrtten π (a) = π mn (a) + α a ( π max (a) π mn (a) ), (4) where π max (a) and π mn (a) are the bounds mpled by v a and α a s the net effect on s persuasve effectveness mpled by the actons n a. In closng ths secton, t s worth pontng out that the bform setup opens strategy analyss to the entre toolbox of NGT. For example, most strategy applcatons to date have used Nash, or Bayesan Nash, as a soluton concept n makng theoretcal clams n specfc settngs. However, those nterested n strategc settngs of bounded ratonalty mght employ subjectve equlbrum (Kala and Lehrer, 1995; Ryall, 2003, for a strategy applcaton) or ambguty-averse Nash equlbrum (Ellsberg, 1961; Ryall, 2009, for a strategy applcaton). On ssues of persstent performance heterogenety, the model can be expanded nto a repeated game. In addton, methods used n studes of cheap talk, nformaton asymmetry, and behavoral economcs can all be adapted to ths framework. All of these powerful modelng technques can be brought to bear to examne how frms n a wde varety of settngs behave and how those behavors affect value capture under competton. For example, consder applcaton of subjectve equlbrum n a smple settng. A subjectve equlbrum arses when (1) each agent chooses a strategy optmzng ts expected payoffs gven ts subjectve belefs and (2) actual expected payoffs nduced by these strategy choces are consstent wth subjectve expectatons. In other words, the consequences of agent actons are consstent wth ther subjectve belefs along the path of play but may be wrong n crtcally mportant ways off the equlbrum path. To see ths, suppose there are n symmetrc frms facng n buyers. Each frm can produce one unt of product at cost c. Buyers value one unt of product at u = x + c where x > 0. Here, each frm s essentally n a pure barganng contest wth ts buyer: any splt of x between the buyer and seller s possble. Assume the frms begn wth α = 0. However, n the NGT stage, each frm chooses ether to nvest n barganng tranng or not. The cost of the tranng s 0 < z < x, the consequence of whch s to shft the frm α from 0 to 1. The unque Nash equlbrum for ths game s for every frm to nvest n the persuasve resource and receve a CGT-stage payoff of (x z) > 0. Suppose, however, that the frms beleve (ncorrectly) that they are n a tradtonal perfectly compettve market that s, n whch π max = π mn = 0. In such a stuaton, persuasve resources are useless. Based upon ths belef, the subjectvely optmal choce s not to nvest n barganng. Then, n the CGT stage, α = 0 for all frms and, as a result, actual value captured s π = 0. Of course, ths s exactly as expected. Ths s a subjectve equlbrum: poor performance s attrbuted to tough competton when, n fact, t s due to zero nvestment n persuasve resources and no nvestment wll occur as long as markets are beleved to be tough.
28 J. Gans and M. D. Ryall COMPARISON TO OTHER MODELING APPROACHES Many readers for whom the precedng formalsm s novel wll already be qute famlar wth the standard models of NGT (e.g., Cournot, Bertrand, Stackelberg, and varatons). These models are workhorse theoretcal tools n ndustral organzaton economcs. Thus, a perfectly legtmate queston s: Why should strategy go n the drecton of bform games rather than follow the standard adopted by economcs? Essentally, ths artcle taken as a whole s ntended to provde a compellng answer to that queston. Even so, ths s a good pont at whch to provde a couple of more specfc answers to t. Frst, optmal model selecton s hghly context-dependent whch approach s best depends upon the questons beng asked. That sad, our hope s that the precedng dscusson llustrates why the bform model s deal when the questons beng asked are general ones about value creaton and capture n market settngs. In the standard market models of NGT, a raft of assumptons must be made, ncludng whether managers set prces or quanttes, the precse order of moves, what managers know when they move, specfc functonal forms for costs and demand, etc. If these detals are avalable to the nvestgator, great. Most of the tme, however, economc actvtes n real markets often nvolve messy, arm s-length wheelngs and dealngs that are ncompatble wth ths mnute level of specfcty. The CGT framework, n contrast, nvokes relatvely weak premses. These grant the analyst consderable freedom of nterpretaton wth respect to the detals of value creaton beng represented by the formalsm. As a result, the fndngs derved va CGT tend to be applcable to a broad spectrum of settngs of nterest to strategy scholars. Second, there are nstances of papers that provde formal translatons between the varous standard models used to analyze competton. The most famous of these s Kreps and Schenkman (1983). In ther model, frms choose capactes ahead of a Bertrand prce-settng game. The man result s that, under certan ratonng rules, the equlbrum of the game gves rse to the same equlbrum result n prces and quanttes as would arse under a sutably-chosen Cournot game. In other words, they show the sense n whch Cournot can be thought of as a specal case of a Bertrand model wth capacty choces. Stuart (2005) demonstrates that Cournot can also be thought of as a specal case of a bform game wth capacty choces. The mappng from smultaneous-move Bertrand games to CGT games that result n equvalent value-capture outcomes s relatvely trval. Hence, Cournot and Bertrand are often specal cases of a more general cooperatve game. 20 Choce of soluton concept s another ssue. CGT sports a number of dfferent soluton concepts the core, stable set, strong epslon-core, Shapley value, kernel, nucleolus, and Nash barganng. In strategy, the core s typcally the soluton concept of choce. Why the core? Because, as already noted, t mposes a weak set of compettve consstency condtons that seem reasonable n market settngs. Moreover, we argue throughout, the dentfcaton for each agent of an nterval of appropraton consstent wth these condtons (.e., rather than a pont-estmate) s actually a desrable feature one that generates several mportant nsghts about the effects of competton on value capture. There are examples of bform game applcatons outsde of strategy that use other soluton concepts. For example, the property rghts theory of the frm by Hart and Moore (1990) uses the Shapley value. The Shapley value s sensble n ths settng because there are no compettve externaltes requrng resoluton outsde of the game. Ths s not the case n many strategy contexts (de Fontenay and Gans, 2005, 2014). Also, some recent ndustral organzaton papers dong structural estmaton of vertcal relatons use the Nash barganng soluton for the CGT stage (Collard-Wexler, Gowrsankaran, and Lee, 2014). Ths also poses dffcultes for dealng wth compettve externaltes (that arse when competng frms are prevented, say by anttrust laws, from negotatng drectly wth one another), but t has proven to be tractable for the study of vertcal relatons when downstream frms operate n dstnct markets. The prmary ssue rased aganst the core s that the prmtves of value creaton may be such such that there are no π s satsfyng condtons (1) and (2). Ths s of suffcent concern to Lppman and Rumelt (2003) that, at the same tme they argue eloquently n favor of usng CGT as a foundaton for strategy theory, they also express reservatons 20 Byford (2010) provdes a varant on the bform model n whch the second stage s a CGT, but wth lnear prces as assumed by Kreps and Schenkman.
Survey of Value Capture Theory 29 about usng the core as a soluton concept. The source of the problem n such stuatons s always the same: V s too meager to be shared n a way that prevents every group G from actng on ts alternatve, v(g). 21 The frequency of such stuatons n the real world s an open emprcal queston. 22 Moreover, Stuart (1997) demonstrates that the core does, n fact, exst for a wde range of stuatons relevant to strategy research. In our judgment, the overall benefts of usng the core to develop strategy theory, partcularly n terms of the nsghts t provdes nto value capture under competton, presently outwegh these concerns. GENERAL PRINCIPLES The extant theoretcal lterature usng cooperatve or bform games to nvestgate ssues n busness strategy can be categorzed nto two substreams. The frst takes characterstc functons as gven, operatng at the general, abstract level to develop general prncples wth respect to value creaton, competton, persuasve resources, and frm performance. The second bulds up the characterstc functon from prmtves that are relevant to a partcular ssue. For example, the analyss may be specfc to two-sded markets, productve networks, or dfferentated products. These studes begn wth specfc assumptons about agents and ther roles, buyer preferences, producton technologes, costs, capactes, etc. The prmtve assumptons are then used to construct the mpled characterstc functons that arse from the agents varous strategc choces (.e., n a bform game). In ths secton, we focus upon the hstorcal development of the former and hghlght ts most sgnfcant fndngs. The frst paper to use CGT to examne value capture n strategy s Brandenburger and Stuart (1996). Ths paper ntroduces the strategy audence to the formal noton of agent added value. 23 Informally, an agent s added value s the dfference between 21 Put another way, for any collecton of nontrval v(g)s, there s a mnmum V below whch there are no dstrbutons of value satsfyng core condtons (1) and (2). 22 In the real world, there are many ways competton may be softened to admt exstence. For example, f anttrust law prohbts the agents n G from transactng, then v(g) = 0. Alternatvely, f the agents n G are unaware of ther productve possblty then, agan, v(g) = 0. 23 Ths dea arses n economcs at least as early as Edgeworth (1881). More recently, economsts Makowsk and Ostroy, n a substantal lne of jont work, demonstrate the mportance of the aggregate value created n a market n whch the agent partcpates and the amount of value that could be created were that agent to be removed from the market (alternatvely, were all the other agents to shun transactons wth that agent). Formally, the added value of agent s: av V v ( N ), (5) where N denotes the set of agents other than. Prncple of the added value (GP1) From Equaton (5), t follows that added value places an upper bound on what an agent can approprate (Brandenburger and Stuart, 1996): If π > av, then satsfacton of Equaton (1) mples j N < v ( ) N, whch volates Equaton (2). In words: postve added value s a necessary condton for value capture. Here, competton works aganst n the sense that, the agents on the other sde of the transactons wth that contrbute to V must be nduced to freely accept these and not some other set of transactons from whch s excluded n ths case, the ones nvolved n the producton of v(n ). The added value of s an upper bound on the other agents wllngness-to-pay for s nvolvement n the producton of V. When π = av, agent s sad to be a full approprator. Prncple of addng up (GP2) Brandenburger and Stuart (1996) clearly state that added value s a necessary but nsuffcent condton for value capture (p. 14). Nevertheless, ther analyss proceeds (from p. 15) under the premse that achevng postve added value s the path to value appropraton (.e., rather than beng one step on that path). They then llustrate several examples n whch every agent captures exactly ts added value no more, no less. These examples are bult on an nterestng condton known as the addng-up property: f the agent added values themselves sum to V, then every agent captures understandng that, n a general equlbrum model, agents and the value they capture are the mathematcal dual to solutons based upon products and prces (see, e.g., Makowsk and Ostroy, 1995). They refer to added value as agent margnal product. Brandenburger and Stuart (1996) cte ths work as havng had n mportant nfluence on ther paper (p. 23). See Makowsk and Ostroy (2001) for a wde-rangng, hghly accessble revew.