A b s t r a c t

In order to reach the goal of frictionlessinformation sharing, firms form differenttypes of business-to-business (B2B) market-places that facilitate transactions amongtrading partners along any supply chain.Forecasts of the amount of revenue thatwill be generated over these technologyplatforms reach billions of dollars. Our aimin this paper is to present a novel approachto look at the formation of networks offirms. Unlike the previous research thatanalyses B2B networks after they areestablished, we look at the dynamics ofhow they come into existence and wherethey can be expected to converge. We usetools from non-cooperative game theoryand strategic network formation literatureto study the evolution of B2B marketplaces.The paper provides conditions under whichan exchange-based B2B is preferred to apeer-to-peer (P2P) network. It also indicatesthe importance of asset specificity in thestrategic link formation and shows ways toincorporate this effect in the framework itattempts to establish.

A u t h o r s

Kerem Tomak(Kerem.tomak@bus.utexas.edu) is anAssistant Professor in the MSISDepartment of the Red McCombsSchool of Business, where he teachesDigital Economy and Commerce.His primary research examines theeconomics of information systems, andrecent projects have examined thearena of online auctions and onlinepurchasing behaviour. Dr. Tomak’sresearch activities fall broadly into threeareas: pricing and market segmentationin data networks, online auctions andsoftware agents in network resourceallocation, concentrating on topicssuch as application service providers,metamediaries, and economic analysisof information goods.Mu Xia (mxia@uiuc.edu) is an assistantprofessor of Information Systemsin the Department of BusinessAdministration at the Universityof Illinois at Urbana-Champaign.His research interest focuses on theeconomic aspects of e-commerce,especially B2B e-commerce. He receivedhis PhD from the University of Texas atAustin.

INTRODUCTION

For the past several years we havewitnessed the emergence of variousbusiness models, successful or unsuc-cessful, which created a lot ofexcitement about the technologyunderlying electronic business. Assystems and businesses matured, firmswithin and across industries started touse the Internet in places where theybelieved efficiency gains would bemaximal. One particular area in whichwe have seen exponential increase isbusiness-to-business (B2B) electroniccommerce (EC). Several analystsforecast B2B EC to reach a level of bil-lions of dollars by 2005. JupiterResearch reports that B2B Net Marketinfrastructure spending in the USwill grow from $2.1 billion in 2000to $80.9 billion by 2005. In spite ofthis and similar forecasts, over the pastcouple of years, we saw a dramaticrevision of the numbers. For example,while Gartner Group forecasts world-wide B2B Internet commerce to swellto $5.9 trillion by 2004, that is downfrom the $7.3 trillion Gartner forecasta couple of years ago.

A conclusion one can clearly deductfrom these observations and forecastsis that B2B EC is in a constant flux.In the initial stages of B2B EC,independent exchanges were fore-casted by a majority of the analysts tobe the most successful B2B model.Today, we are witnessing the move

towards privately owned, exchange-based B2B networks (e.g., Walmart’sprivate exchange) or consortia backedexchanges (e.g., Covisint), althoughthere are independent exchanges thatare relatively successful (e.g., RetailEx-change.com). EDI is still widely usedby large corporations and Web-EDIis taking its place among small- andmedium-scale enterprises.

Most of these transactions are cur-rently handled over private or neutralthird-party exchanges and traditionalvalue added networks and EDI systemsintegrated with the Internet. Recently,several authors suggested peer-to-peer(P2P) networks for B2B solutions(e.g., McAfee 2000; Parameswaran etal. 2001) due to their decentralizedinformation management potential.The compelling reason behind such anapplication of P2P technology is thedecentralized structure that will helpcompanies everywhere to locate trad-ing partners on the fly and completetransactions swiftly, securely and effi-ciently without the need for any centralaggregator or facilitator.

In this paper we provide answers tothe following research questions:

• How do trading networks form inelectronic B2B environments?

• What network types can be expectedto form in the long run?

We start by discussing the value prop-osition of electronic marketplaces. We

Evolution of B2B Marketplaces

KEREM TOMAK AND MU XIA

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then provide an economic modelling approach that mayadvance our understanding of which electronic struc-tures constitute potential convergence points and hencesustainable business models for B2B marketplaces.

VALUE PROPOSITION OF ELECTRONIC MARKETPLACES

B2B trade is extremely complex involving countless trans-actions along the supply chain. Demand triggered by acustomer may generate hundreds of B2B transactions thatoccur before the purchase is completed. Furthermore,each transaction typically involves multiple parties beyondthe buyer and the seller including providers of insurance,inspection, escrow, credit, warehousing and transportation.The main goal of business automation is not only to givean electronic form to existing business processes and rela-tionships but also, more importantly, to help firms lay afoundation for establishing new relationships much moreefficiently.

There are several distinctive economic characteristics ofelectronic markets (Bakos 1991). If we regard both a pur-chasing firm and an individual customer as the consumer,electronic markets can reduce the costs of obtaining infor-mation about the prices and product offerings of alternativesuppliers as well as suppliers’ costs of communicatinginformation about their prices and product characteristicsto additional customers. Benefits of participating in anelectronic market increase as the number of individualmember firms increases, commonly known as the networkexternality effect (Katz and Shapiro 1985). If being amember of an electronic market requires a significantinvestment from their participants and hence becomes astrategic relationship, resulting switching costs may be toohigh.

Beyond these characteristics shared by both the con-sumer and business-oriented electronic markets, there arefeatures specific to B2B transactions that distinguishB2B from B2C markets. One such characteristic is assetspecificity. It refers to the relative lack of transferability ofassets intended for use in a given transaction to otheruses. Highly specific assets represent sunk costs that haverelatively little value beyond their use in the context of aspecific transaction. High asset specificity requires strongcontracts or internalization to protect the company fromthe threat of rivalry. This has a fundamental impact on theform of the electronic marketplace that is sustainable in thelong run. One would expect, for example, that a companypurchasing highly specific assets for production will nottrade over a third party owned (neutral) marketplace. Arecent study by Kauffman and Mohtadi (2002), addressesthe problem of incentive alignment for B2B e-procurementtechnology investments that permit inventory coordinationand operating cost control. They find that larger firmstend to adopt costlier, but more certain procurementtechnologies such as proprietary EDI. Smaller firms, on theother hand, tend to adopt less-costly procurement solutions

that entail greater supply uncertainties, such as open B2Bprocurement platforms like exchange-based B2B networks.In a related paper, Tomak (2000) describes conditionsunder which firms may choose to join a B2B marketplace.

There is little empirical work in the area of B2B market-places on the Internet. One reason for this may be thelimited availability of the data pertaining to the innerworkings of such digital platforms. Most of the firmsoperating such marketplaces keep the data confidential dueto the nature of the relationships among the trading parties.

Garicano and Kaplan (2000) posit that the key impact ofB2B EC is to change the costs of transaction via changing/improving processes, the nature of the marketplace,decisions, the degree of information incompleteness andthe ability to commit. They find little evidence that infor-mational asymmetries are more important in the electronicmarketplace they study than the existing physical ones.However, generalization of their conclusions to all types ofB2B marketplaces is questionable due to the characteristicsand size of the sample used in the study.

We approach the B2B structures as networks of relation-ships among participating companies. Due to the nature oftrade along the supply chain, each participating memberactually establishes a close relationship with the rest andmakes complementary EC investments. Although notpresented in this paper, our approach establishes a frame-work in which one can test the sensitivity of the networkforms to the existence of informational asymmetries. Thereis research under way by the authors of this paper whichlooks at the impact of information asymmetry on theincentives to join exchange-based B2B networks.

Intermediated vs. Peer-to-peer networks

Exchange-based B2B models are in essence a collection ofcentrally managed client–server networks which are highlyintegrated in order to make the transactions among them asflawless and fast as possible. As McAfee (2000) also pointsout, these exchanges have two main roles: aggregation andfacilitation. Their aggregation role is fulfilled by bringinga group of dispersed trading partners under the umbrellaof a virtual marketplace. They also facilitate transactionsby providing the necessary software tools and protocols.Hence, an exchange-based B2B network can be imaginedas a star-like structure as in Figure 1.

In P2P networks however, the client–server relationshipis partially if not completely abandoned. Napster’s tech-nology still centrally manages the directory and user infor-mation but the actual files reside on separate locations.Gnutella further decentralizes the network structure bytreating users as independent nodes among which theinformation needs to be transacted. P2P networking is away of sharing of computer resources and services by directexchange between systems. These resources and servicesinclude the exchange of information, CPU time, datastorage, and file transfer. Peer-to-peer computing takes

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advantage of existing desktop computing power and net-working connectivity, allowing clients to leverage theircollective power to benefit the entire network. In a peer-to-peer architecture, computers that have traditionally beenused solely as clients communicate directly among them-selves and can act as both clients and servers, assumingwhatever role is most efficient for the network. This reducesthe load on servers and allows them to perform specializedservices (such as billing, etc) more effectively (for details seefor example, Intel P2P Working Group http://www.peer-to-peerwg.org/whatis/index.html or Parameswaran et al.(2001)). A P2P network can then be pictured as a wheel-like network such as the one in Figure 1.

A MODEL OF B2B RELATIONSHIPS

Aside from the operations management literature, there is alimited number of papers in the IS literature addressingeconomic problems related to B2B marketplaces. Anexcellent survey in the B2B as well as the B2C area listing alarge body of literature in the economics of IS area can befound in Kauffman and Walden (2001). Dai and Kauffman(2001) also explore several online business models andthe adoption of purchasing firms. They posit that privateaggregating and negotiating mechanisms are being adoptedfor large quantity business supply purchases and publicmarket mechanisms are more often adopted when firmsface uncertain and high variance demand. Their study pro-vides support to our assessment of the linkage betweenasset specificity and the B2B network structure.

Nault and Dexter (2000) look at the investments to inte-grate electronic marketplaces in the buying and sellinginfrastructure of firms from a strategic point of view andsuggest that a pure strategy Nash equilibrium in invest-ments is not assured in such environments. Based on their

Figure 1. Star like networks mainly represent exchange-based B2Band wheel networks correspond to peer-to-peer structures.

models of information sharing, Seidmann and Sundararajan(1997) classify different forms of relationships betweenindependent – yet virtually integrated – companies. Fourprimary types of such relationships include EDI, vendormanaged inventory, continuous replenishment, andcategory management. They also show how retailers andother buyers can successfully contract to end up with morevalue through sharing information.

In a related paper, Yu and Chaturvedi (2001) study theproblem of what the structure of the B2B marketplace willbe. They base their model on Gehrig’s (1996) paper, whichtakes the number of participants in a particular networkstructure set exogenously, similar to the existing research inthis area. Furthermore, marketplaces in an industry aretreated as islands that consist of a number of firms setex-ante. A major difference between our work and theirsis that we take the network type as a side result of theequilibrium of a game that is played among the participantsin a market rather than assume it to be set already,exogenously.

In this paper, we use game theory as our main toolfor modelling. There are mainly two branches of gametheory that study strategic interactions among individualsor groups. Cooperative game theory, unlike its non-cooperative counterpart, allows for the existence ofenforceable binding agreements and also for side payments.Hence, fair allocation of costs or revenues becomes themain problem. In the context of our problem setting, thisapproach can be used to address questions such as ‘Howcan profits from a consortia-backed B2B marketplace beshared among the participants? What is a fair and envy-freeallocation to all the participants so that proper incentivesfor membership to the B2B marketplace can be given toall the suppliers and manufacturers in the industry?’ Oneapproach in the cooperative framework concentrates on thecosts of forming social and economic relationships (Hallerand Sarangi 2000). An excellent survey of this literature canbe found in Borm et al. (1994).

A large portion of the papers in the intersection of OMand IS literature, including this paper, use non-cooperativegame theory. Unlike the cooperative version, enforceablebinding agreements are assumed not to be possible.Individual incentives and strategic interactions become thecentre of attention. Non-cooperative games take players asindividual decision makers who base their decisions onopportunistic strategies that lead to desired outcomes. Thisapproach is more suitable for the type of problems thatinvolve individual firm decision making under uncertainB2B liquidity and potential for opportunistic use of thetrade platform. Several trade structures may also result fromthe relationships between suppliers and manufacturers.Examples include vertical integration, markets and networkforms. Kranton and Minehart (2000) apply the model pro-posed by Jackson and Wolinsky (1996) to a buyer–sellernetwork structure and compare economic welfare of such anetwork with vertical integration. They find that networkscan yield greater social welfare than vertically integrated

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firms when there are large idiosyncratic shocks in demand.They also show that individual firms have the incentive toform the network structure. An application of their findingsto B2B networks suggest that formation of industrial net-works are to the benefit of all parties involved especiallywhen the industry operates under high uncertainty, butthird party ownership may curtail this activity. Figure 2shows an example of a graph that represents a supply chainstructure.

The direction on an arrow implies that there is a linkin that direction to the node it points to from the node itoriginates. Furthermore, the direction indicates the path ofinformation flow. Most of the communication that takesplace on B2B networks is bi-directional. However, thereare examples, such as electronic catalogues that suppliers ormanufacturers use to inform their customers about theirproduct offerings and prices, in which the direction ofinformation on the B2B platform is one-way. By two-waycommunication, we mean that data is transferred from anorigin to a destination and back as in a proprietary networksetup like an EDI system.

In our example, suppliers 1, 2 and 3 do not have anyconnections with the rest of the network structure as thereis no arrow pointing outwards from them to the next nodethey are connected to while it is possible for the rest ofthe network to link to them. This situation may arise ifa supplier is small and the only way it can attract customers

is by putting ads on specialized catalogues and expectingcustomers to visit it. Hence these suppliers can beenvisioned to lack technology-based links to the sub-contractor or simply have chosen not to link to thesubcontractor since it may be too costly to them. Theburden of maintaining the link is on the subcontractor.On the other hand, Suppliers 4 and 8 have at least anEDI connection with their trading partners to allowfor two-way communication between them. In order tokeep the exposition simple, we assume that the links arebi-directional. All notation used in this article is shown inTable 1.

We let N = {1, . . ., n} n ≥ 3 represent the set of playerswith locations at the nodes of a graph before the graph isformed. We assume that the reason why the links areformed is the gains from information sharing by doing so.A typical supply chain information flow is a good examplefor this setup. A strategy of a player i ∈N is a vectorsi = {si,1, si,2, . . ., si,i − 1, si,i + 1, . . ., si,n} where si, j = 0 if i doesnot have a link with j and si, j = 1 otherwise. The set ofall strategies of player i is given by Σi. In this setting, alink si,’j is represented by an edge starting at j with thearrowhead pointing at i. For example, in Figure 2,ss3,cs = ss2,cs = ss1,cs = 1.

Literature on non-cooperative strategic network forma-tion, such as the one we have just depicted, deals with theflow of information from one agent to another and looks at

Figure 2. A supply chain network structure and its graph form. Any supply chain relationship can be reduced to its graph form andrepresented as a stage in a finite horizon dynamic network game.

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Table 1. Notation used in the paper

N = {1, . . . n} n ≥ 3 set of players with locations at the nodes of a graph.si = {si,1 , si,2 , . . . , si,i − 1, si,i + 1, . . . , si,n} Strategy of player i where si, j = 0 if i does not have a link with j and si, j = 1 otherwise.Σi Set of all strategies of player i.Li Set of players with whom i maintains a link.L̄̄i Set of all players whose information i has access to either through a link or through a sequence of links

via an intermediary.c > 0 The cost to each player of forming the link.| L M

i | Number of links that firm i establishes with exchange based B2B networks.| L D

i | Number of direct links that firm i establishes with buyers.cs Cost to the supplier firms for forming a link with the buyers.cb Cost to the buyer firms for forming a link with the suppliers.cm Cost of a link with a marketplace.

issues such as information transmission with unreliablelinks.

We now define Li = {k ∈N | si,k = 1} as the set of playerswith whom i maintains a link. It is also important to findout all players whose information i accesses either througha link or through a sequence of links with an intermediaryin between. Let such a set be given by

L̄̄i = {k ∈N | either si,k = 1 or there exists jl ∈N (l = 1, . . . ,m) such that si, j1

= sj1, j2= . . . = sjm,k = 1}

Finally, the payoff to each player is given by Πi =| L̄̄i | − |Li | c where | L̄̄i | measures the benefit that a player ireceives from his/her links and |Li | c measures the costassociated with maintaining them with c > 0 being the costto each player of forming the link. This particular setup ofthe profit function implies that the benefit to the playerincreases by the number of links he/she forms with otherfirms. Using this approach, we are able to account for thenetwork externality effect that is inherent in most ofthe network forms, especially in B2B relationships (see forexample, Dai and Kauffman (2001)). However this benefitis weighed by the cost of actually maintaining the links.Hence the more the number of links, the better; includingthe indirect ones, net of costs of establishing the directlinks. Finally, we assume that Πi is strictly increasing in|L̄̄i | and strictly decreasing in |Li |. This assumption impliesthat increasing the number of links to other firms adds tothe profits of the firm. It also implies that increasing thenumber of links that needs to be maintained by the firmhimself/herself adds to the cost and hence decreases theprofits.

Given this formulation, these links can be approached intwo ways. One can take the links as one of EDI or B2Bmarketplace link types with their associated costs or takethem as the aggregate cost of establishing a relationshipbetween a buyer and a supplier. In this paper, we take thelatter approach. Furthermore, there may be several formsof network structures. The most common ones are star orwheel networks given in Figure 1. Star networks can be

interpreted as public or private networks with the centreformed by either a firm, a third party or a consortium.Wheel network structures can be interpreted as peer-to-peer (P2P) networks. A network structure is Nash ifno individual link owner benefits by deviating from theexisting network structure he/she belongs to by severinghis/her link or by adding another link. The uniqueness ofthis approach comes from the treatment of the evolutionof network forms in the B2B context. We let the B2B rela-tionships form endogenously as opposed to the previousapproaches in the IS literature, which assume that networksare formed a priori or investment in networks is consideredto be over a pre-designed network structure (Nault andDexter, 2000).

If all the players in the game described above try tomaximize their individual payoffs, the resulting equilibriumis described by the following proposition:

Proposition 1: Starting with a random network structurebetween buyers and sellers, let them decide on whether tomaintain or sever a link from their set of links. If this processconverges to a state where none of the parties involved wouldrather change their existing links, the resulting exchange-based B2B (private or public) network will take the form of astar-like Nash network.

This Proposition implies that if the firms act selfishly andform their links with each other on the basis of increasingtheir information sharing capabilities, an exchange-basedB2B network structure can be supported in steadystate. Once it is formed, no firm would have any incentivesto deviate to other networks or connect to each otherdirectly. One can easily envision such conglomerateexchanges emerging in every industry which valuessharing information along different supply chain archi-tectures. eBay is an excellent example in the value chainside. With 100,000 trading partners and one billiontransactions processed annually, GE Global eXchangeServices (GXS) is a good example of such a conglomeratein the B2B side.

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The cost to the seller and buyer are different when theyform links with each other or through a marketplace due tothe asset specificity of the processes each gets involved in.Let cb be the cost to the buyer firms for forming a link withthe suppliers. For both the buyer and the seller, cost of alink with a marketplace is given by cm. For the suppliers,direct link cost is assumed to be cs. We rewrite the payofffunction to incorporate these changes as follows

Πi,b = | L̄̄i | − |LDi | cb − cm |LM

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Πi,s = | L̄̄i | − |LDi | cs − cm |LM

i |.

Here, |LMi | corresponds to the number of marketplaces

that the buyer (supplier) firm establishes a link with and|LD

i | is the number of direct links to the buyers (suppliers).In order to understand how asset specificity plays animportant role, let the cost of the link be directly pro-portional to the cost of acquiring the product. The moreasset-specific the production process is, the more the cost ofthe link to the marketplace for the buyer. This is because ofthe fact that the risk a buyer incurs by going to the market-place for highly asset-specific processes is quite high.Assumption on the payoff function implies that as |LD

i |increases, profit falls. Hence, we expect that |LD

i | decreasesand |LM

i | tends to zero for highly asset-specific processesof the buyer. Similar observation holds for the suppliers.

Proposition 2: High asset specificity leads to a wheel-likeNash network at the steady state whereas low asset specificityresults in a star-like Nash network.

This is a rather insightful result since it suggests that peer-to-peer networks have a higher chance of succeeding inestablishing connections among trading partners for highlyasset-specific processes, whereas exchange-based B2B net-works play more of a role in facilitating transactions for lowasset-specific tasks.

CONCLUSION

Motivated by the recent business model transformations inexchange-based B2B network structures, our researchfocused on the endogenous formation of B2B relationships.In particular, we studied the strategic choice of a buyer orseller, of linking to a marketplace or participating in a peer-to-peer network. Although our model is representative ofthe establishment of actual B2B exchanges, we recognizethat the results are limited to the setting we consider. Inour model, links are formed because of the gains frominformation sharing. Although this assumption is necessaryto provide focus to our study, in reality, there may be manyreasons why links are formed. A link to a marketplace forprocuring indirect materials such as office supplies does nothave any strategic context other than cutting costs of suchan activity. Another restriction comes from the homo-

geneity of costs among the buyers and sellers. Obviously,costs of establishing B2B links vary for different suppliers ofheterogeneous sizes. The assumption of a two-way com-munication channel does not play a significant role in ourmodel although assuming one instead of two-directionallinks would change the nature of the equilibrium networkstructure (see Bala and Goyal (2000)).

Our results show the significance of letting the B2Bnetwork relationships form endogenously as opposedto exogenously. Previous literature has predominantlyassumed the network structure given, which limited ourunderstanding of how exchanges and trade networks form.We contribute to the existing literature by introducing acomplementary view of B2B exchanges and networks. Inthe context of non-cooperative relationships, it is importantto look at a similar game with either heterogeneous playersand/or informational asymmetries among them. Thisextension will make the model more realistic and lead totestable hypothesis if relevant data can be found in thefuture. In order to study consortia-backed exchanges, oneneeds to look at cooperative rather than non-cooperativesettings. This route would help us understand and deviserevenue sharing models for B2B exchanges as well as linkthe network forms in equilibrium with concepts such asfairness and governance. Another promising extension isthe study of the impact of upstream cooperation anddownstream competition – such as the case of Covisintexchange – on the sustainability of exchange based B2Bnetwork form.

ReferencesBakos, Yannis (1991) ‘A Strategic Analysis of Electronic

Marketplaces’, MIS Quarterly 15(3), 295–310.Bakos, Yannis and Nault, Barrie (1997) ‘Ownership and

Investment in Electronic Networks’, Information SystemsResearch 8(4), 321–41

Bala, Venkatesh and Goyal, S. (2000) ‘A Non-cooperativeModel of Network Formation’, Econometrica 68(5),1181–230.

Borm, P., van den Nouweland, A. and Tijs, S. (1994)‘Cooperation and Communication Restrictions: A Survey’,in Gilles, R.P. and Ruys, P.H.M. (eds), Imperfections andBehavior in Economic Organizations, Boston: KluwerAcademic Publishers.

Dai, Q.Z. and Kauffman, R.J. (2001) ‘Business Models forInternet Based E-Procurement Systems and B2BElectronic Markets: An Exploratory Assessment’,Proceedings of the 34th Hawaii International Conferenceon System Sciences.

Debreu, G. (1969) ‘Neighboring Economic Agents’, LaDecision 171, 85–90.

Garicano, Luis and Kaplan, Steven N. (2000) ‘The Effects ofBusiness-To-Business E-Commerce on Transaction Costs’,Working Paper 8017, National Bureau of EconomicResearch.

Gehrig, T. (1996) ‘Natural Oligopoly and Customer Networks

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in Intermediated Markets’, International Journal ofIndustrial Organization 14, 101–18.

Haller, Hans and Sarangi, S. (2000) ‘Nash Networks withHeterogeneous Agents’, Working Paper, Dept. ofEconomics, VirginiaTech.

Jackson, Matthew and Wolinsky, A. (1996) ‘A Strategic Modelof Social and Economic Networks’, Journal of EconomicTheory 71(1), 44–74.

Katz, Michael and Shapiro, Carl (1985) ‘NetworkExternalities, Competition and Compatibility’, AmericanEconomic Review 75(3), 424–40.

Kauffman, Robert J. and Mohtadi, Hamid, (2002)‘Information Technology in B2B E-Procurement: Open vs.Proprietary Systems’, Proceedings of 35th HawaiiInternational Conference on System Sciences.

Kauffman, Robert J. and Walden, Eric A., (2001) ‘Economicsand Electronic Commerce: Survey and ResearchDirections,’ International Journal of Electronic CommerceSummer.

Kranton, Rachel E. and Minehart, Deborah F. (2000)‘Networks Versus Vertical Integration’, Rand Journal ofEconomics 31(3), 570–601

McAfee, Andrew (2000) ‘Napsterization of B2B’, HarvardBusiness Review November-December, 2–3

Nault, B., and Dexter, A.S. (2000) ‘Investments in ElectronicMarkets’, in Kalvenes, J. and Mendelson, H. (eds),Proceedings of the Fifth INFORMS Conference onInformation Systems and Technology (INFORMS CIST),San Antonio, TX.

Parameswaran, M., Susarla, A. and Whinston, A. B. (2001)‘P2P Networking: An Information Sharing Alternative’,IEEE Computer July, 1–8.

Seidmann, A. and Sundararajan, A. (1997) ‘Building andSustaining Interorganizational Information SharingRelationships: The Competitive Impact of InterfacingSupply Chain Operations with Marketing Strategy’,Proceedings of ICIS’97.

Tomak, Kerem (2000) ‘On the Incentives to Join a DigitalMarketplace’, Working Paper, University of Texas atAustin.

Yu, L. and Chaturvedi, A. (2001) ‘Competition Between B2BElectronic Marketplaces: Differentiation, Pricing Strategy,and Industrial Structure’, Proceedings of the 7th AMCIS,2001.

TECHNICAL APPENDIX

Proposition 1

Starting with a random network structure between buyersand sellers, let them decide on whether to maintain orsever a link from their set of links. If this process convergesto a state where none of the parties involved would ratherchange their existing links, the resulting exchange-basedB2B (private or public) network will take the form of astar-like Nash network.

Proof

We will provide a sketch of the proof. For details, see Balaand Goyal (2000). Let f (k) = | L̄̄i |, g(k) = |Li |. Note firstthat due to the assumption on the payoff structure,

f (n) − g(n − 1)c > maxx ∈ [0,n − 2]{f (x + 1) − g(x)c}. (1)

To show that this implies the equilibrium network structureis a star-like Nash network, we start by assuming that theinitial random network is such that every pair in the net-work is connected either directly or indirectly to each otherin at most one way and that it is Nash. This implies thatthere is only one path between every pair in the networkand deleting a link would isolate at least one player in thenetwork. Furthermore, there is a unique path for each pairin the network. Multiple paths are not allowed. Now,let i and j be firms such that si, j = 1. We claim thatmax{sj, j ′ sj ′, j} = 0 for any j ′ ∉ {i, j}. If this did not hold,then i can delete his/her link with j and form one withj ′ and receive the same payoff, which contradicts the Nashassumption of the initial network. Hence, any agent withwhom i is directly linked, cannot have any other links.Since, by assumption, every player is linked to each other ina unique way, i must be the centre of a star.

To show the convergence, let each player move sequen-tially and decide on whether to keep an existing link, buildone or sever it. Note that if the resulting network is notempty, it must be that each player is uniquely linked toeach other. As identity (1) holds, a firm’s best response isto form links with all the others and hence a star-network isformed.

Proposition 2

High asset specificity leads to a wheel-like Nash networkat the steady state whereas low asset specificity results in astar-like Nash network.

Proof

As |LMi | tends to zero for highly asset specific processes by

the argument given prior to the Proposition, the payofffunction for the buyer reduces to

Πi,b = | L̄̄i | − |LDi | cb.

Let cb > cs and f (k) = | L̄̄i | , g(k) = |Li | . Then for thebuyer, due to high asset specificity,

f (n) − g(1)cb > f (n) − g(n)cb.

But since f (n) − g(1)cs > f (n) − g(1)cb it is also beneficialfor the seller to establish a unique direct link with the

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buyer. Since each firm values linking to as many firmsas possible but prefers only direct links with his/herimmediate neighbour, a wheel type network arises inequilibrium.

If the process has low asset specificity, cb = cs and the pay-off function for the buyer is

Πi,b = | L̄̄i | − |LDi | cb − |LM

i | cm.

If cb = cs, by Proposition 1, the equilibrium network is ofstar type. If cm ≠ cb, then either |LM

i | or |LDi | tend to 0 and

again, by Proposition 1, we have a star-like Nash networkas the equilibrium of the game.

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