How Do Value Creation and Competition Determine Whether a Firm Appropriates Value?

Transcription

1 Unversty of Toronto From the SelectedWorks of Mchael D Ryall 2004 How Do Value Creaton and Competton Determne Whether a Frm Approprates Value? Mchael D Ryall, Melbourne Busness School Glenn MacDonald Avalable at:

2 MANAGEMENT SCIENCE Vol. 50, No. 10, October 2004, pp ssn essn nforms do /mnsc INFORMS How Do Value Creaton and Competton Determne Whether a Frm Approprates Value? Glenn MacDonald Oln School of Busness, Washngton Unversty n St. Lous, St. Lous, Mssour 63130, macdonald@wustl.edu Mchael D. Ryall Smon Graduate School of Busness, Unversty of Rochester, Rochester, New York 14627, ryall@smon.rochester.edu How does competton among economc actors determne the value that each s able to approprate? We provde a formal, general framework wthn whch ths queston can be posed and answered, and then provde several results. Chef among them s a condton that s both requred for, and guarantees, value appropraton. We apply our methodology to () assess the famlar noton that unqueness, nmtablty, and competton mply value appropraton, and () determne the value appropraton possbltes for an nnovator whose unque dscovery s of use to several others who can compete for the rght to use t. Key words: value appropraton; competton; compettve advantage; mtaton; nnovaton Hstory: Accepted by Danel Levnthal, busness strategy; receved June 1, Ths paper was wth the authors 3 months for 1 revson. 1. Introducton A fundamental queston n busness strategy s: How does competton among economc actors determne the value each approprates? There are many approaches to answerng ths basc queston. One comparatvely formal one s based on the famlar ndustral organzaton contnuum n whch, at one extreme, perfectly compettve frms surely do not approprate, and at the other, monopolsts surely do (at least under some assumptons more on ths below). What happens between competton and monopoly s less clear, but ntuton that the more the stuaton seems monopoly-lke, the better the prospects of appropraton are, s commonplace; see, e.g., Saloner et al. (2001, Chapter 7). Less formal, but hghly nfluental, the resource-based vew equates the ablty to approprate wth ownershp of somethng valued by others and n lmted supply. For example, Colls and Montgomery (1998, p. 39) say: the resource-based vew argues that profts can be attrbuted to the ownershp of a scarce resource. These and other famlar approaches to answerng the basc queston set out above appear to be founded on the noton that appropraton s fostered by control over some useful entty a patent, a new process, a unque organzaton, specal human captal assets, locaton for whch there s competton. Despte the volume of research on ths topc, there s no general, formal framework to address ths fundamental queston or to unfy and assess the many exstng approaches. In ths paper, we present such a framework, use t to provde a complete characterzaton of the features of a compettve nteracton that ensure an agent can approprate, and provde nsghts nto the nner workngs of a varety of famlar deas from strategy; for example, what s mtablty, and how does t lmt appropraton possbltes? We show that () there s a feature of competton that s requred for a frm to approprate, but does not guarantee ths; () there s a dfferent feature that actually guarantees appropraton, but s not requred for t; and () yet another feature s both requred for, and guarantees, appropraton; t also yelds a new set of very ntutve condtons that are jontly necessary. We employ these results to explore a par of related strategy ssues n whch the role of competton s central. Frst, do unqueness, nmtablty, and competton assure appropraton? Second, s a technology nnovator assured appropraton when there are multple frms that value the technology, but none can reproduce t on ther own? We also show that n any gven economc nteracton, there are both a mnmum and a maxmum level of appropraton guaranteed by the alternatves avalable to the varous actors. When one s maxmum and mnmum dffer, any level of appropraton n between s possble. In ths case, somethng other than competton (.e., barganng ) determnes an ndvdual s precse level of appropraton. We focus prmarly on the mnmum and, when t exceeds the normal rate of return (.e., mples supranormal 1319

3 1320 Management Scence 50(10), pp , 2004 INFORMS profts), say the correspondng ndvdual has a compettve advantage. 1 Why ths focus? Frst, an agent s havng compettve advantage, as we have defned t, suffces for that agent to partcpate n the value creaton actvty. Next, havng a compettve advantage mples that an ndvdual need not rely on whatever barganng mght ental to acheve supranormal profts. (Ths s not to say that good barganng would not enhance appropraton, just that ths may not be needed for appropraton.) Fnally, the determnants of the mnmum, once uncovered, reveal a lot about how competton leads to value appropraton. The avenues through whch alternatves foster or work aganst appropraton turn out to be qute subtle, and the mplcatons sometmes surprsng. Formally, the framework we study s a general coaltonal game wth transferable payoff. Ths setup has a long hstory n game theory and has been studed extensvely; Osborne and Rubnsten (1994) provde a good ntroducton. We are not, however, smply adaptng results from ths lterature. Our work n ths paper and related research makes several novel contrbutons to game theory; we elaborate below. At the same tme, we also attempt to contrbute by makng accessble to those whose specalty s not game theory, some very nformatve, but mathematcally elaborate, materal. The structure of ths paper s as follows. In the balance of ths secton, we comment on where ths paper fts nto the game theory and strategy lteratures. In 2, we provde examples that motvate the ngredents of our approach and suggest the knd of general results we later develop. In 3, we descrbe our framework; the man results appear n 4. We close wth the applcatons to unqueness/nmtablty/competton and technologcal nnovaton n 5, and a dscusson of some subtletes and lmtatons of our approach n Lterature Brandenburger and Stuart (1996) were the frst to suggest that coaltonal games can frutfully be appled to study foundatonal ssues n busness strategy. Our paper makes several contrbutons to both strategy and game theory, and so we dscuss the relevant lterature n both felds. 1 Ths termnology dstngushes between an agent earnng supranormal proft and those features of the economc stuaton that cause ths. We emphasze ths dstncton because, as our results show, there are many dfferent ways n whch the structure of competton can lead to supranormal profts. The common practce of loosely equatng compettve advantage wth features thought to delver t can be msleadng. Game Theory. Economsts have long known that the set of equlbrum payoffs for an ndvdual n a coaltonal game s a closed nterval, but lttle s known about what determnes the bounds of ths nterval n a general game. Shapley (1971) showed that n a restrcted class of games (convex), the bounds on a player s equlbrum payoff are equal to the lowest and hghest contrbuton of that player to some group. MacDonald and Ryall (2003a) provde the frst complete characterzaton of the upper and lower bounds on ndvdual equlbrum outcomes for general coaltonal games wth transferable payoff. In ths paper, we defne three concepts that emphasze dfferent dmensons of competton margnal product, mnmum resdual, and mnmum total value and then lnk them to value appropraton. The latter two defntons are new. Of the results that follow, Proposton 1 s a well-known result n coaltonal game theory; Proposton 3 s from MacDonald and Ryall (2003a); Proposton 4 s a smplfed verson of a result n that paper; and Propostons 2, 5, and 6 are new. 2 Brandenburger and Stuart (2003) s especally relevant. They develop a hybrd noncooperatve/ coaltonal formalsm called a bform game. Specfcally, n the frst of two stages, agents actng noncooperatvely make choces that determne the structure of the second-stage coaltonal game. For example, frms mght make capacty choces n the frst stage, and later, gven capactes, nteract n the free-form way the coaltonal structure emphaszes. Brandenburger and Stuart develop an axomatc approach to resolvng the barganng problem one that mples a unque expected outcome wthn the agent s range of possble equlbrum payoffs n the coaltonal game. Our work complements thers by showng how competton determnes ths range, and expands the applcablty of the bform model by sheddng lght on, e.g., how a frm s ncreasng capacty alters the range of possble equlbrum payoffs t faces. We elaborate brefly n 6. Strategy. One key objectve of strategy research s to dentfy general features of the economc envronment that determne how competng frms approprate value. For example, Porter (1980) says, The essence of strategy formulaton s copng wth competton, and goes on to enumerate fve forces that determne the relatve ntensty of competton n an ndustry, whch n turn determnes the performance prospects for ts members. Wernerfelt (1984) analyzes the relatonshp between frm resources and proftablty, and argues that resource poston barrers 2 The proof of Proposton 2 s straghtforward and appears n 4.2. Proofs of Propostons 5 and 6 are avalable on the Management Scence webste (mansc.pubs.nforms.org/ecompanon.html).

4 Management Scence 50(10), pp , 2004 INFORMS 1321 are assocated wth hgh profts. Barney (1991, p. 101) examnes the role of dosyncratc, mmoble frm resources n creatng sustaned compettve advantage, argung that ownershp of resources that are valuable, rare, and mperfectly mtable mples sustaned performance advantage. 3 Ths focus s also artculated n modern strategy texts. Colls and Montgomery (1998, p. 5) tell us that value creaton s the ultmate purpose of corporate strategy and that one of the most fundamental questons of strategy s, What makes compettve advantage sustanable? Saloner et al. (2001) say that a frm must not only be able to create value, but In order to prosper, the frm must also be able to capture the value t creates (p. 39). Evdently, dentfyng general prncples leadng to value appropraton under competton s an mportant ssue n busness strategy. We address ths same ssue and are motvated by some of the deas and phenomena rased by those mentoned above. However, our approach dffers n an essental way: We provde a formal, general descrpton of a strategc nteracton, an agent s role n t, and how alternatves avalable to ndvduals nfluence appropraton. Throughout, the reader can determne: what our theory assumes, whether t s nternally consstent, to whch class of stuatons t apples, and so on. Ths precson and specfcty allow us to gve unequvocal defntons of, and to conduct logcal tests on, some of the mportant deas dscussed nformally n the work mentoned above. Indeed, we provde a precse, general answer to the queston, When s an agent guaranteed appropraton under competton? Whle t s easy to argue that methodologcal debates rarely produce much of value, we thnk the sectons that follow persuasvely establsh the utlty of our formalsm n understandng foundatonal ssues n strategy. In addton to provdng answers to basc questons, our analyss uncovers subtletes of competton that sometmes have surprsng mplcatons. For example, we show that valuable, rare, and mperfectly mtable resources are, n general, nether necessary nor suffcent for sustaned performance advantage. Conversely, we dentfy the types of stuatons n whch these qualtes are mportant. We vew our work as a companon to the nformal theory that precedes t, and a natural next step n strategy s maturaton as a feld bult upon a logcally consstent body of theory and evdence. In MacDonald and Ryall (2003b), we explan and llustrate how our formalsm can be employed to assst n uncoverng and evaluatng opportuntes for value creaton and 3 Many strategy theorsts trace ther ntellectual roots to Penrose (1959), who argued that frms should be vewed as unque bundles of productve resources; Peteraf (1993) surveys the early lterature. appropraton what data are requred, how the requste calculatons can be carred out, how the calculatons can be used to quantfy the value of new ntatves, etc. 2. Examples We begn wth some smple examples that ntroduce the theoretcal setup and behavoral hypotheses we analyze n detal below. The examples demonstrate some of the subtletes n the way agents alternatves nfluence ther ablty to approprate value, and llustrate the lmts on the nformatveness of some famlar models of markets. These examples are not ntended to be realstc applcatons. Rather, they are ntended to motvate why coaltonal games are a useful way to study value appropraton under competton and to llumnate the power of agent s alternatves n shapng ndvdual value appropraton. Example 1 (Pure Barganng). Consder a stuaton wth one frm and one buyer, labeled F 1 and B 1. F 1 can produce one unt of ts product at cost normalzed to zero. B 1 seeks to purchase at most one unt of product, and dong so yelds utlty of $1. Nether F 1 nor B 1 have any outsde alternatves, so the only optons avalable to F 1 and B 1 are to produce $1 of value together, or not. It s ntutve (and an mplcaton of the model see below) that $1 of value wll ultmately be created. However, as wll become apparent from the sequence of examples, the alternatves avalable to agents play a key role n determnng how much of the value any ndvdual s guaranteed to receve. How does ths work? Suppose F1 and B1 are the values approprated by F 1 and B 1, respectvely; we wll call F1 B1 a dstrbuton of value. If s a plausble canddate for an outcome gven the assumed value creaton possbltes, what condtons should satsfy? One obvous condton s feasblty: Value dstrbuted cannot exceed the value avalable for dstrbuton. In ths example, F1 + B1 1 (2.1) The second condton, stablty, descrbes how agents alternatves structure ther appropraton. We suppose agents have freedom of choce n ther busness dealngs, so that f specfes some agent to approprate less than he could by actng on hs own, ths agent wll smply go ahead and act on hs own. (More generally, when there are more than two agents nvolved, we wll also suppose that f any subgroup of agents could do better by actng on ther own, they wll.) In ths example, stablty mples three restrctons on : F1 + B1 1 F1 0 and B1 0 (2.2)

5 1322 Management Scence 50(10), pp , 2004 INFORMS Because stablty requres F1 + B1 1, and only $1 can be dstrbuted, any plausble outcome of ths value creaton opportunty must have F1 + B1 = 1;.e., B 1 acqures a unt of Product 1 from F 1, and pays some fracton of $1 for t. Do the alternatves avalable to the agents mpose any further constrants? It s easy to see that the feasble and stable dstrbutons nvolve any splt of $1 between F 1 and B 1. Consder the extreme outcome n whch F 1 approprates $1, leavng B 1 wth nothng. Ths dstrbuton of value s stable because the only alternatve avalable to B 1 s not consumng at all, and s also valueless to B 1.For smlar reasons, B1 = 1 and F1 = 0 s also stable. In ths stuaton, the two agents have no valueproducng alternatves to dealng wth each other. Thus, however the dollar s splt, t wll not be the result of competton. Ths s why ths case s referred to as pure barganng. Because ether agent mght approprate nothng, we say that nether has a compettve advantage. One reasonable reacton to the possblty of such extreme outcomes s that (n any real economc nteracton) they are unlkely to occur F 1 and B 1 sharng the dollar more equtably, possbly as the result of some sort of barganng, seems more plausble. We agree, but the mportant pont s that there s nothng about the agents alternatves that rules out these extreme outcomes. Note that n ths example, F 1 mght be nterpreted as a frm wth a valuable product that none can mtate;.e., as an nstance n whch F 1 controls a unque, nonmtable, and valuable resource. Nevertheless, the compettve envronment offers no guarantee that F 1 wll receve a postve share of the value. Nor does t requre F 1 to gve up any value. The reason s that F 1 s product, despte ts unqueness, etc., s not valuable wthout B 1. Dependng upon what one assumes about how barganng between F 1 and B 1 s lkely to turn out, F 1 may or may not approprate value. 4 From the perspectve of ths paper, the nterestng pont s that whatever F 1 ends up appropratng, the reason wll not be that ts product s unque, valuable, and nmtable. Example 2 (Perfect Competton). Consder the same stuaton as n the prevous example, but now assume F 1 and B 1 each have an outsde alternatve worth $0.5. Now, stablty requres that F1 + B1 1 F1 0 5 and B1 0 5 whch, gven that there s just $1 to dstrbute, mply F1 = B1 = 0 5. Thus, although the value approprated n ths nteracton s strctly postve, t s exactly equal to the agent s next-best alternatve. Not only does competton fully determne the dstrbuton of value, no one approprates supranormal profts. 5 Example 3 (Capacty-Constraned Monopoly). In pure barganng, the sole source of value s not F 1 s product, but, nstead, the nteracton between F 1 s product and B 1 s enjoyment of t. Thus, t s ntutve that the addton of a second buyer, say B 2, who values the product as much as B 1 does, wll generate competton that guarantees F 1 can approprate some or all of the value. Formally, as above, assumng F 1 has just one unt for sale, there s just $1 to dstrbute. Because F 1 and ether buyer can create $1 n value on ther own, stablty requres both F1 + B1 1 and F1 + B2 1 whch, wth just $1 to dstrbute, can only be satsfed by F1 = 1. Thus, the only stable dstrbuton of value nvolves F 1 appropratng all value;.e., one buyer acqures a unt of the product and pays $1 for t. Intutvely, f, for example, F 1 and B 1 were to share the $1 equally, leavng B 2 wth nothng, B 2 could offer to dsplace B 1 and accept just $0.4, payng $0.6 to F 1, who would happly accept ths offer. An analogous counteroffer can be found whenever F 1 approprates less than $1. Ths s the classc case of capacty-constraned monopoly. Note that f F 1 has two unts for sale (agan wthout costs), because each buyer desres only one unt, the capacty constrant s rrelevant and there s no need for buyers to compete. In fact, the stuaton s effectvely pure barganng between F 1 and each buyer. Ths s an example of a general theme that we explore n depth below, that an abundance of resources.e., wth the capacty constrant, there s just $1 to dstrbute, but wthout t there s $2 generally reduces the least an agent mght approprate. Evdently, when there s competton to do busness wth an agent, that agent s appropraton prospects mght mprove. Let us pursue ths pont a lttle further. Our descrpton of the value creaton possbltes allows us to quantfy the value each agent adds. Followng Brandenburger and Stuart (1996), F 1 s valueadded s the dfference between the value that could be created by all the agents, ncludng F 1, and the value created by all the agents wthout F 1 (and lkewse for B 1 and B 2 ). In keepng wth the economcs lterature, we call ths dfference an agent s margnal product, and denote t by mp (subscrpted to dentfy the agent as needed). An agent must have a postve margnal product for that agent to approprate value; see Proposton 1. To see ths, observe that f an agent for whom mp = 0 s magned to approprate some value, the others could, nstead, smply gnore 4 Lppman and Rumelt (2003) provde dscusson of varous barganng notons for coaltonal games. 5 Makowsk and Ostroy (1995) generalze ths dea and demonstrate that t mples effcent, prce-takng behavor n an economy.

6 Management Scence 50(10), pp , 2004 INFORMS 1323 Table 1 Full Appropraton Example Table 2 Less-Than-Full Appropraton Example Group Value Group Value Group Value F 1, F 2, B 1, B 2 4 F 2, B 1, B 2 3 F 2, B 1 2 F 1, F 2, B 1 3 F 1, F 2 0 F 2, B 2 2 F 1, F 2, B 2 3 F 1, B 1 2 B 1, B 2 0 F 1, B 1, B 2 3 F 1, B 2 2 sngle agent 0 Group Value Group Value Group Value F 1, F 2, B 1, B 2 3 F 2, B 1, B 2 2 F 2, B 1 2 F 1, F 2, B 1 2 F 1, F 2 0 F 2, B 2 2 F 1, F 2, B 2 2 F 1, B 1 1 B 1, B 2 0 F 1, B 1, B 2 1 F 1, B 2 1 sngle agent 0 that agent wth no effect on the value produced, and then share what the agent was to approprate. In the pure barganng example, mp F1 = mp B1 = 1, so both F 1 and B 1 have the prospect of appropratng value. On the other hand, the same example shows that postve margnal product does not guarantee appropraton. In the capacty-constraned monopoly example, because F 1 s partcpaton s requred for $1 to be created, mp F1 = 1. However, because ether B 1 or B 2 can always be removed wthout harmng the value creaton opportunty, mp B1 = mp B2 = 0. Thus, only F 1 has any possblty of appropratng, and so approprates all the value. Example 4 (Full Appropraton). We now enrch the stuaton by addng a second frm, F 2. Assume each frm can produce two unts of product, the frst at zero cost and the second at a cost of $1,.e., ncreasng margnal cost. Assume buyers vew the frm s products as perfect substtutes, and that each buyer obtans $2 n value by consumng a unt of ether frm s product, $3 by consumng two unts of product, and no addtonal value for consumpton above two unts. Enumeratng the value creaton alternatves avalable to the partcpants n ths nteracton, we have the results n Table 1. The value generated by all agents partcpaton s $4. Ths s the value created when ether each frm produces one unt and each buyer consumes one, or each frm produces two unts and each buyer consumes two. Lkewse, two frms and a buyer can generate $3 by each frm producng one unt and the buyer consumng both, and so on. In ths example, every agent has mp = 1. Because an agent can never approprate more than hs or her margnal product, t follows that F 2, B 1, and B 2 can approprate, at most, $3 between them. Ths leaves a resdual, $4 $3 = $1, that can only go to F 1. Ths s smlarly true for all the other agents. Thus, each agent approprates exactly $1. Because everyone s guaranteed to approprate ther margnal product, ths example s one of full appropraton. In ths example agents alternatves are so perfectly balanced that they mply a unque, feasble, and stable dstrbuton n whch all agents approprate ther margnal product there s no room for barganng. Ths stuaton s a very unusual one n that t occurs f and only f the sum of agents margnal products equals the value that s avalable to be dstrbuted. 6 Note that the perfect competton and capacty-constraned monopoly also have ths feature, and so mply full appropraton. Example 5 (None of the Above). Despte ther famlarty and frequent applcaton, the perfect competton and capacty-constraned monopoly scenaros, because they mply full appropraton, are qute specal. In some stuatons of nterest, the assumpton that the value to be dstrbuted s equal to the sum of the margnal products may be descrptve, but we know of no reason to expect that ths s generally the case. When t s not, ntuton based on these polar treatments of market structures can be msleadng. In partcular, the forecast that agents approprate fully may not even be a logcal possblty, and the mportance of barganng may be understated. A smlar remark apples to pure barganng, n whch agents alternatves only affect ther appropraton possbltes trvally. Intuton based on ths setup tends to understate the mportance of agents alternatves and the competton they mply. The stuaton need only be slghtly more complcated than the prevous examples for the way appropraton possbltes shape appropraton to be more subtle. To see ths, consder a smple duopoly model wth vertcal product dfferentaton and capacty constrants. Specfcally, suppose each frm has one unt of capacty and each buyer values only one unt of consumpton. Also, assume both buyers get $2 from consumng F 2 s product, versus just $1 from F 1 s. Ignorng costs agan, the value creaton possbltes are shown n Table 2. Frst, s ths stuaton well modeled by perfect competton or monopoly? Clearly, nether. F 2 s margnal product s $2, and the others margnal products are all $1. Thus, the sum of the margnal products exceeds the $3 n dstrbutable value, rulng out full appropraton, and along wth t, perfect competton and monopoly. How about pure barganng? For example, 6 Ths s easy to see. If mp s dstrbuted to, and V s the total avalable for dstrbuton, then feasblty requres mp V, whereas stablty requres mp V ; together mp = V. On the other hand, suppose mp = V. As usual, an agent cannot receve more than mp. However, t s also true that no agent can receve less. Were to receve less than mp, that all value must be dstrbuted means that some other agent, j, would have to receve more than mp j. Proposton 1 tells us that ths outcome cannot be both feasble and stable.

7 1324 Management Scence 50(10), pp , 2004 INFORMS can t turn out that F 2 approprates nothng? Clearly, not. Because F 2 and ether buyer can create $2 on ther own, f F 2 approprates $0, stablty requres each buyer to approprate at least $2. However, there s only $3 to dstrbute. Thus, F 2 must approprate. Overall, whle ths example s not unusual, t s not well descrbed by any of the famlar cases set out above. A more general approach s needed. We have already argued that F 2 must approprate, but we can be much more specfc. Indeed, F 2 must approprate at least $1 n any stable dstrbuton of value. To see ths, suppose F 2 approprates only $0.9, say by sellng ts unt of Product 2 to B 1 for $0.9. Ths leaves B 2 to purchase a unt of Product 1. Suppose B 2 has made the best possble deal wth F 1 ;.e., B 2 pays $0 for ts unt of Product 1, and so approprates all the created value, $1. Even so, F 2 could offer to sell ts unt of Product 2 to B 2 for $0.95, and both F 2 and B 2 would prefer ths to the contemplated dstrbuton. Thus, F 2 cannot receve as lttle as $0.9. The same argument apples whenever F 2 approprates less than $1. Despte F 2 s margnal product beng $2, all that competton ensures F 2 s $1. The reason s that whle buyers compete to buy from each frm, frms also compete to attract buyers. So F 2 s superor product allows the competton among buyers to guarantee F 2 some of the created value, but the competton among frms lmts how much F 2 s assured of appropratng. What s the most F 2 can approprate? It s easy to check that f F 2 approprates $2, and F 1 $1, leavng nothng for the buyers, the buyers alternatves do not allow them to avod ths outcome. Thus, the maxmum F 2 can attan s $2, hs margnal product. Because the range of outcomes consstent wth agents alternatves leaves F 2 wth a broad range of possbltes,.e., 1 2, barganng wll play an mportant role n determnng the fnal dstrbuton of value. These examples llustrate several ponts. Frst, the structure of one s compettve alternatves can guarantee an agent postve value appropraton rrespectve of one s barganng skll. Second, there are reasonable scenaros where the famlar full appropraton models are msleadng even n very smple nteractons and under substantal smplfyng assumptons, the forces of competton can work n subtle ways. The addton of more realsm to these examples shows no sgn of reversng ths concluson. Thrd, whle the ntutve, well-known measure of ndvdual value-added margnal product does provde useful nsghts, t does not capture the complete, compettve pcture. Our goal s to develop some general prncples regardng the relatonshp between competton and value appropraton. Ths s the task to whch we now turn. 3. Theoretcal Framework In ths secton, we set out the general coaltonal game framework used to derve our results. As n the precedng examples, the key element of the framework s a formal descrpton of the value creaton alternatves avalable to the agents partcpatng n any strategc nteracton Value Creaton Consder a strategc nteracton among some agents, e.g., frms, supplers, consumers, employees, regulators, etc. As n the examples, we need a way to descrbe varous groups of agents and the value that mght be created by these groups. Let the set N 1 2 n enumerate all the agents n the nteracton;.e., Agent 1 Agent 2 agent n. Any subset of N (a group ) s denoted G; we call an arbtrary ndvdual agent. IfG ncludes, the group obtaned by removng s wrtten G ; for example, N s the group consstng of all agents except. Lkewse, f G does not nclude, the group obtaned by ncludng s wrtten G +. We have nothng new to say about the process leadng to value creaton opportuntes. Thus, we treat agents value creaton possbltes as a prmtve and leave ths as general as we can. Specfcally, for any group G, v G s the value G can create ndependently of agents outsde G. We emphasze that for any group G, whle v G s just one number, t can be employed to descrbe a multfaceted stuaton. That s, v G represents the maxmum value G can produce, mplctly accountng for lmtatons mpled by nformaton and agency consderatons, transactons costs, confguraton of productve resources, barrers to technology transfer, nsttutonal structure, regulaton, and so on. In partcular, f members of G can collude, then v G s ther greatest collusve payoff. If colluson s ether prohbted, or mpossble for agents to montor and enforce, then v G s ther maxmum noncollusve payoff. Wthout loss of generalty, we assume the values are normalzed so that v G represents the value group G can generate n excess of the outsde optons of ts members; that s, for all v = 0. 7 We also assume that ncludng agent n a group never reduces the value that group mght generate. Ths mples that for any group G, V v G. Also, for any G ncludng v G v G, specfcally V v N. Gven the set of players, N, let v be a vector whose components are v G, for all the possble groups G; we 7 For applcatons, the calculaton of v G s crtcal. In partcular, attenton must be gven to the way value arrves over tme, uncertanty, and any antcpated actons by other players. In MacDonald and Ryall (2003b), we detal the nterpretaton of v G and how t can be calculated.

8 Management Scence 50(10), pp , 2004 INFORMS 1325 wll call N v a strategc nteracton. Because 2 n 1 nonempty groups can be formed from N, v has 2 n 1 components. Also, because v N appears frequently n what follows, we gve t the specal label V Impact of Agents Alternatves In 2, we defned a dstrbuton of value, and dscussed how feasblty and stablty (formalzed as (2.1) and (2.2)) constran how value created may be dstrbuted. In ths secton, we generalze these notons. Gven a strategc nteracton N v, let denote the amount of value obtaned by agent and refer to = 1 n as a dstrbuton of value; where convenent we focus on agent by wrtng =, where s a dstrbuton of value among members of N. The general verson of (2.1) takes account of the fact that the group that creates the most value s the one ncludng all agents: feasblty: V (3.1) The generalzaton of (2.2) requres that for each group G, no alternatve, v G, yelds G more total payoff than the dstrbuton of value: stablty: for all G j v G (3.2) A couple of ponts are worth hghlghtng. Frst, because N s one of the groups referred to n (3.2), N V. That s, altogether, at least V must be dstrbuted among the agents. Together wth (3.1), a feasble and stable dstrbuton of value always dstrbutes exactly V ;.e., = V (3.3) N Second, t proves useful to observe that (3.2) can be stated as for all G ncludng j v G and j G N j G j G j v G (3.4) As n the examples, there may be many dstrbutons of value that are both feasble and stable. What determnes whch dstrbuton ultmately occurs? Both feasblty and the mpact of agents alternatves have already been taken nto account. Thus, the thrd force determnng how value can be dstrbuted s the abovementoned barganng process, a catchall for all the means apart from the threat of exercsng ther strategc alternatves as emboded n (3.2) that agents mght employ to cajole one another nto partng wth value. Instead of makng partcular assumptons about how barganng operates and focusng on the mpled dstrbuton(s) of value, we consder a dstrbuton of value to be a plausble canddate for an outcome of an nteracton f t s smply feasble and stable. Any such dstrbuton s consstent wth value creaton and competton, but s not relant on some arbtrary barganng procedure. If s a feasble and stable dstrbuton of value, we wll refer to t as an FSD. 4. Value Appropraton: General Prncples The value agent approprates depend on whch FSD occurs; and typcally there are numerous FSDs. From agent s perspectve, f all FSDs result n hs recevng postve value, then no matter how barganng ultmately determnes precsely whch FSD occurs, the nature of s alternatves and the mplct competton for hs partcpaton n the value creaton actvty mean he s assured of appropratng some part of the created value. Thus, to emphasze the crucal role of an agent s competng alternatves, we say that agent has a compettve advantage f > 0 n every FSD. If one consders all FSDs, the possble payoffs to any ndvdual agent form an nterval, whch we desgnate mn max. That s, gven the strategc nteracton N v, there are FSDs n whch receves exactly mn, exactly max, or any amount n-between. Thus, agent s havng a compettve advantage concdes wth mn > 0. In ths secton, we explore the features of the strategc nteracton that yeld compettve advantage. We begn wth a well-known necessary condton, then use ths to derve a new suffcent condton. We go on to provde a novel characterzaton (.e., condtons that are both necessary and suffcent) of havng a compettve advantage, then develop a new set of smple, hghly ntutve, jontly necessary condtons. The characterzaton emphaszes that how much value s created plays a key role n determnng how that value s dstrbuted. Perhaps counter to ntuton, there s a clear sense n whch a lot of value beng created blunts the competton for an agent, thereby removng hs compettve advantage. The jontly necessary condtons reveal the structure of the competton that can yeld compettve advantage A Condton Necessary for Compettve Advantage Brandenburger and Stuart (1996) emphaszed the role that an agent s value-added plays n allowng value appropraton. Ths dea s relevant to, and consstent wth, our results. In our notaton, agent s margnal product, mp, s the dfference between V and the

9 1326 Management Scence 50(10), pp , 2004 INFORMS value that could be created by all agents other than, v N,.e., mp V v N Because v N s the maxmum value that can be created wthout, mp measures the ncremental value adds to the strategc nteracton. It s easy to see that cannot approprate more than mp. That s, f the dstrbuton of value resulted n recevng more than hs margnal product, there would be so lttle left to dstrbute among the other agents that they would fnd creatng value on ther own preferable. 8 So f cannot approprate more than mp, and f s assured of appropratng.e., has compettve advantage then he must also have a postve margnal product. Proposton 1. Gven a strategc nteracton, N v, postve margnal product s necessary for compettve advantage: mn > 0 mp > 0. Ths result s ntutvely appealng. However, t s also weak n the sense that whle postve margnal product opens up the prospect of appropratng value, t n no way guarantees t;.e., mp s necessary for compettve advantage, but not suffcent. The ntuton s clear from the frst example n 2. In that example, each of F 1 and B 1 has a postve margnal product, but both are needed to create value. Thus, stablty demands only that all value be approprated by F 1 and B 1, but ths allows the possblty that one or the other wll receve nothng. More generally, a postve margnal product does not mean that the competton mpled by the structure of s alternatves s such that s assured appropraton A Condton Suffcent for Compettve Advantage Proposton 1 can be turned around to yeld a suffcent condton for compettve advantage. To see how, recall the monopoly example n 2. There, V = mp F1 = 1 and mp B1 = mp B2 = 0. Because $1 must be dstrbuted, and the structure of agents alternatves (va Proposton 1) prevents ether buyer from 8 Formally, suppose >mp. Usng the defnton of mp and rearrangng, we get v N >V. The rght-hand sde s the value that can be dstrbuted to others f approprates, and the left-hand sde s the value others can approprate wthout. 9 In fact, player can have postve margnal product and no possblty of appropraton;.e., mn = max = 0. In the example followng, the unque FSD dstrbutes $1 to each of F, B 1, and B 2, and nothng to B 3, despte B 3 s margnal product beng $1. Example wth mp > 0 and No Compettve Advantage Group Value Group Value Group Value F, B 1, B 2, B 3 3 F, B 1 2 B 1, B 2 0 F, B 1, B 2 2 F, B 2 2 B 1, B 3 0 F, B 1, B 3 2 F, B 3 0 B 2, B 3 0 F, B 2, B 3 2 B 1, B 2, B 3 2 sngle agent 0 appropratng any value, the only FSD nvolves F 1 appropratng all the value. A smlar noton holds n general. To see ths, recall that V s the value that must be dstrbuted among agents n any FSD, and defne s mnmum resdual, mr,by mr V mp j j N Because no agent can approprate more than hs margnal product, j N mp j s the maxmum amount of value that agents other than can concevably approprate. Because V s the value to be dstrbuted, mr s the least that can concevably be left over for. Therefore, f mr > 0, s assured of appropratng,.e., has compettve advantage. 10 Proposton 2. Gven a strategc nteracton, N v, postve mnmum resdual s suffcent for compettve advantage: mr > 0 mn > 0. Why s havng a postve mnmum resdual not necessary for compettve advantage? Frst, the calculaton of mnmum resdual supposes that all players other than smultaneously approprate ther margnal product. However, there may be no FSD wth ths feature. In Example 5, mp F1 = mp B1 = mp B2 = 1, mp F2 = 2, and V = 3, so t s not possble for all agents other than F 1 to approprate ther margnal product (ndeed, mr F1 = 1). Thus, the least that s left over for s generally larger than mr, n whch case mght be assured of appropratng value even though mr 0. Second, mnmum resdual s determned solely by the value created n groups of sze n and n 1. However, t may be that there are smaller groups, ncludng, whch can create a great deal of value on ther own. If such groups exst, resolvng competton for s partcpaton may further lmt how lttle can receve, and yeld compettve advantage despte mr 0. Proposton 2 reveals a subtle feature of the mpact of agents alternatves and the mpled competton. Consder some agent j, other than. Proposton 1 also tells us that agent j can never receve more than hs margnal product, for ths would make the prospect of creatng value wthout j attractve to the others, ncludng. Thus, s havng to approprate at least mr, as per Proposton 2, s due to the fact that f were to approprate less, some other agent j would have to approprate too much to keep and the others from smply creatng value wthout j. Thus, s guarantee of value appropraton s due to a blend of hs value creaton possbltes and the alternatves avalable to and to the other agents The assumpton that there s at least one FSD mples mr mp. If mr >mp, there are no FSDs. 11 Brandenburger and Stuart (1996, pp ) suggest four valuebased strateges for creatng strategc stuatons wth favorable

10 Management Scence 50(10), pp , 2004 INFORMS Characterzaton of Compettve Advantage, and Jontly Necessary Condtons The margnal product and mnmum resdual concepts provde nsght nto the sources of compettve advantage, and Propostons 1 and 2 sometmes gve a clear answer about whether agent has one: yes f mr > 0, and no f mp = 0. However, n many cases the structure of value creaton s not so extreme;.e., mr 0 and mp > 0. When ths occurs, Propostons 1 and 2 do not settle the queston of whether an agent has a compettve advantage. We now provde a more elaborate, but complete, descrpton of the feature of the strategc nteracton that s both necessary and suffcent for compettve advantage, and that allows us to hghlght how an agent s alternatves, and the mplct competton for hs partcpaton, work to yeld or undermne compettve advantage. Before developng the characterzaton, t s useful to start by revstng Example 5. In that example, F 2 has compettve advantage and, n partcular, s assured of appropratng at least $1. The argument s that because F 2 and ether buyer can create $2 of value on ther own, any FSD must result n F 2 and ether buyer appropratng at least $2 between them. Supposng F 2 s to approprate $0, each buyer must then approprate at least $2. However, there s only $3 to dstrbute not enough. Thus, F 2 must approprate more than $0, ndeed, F mn 2 = 1. Intutvely, any dvson of $3 between the buyers leaves one, or both, n the poston of beng able to do better by creatng value on hs own wth F 2. In ths sense, f F 2 s to approprate $0, buyers compete to act on ther alternatve wth F 2. F 2 s appropratng at least $1 s the only way to resolve ths competton whle dstrbutng a total of just $3. Now modfy the example slghtly by assumng there s a network externalty n whch each buyer s enjoyment of ether product ncreases f the other buyer consumes the other product. The only entry n the table that s altered by ths change s the $3 fgure, because the group comprsng both frms and both buyers s the only one n whch both buyers end up purchasng. Suppose the value created ths way s $4. It s easy to check that the dstrbuton of value n whch each frm approprates $0 and each buyer approprates $2 s an FSD;.e., F mn 2 = 0 and F 2 no longer has compettve advantage. The ntroducton of the network externalty does not change the fact asymmetres. They do not defne favorable asymmetres, but Proposton 2 may have somethng to say about what they had n mnd. The condton mr > 0 can be rearranged to mp > j N mp j v N. Thus, has compettve advantage f hs margnal product s suffcently large relatve to the margnal products of others. It follows that actons yeldng ths sort of asymmetry are suffcent for compettve advantage. that F 2 and ether buyer must approprate at least $2 between them, so that f F 2 s to approprate $0, each buyer must approprate $2; the competton to create value wth F 2 s exactly as before. However, the extra value created by the network externalty allows ths competton to be resolved by each buyer appropratng $2, leavng F 2 wth no compettve advantage. 12 These examples suggest two closely related ways to look at what determnes whether agent has compettve advantage. Frst, f enough value s created, as occurs n the network externalty example, value can be dstrbuted among the other agents so that even f s to approprate nothng, no group can mprove by creatng value on ts own wth. When ths s so, cannot be assured of appropraton, and so does not have compettve advantage. Our characterzaton formalzes ths dea. Second, f has compettve advantage, as n the example wthout the network externalty, the reason s that f s to approprate nothng, some sort of competton to act on alternatves along wth arses, and ths can only be resolved by appropratng. Our jontly necessary condtons uncover, n a very general way, the sort of compettve settng that s needed for compettve advantage Mnmum Total Value. Our characterzaton focuses on whether the value to be dstrbuted among agents, V, s suffcent for the exstence of FSDs n whch agent approprates 0,.e., whether mn = 0. The way we approach ths s to calculate the smallest total value consstent wth the exstence of FSDs n whch approprates 0, and then smply compare V to ths smallest value. Suppose that s an FSD n whch does not approprate value;.e., = 0. If = 0, the stablty condtons, (3.2) and (3.3), mply must satsfy and for all G ncludng j N j = V (4.1) j G j v G (4.2) 12 Although beyond the scope of ths paper, note that ths example, and ts network externalty extenson, mght be employed to thnk about how a frm mght, or mght not, beneft from ntroducng a product wth network externaltes or complementartes wth others products. These externaltes are valuable, and so offer the frm the possblty of value appropraton. However, realzaton of the benefts of the externalty requres the partcpaton of others. As the example shows, the mpact of ths may be to blunt competton n a way that makes t less effectve n fosterng value appropraton. Thus, a frm s ntroducng a product of ths knd may create value, but make competton less mportant and barganng more mportant n determnng who approprates that value. Consderatons of ths sort fgure promnently n the mplementaton-orented dscusson n MacDonald and Ryall (2003b).

11 1328 Management Scence 50(10), pp , 2004 INFORMS Condton (4.2) s smply (3.4), takng account of the assumpton that v G v G, and the fact that when = 0, j G j = j G j. Intutvely, when = 0, any group that s not nterested n actng on ts alternatve wth s also not nterested n actng on ts alternatve wthout. Because = 0, (4.1) requres that V be dstrbuted among players other than. Thus, whether there s any FSD n whch approprates 0 bols down to whether t s possble to dstrbute V among agents n N whle satsfyng both (4.1) and (4.2). To answer ths queston, defne the -mnmum total value by { mv mn j for all G ncludng } j v G j N j G The -mnmum total value s the smallest value that can be dstrbuted among N wthout makng the alternatve of actng on ts own attractve for any group ncludng, despte = 0. Whether agent has compettve advantage bols down to whether the value that can be dstrbuted, V, s great enough to be dstrbuted n such a manner. Proposton 3. Gven a strategc nteracton, N v, has compettve advantage f and only f mv exceeds V : > 0 mv >V. mn Proposton 3 exposes the two opposng forces determnng whether approprates value. To see what these forces are, return to (4.1) and (4.2). The better the alternatves avalable to groups ncludng, the more value must be dstrbuted to agents to encourage them to forego these optons f = 0. Ths puts upward pressure on the least created value that can be stably dstrbuted when = 0. On the other hand, the more value there s, the easer t s to fnd a way to dstrbute t so as to preserve stablty despte = 0. Indeed, because mv s fnte, there s always some level of V that results n s not havng a compettve advantage. In ths sense, no matter what they look lke, the structure of alternatves avalable to agents can never, by themselves, yeld compettve advantage Structure of Competton. Proposton 3 s a complete descrpton of the features of a strategc nteracton that result n an agent havng compettve advantage. Loosely, an agent has compettve advantage when, and only when, hs falng to approprate would necessarly unleash compettve forces that can never be satsfed f he does not approprate. We can say somethng about the nature of these forces. To see the dea, recall Example 5. In that example, competton among buyers gave F 2 compettve advantage. What features do these competng groups have? Frst, each can produce more value wth F 2 than wthout hm,.e., $2 versus zero. Ths opens up the prospect of these groups competng for F 2. Second, no other agent s ncluded n both groups, so that F 2 s appropratng s the only way ths competton mght be resolved (more on ths below). Proposton 4. Gven a strategc nteracton, N v, agent has compettve advantage only f there s a collecton of dstnct groups, G G 1 G 2, each of whch excludes agent and does not nclude every other agent, wth the features 1. Potental competton. There are at least two groups n G that are strctly more valuable f s ncluded: for some G and G n G, both v G+ >v G and v G + >v G 2. Unqueness. No agent s ncluded n every group n G. The ntuton for these condtons s straghtforward and related to the famlar noton that an agent s makng a unque and valuable contrbuton wll lead to value appropraton. The frst condton states that among the groups excludng agent, there must be at least two that are more valuable f s ncluded. The groups G and G are then canddates for competng for n exactly the manner descrbed above. For ths reason, havng just one such group ensures no compettve advantage. Thus, the frst condton may be nterpreted as sayng that compettve advantage requres the potental of competton for. The second condton follows from the fact that f there s an agent j that s ncluded n every one of the groups that mght compete for, the competton s effectvely for the par and j. When ths occurs, and j are, n effect, n a pure barganng stuaton, and dvde whatever value competton allows them jontly to approprate; thus, nether has compettve advantage. 13 Proposton 4 suggests an nterestng observaton. If agent has compettve advantage, there may be many ways n whch competton ensures ths. That s, were agent not to approprate, there can be many dfferent collectons of groups, havng the features descrbed n Proposton 4, that would compete for. In ths sense, there s generally no unque source of compettve advantage. 5. Applcatons We now turn to a par of applcatons n whch the role of competton s central. The frst applcaton employs our framework and results to provde nsghts about a famlar theme n strategy the connecton between nmtablty and compettve 13 MacDonald and Ryall (2003a) provde a closely related, but more specfc, proposton that enables these groups to be dentfed. In MacDonald and Ryall (2003b), we show how to employ the result to search for or evaluate new ntatves.

12 Management Scence 50(10), pp , 2004 INFORMS 1329 advantage. Competton s mportant n ths example because the possblty of mtaton s thought to nfluence value appropraton by stmulatng competton. Ths applcaton requres lttle structure beyond the coaltonal game framework set out above. However, many applcatons have more structure that can usefully be ncluded n the model to draw more specfc conclusons. To llustrate how such structure can be used, and the knd of conclusons that emerge, we develop a second applcaton, a model of nnovaton. In ths applcaton, competton among those who mght use an nnovaton affects how much value the nnovator can approprate Does Inmtablty Yeld Compettve Advantage? That value appropraton s ntmately related to ownershp of value-creatng resources that cannot easly be replcated by others s a wdely accepted dea n strategy. For example, accordng to Coulter (1998), If compettors can copy (mtate) each other, then a sustanable compettve advantage can t be developed and above-average profts can t be earned. Also, the mechansm through whch nmtablty s to operate s ts mpact on competton; see, e.g., Colls and Montgomery (1998, p. 32): Inmtablty s at the heart of value creaton because t lmts competton. Because our approach s desgned to reveal the way competton nfluences value appropraton, we now devote some attenton to mtaton and ts mpact on competton and compettve advantage. The frst step s to state clearly what mtaton means n the context of a strategc nteracton. Of the many possbltes, there are two that appear to capture the flavor of famlar examples. The frst defnton descrbes mtaton as embodyng two features an ablty to produce a product that all purchasers agree s equvalent to the mtated product and also an ablty to expand frm producton and delvery actvtes so that an mtator can compete for all the customers n the market. The latter mples that there are no dseconomes of scale, scarce management talent, etc., that mght lmt the mpact of havng an essentally dentcal product. Ths defnton of mtaton, whch we wll call unlmted product mtaton, s smlar to the Bertrand competton famlar from ndustral organzaton. It allows great scope for mtaton to mpact compettve advantage because t not only embodes the noton of smlarty of products, but also maxmzes ts compettve mpact by allowng an mtatng frm to compete for all customers. In ths sense, unlmted product mtaton s 14 In both cases, our model has a lot to say. However, presentng ths materal n detal s beyond the scope of ths paper. Thus, we wll stck to the smple setups and results that can be stated and explaned concsely. an amalgam of mtatve capablty and other features of frms technologes. Unlmted product mtaton can be descrbed n the context of a strategc nteracton by specfyng that () the set of agents, N, conssts of a set of customers, N C, and a set of at least two frms, N F (.e., N = N C N F ), and () f customers have access to one (or more) frm s product, then because the products are mtatons of one another, no extra value s created by gvng them access to another frm s product. 15 Formally, unlmted product mtaton exsts f, for any group G ncludng all the customers (.e., N C G) and at least one frm (.e., G N F, we have v G = V. Unlmted product mtaton mpacts value appropraton because t nfluences how frms compete for customers partcpaton. That s, f the dstrbuton of value allows some frm to approprate too much, any other frm can attract ts customers by offerng to approprate less, leavng more to be approprated by customers. Because any frm can serve all the customers n the market, and customers value all products equally, t follows that each frm s margnal product s zero; the loss of any one frm does not harm value creaton at all. Thus, Proposton 1 the necessty of postve margnal product for compettve advantage delvers our frst result on mtaton. Proposton 5. Gven a strategc nteracton, N v, wth unlmted product mtaton, no frm has compettve advantage. That s, f 1. N = N C N F, where N C and N F has at least two elements; and 2. for all G such that N C G and G N F, we have v G = V ; then N F mples mn = max = 0. Unlmted product mtaton s a very strong verson of mtaton n that t goes beyond the dea that customers see frms products as equvalent by also makng a set of mplct assumptons about frm technology and organzaton. As Proposton 5 shows, mtatve capablty, together wth the absence of technologcal or organzaton factors that mght lmt frm growth, wpes out compettve advantage. However, the fact that these sze-lmtng features are rarely absent rases the queston of whether mtatve capablty alone s really a threat to compettve advantage. Our second defnton, whch we call capablty mtaton, s also a very strong defnton of mtaton. It dffers from unlmted product mtaton n that t dstngushes the capablty to replcate another frm s product from the ablty to expand output. Capablty mtaton arses when the value created by addng one 15 For smplcty, we assume all frms are mtators. All that s requred for our results s that there are at least two mtators.