Open Source Software: Free Provision of Complex Public Goods

Transcription

1 Open Source Software: Free Provson of Complex Publc Goods By James Bessen* WORKING VERSION 5/01 Abstract: Open source software, developed by volunteers, appears counter to conventonal wsdom about prvate provson of publc goods. Standard theory holds that wthout property rghts (or excludablty), free-rdng nhbts prvate nvestment n non-rval goods such as nformaton and software. But complex open source products challenge commercally-developed software n qualty and market share. I argue that the complexty of software changes the results. For complex goods under asymmetrc nformaton, open source developers self-select, offsettng free-rdng losses. But commercal frms lack nformaton necessary for effectve provson. I compare dfferent forms of provson and dfferent property rghts. Strong property rghts can lmt provson of complex publc goods. JEL codes: H41, L22, L86 Keywords: Software, Publc Goods, Informaton Goods Research on Innovaton Jbessen@researchonnnovaton.org *Thanks for helpful comments from Carlss Baldwn, Karm Lakhan, Justn Johnson, Lawrence Lessg, Jean Trole, Erc von Hppel, Jason Woodard and partcpants at the Harvard Busness School free lunch semnar. Ths research s supported by Research on Innovaton. All errors are the author s responsblty.

2 1 - Open Source Software: - Bessen - 5/01 I. Introducton On frst examnaton, open source software seems paradoxcal. Open source software s a publc good provded by volunteers the source code used to generate the programs s freely avalable, hence open source. Networks of thousands of volunteer programmers have developed wdely used products such as the GNU/Lnux operatng system and the Apache web server. Moreover, these are hghly complex products and they are, arguably, of better qualty than competng commercal products, suggestng that open source provson may be hghly effcent. Ths appears to counter the common economc ntuton, supported by a large lterature, that prvate agents, wthout property rghts, wll not nvest suffcent effort n the development of publc goods. As Arrow [1962] argued about nformaton goods generally, under-nvestment arses because each agent faces a free-rder problem or publc externalty. Although each programmer realzes some beneft from her own development effort, she gans nothng (gnorng altrusm) from the beneft that all the other consumers realze from her software. Snce her effort s guded only by her prvate beneft, she nvests less than the socally optmal amount. As Coase [1960] famously argued, property rghts allow frms to nternalze such externaltes as long as transacton costs are zero. A frm that develops a propretary software product obtans profts from all of ts customers and so t may nvest more. In a large market wth many customers (as opposed to, say, a blateral barganng stuaton), the market centralzes nformaton on the demand for smple commodtes, reducng transacton costs and permttng a greater level of prvate provson. Ths paper argues, however, that software and many other nformaton goods are not usually smple commodtes. Instead, software s a complex product, meanng a product wth many features that work together. Because consumers have dfferent preferences for each feature n a complex product, they use dfferent combnatons of features. Ths creates a problem relatve to smple models because, n effect, the customer consumes only a specfc nstance (the useproduct ) of the general product the frm sells. The frm sells a product wth M optonal features that may or may not be used wth each other. Ths represents only one s of nterest to any gven consumer. M 2 dfferent use-products, of whch Ths dstncton creates a real economc dfference when the frm faces a cost, even a slght cost, for each use-product. And ndeed, the qualty of software depends on the extent to whch dfferent use-product combnatons are tested and debugged. Because the features n a complex software program nteract wth each other, each use-product must be ndvdually tested to ensure

3 2 - Open Source Software: - Bessen - 5/01 that t works. Yet frms cannot feasbly test all possble use-products because the number of possble combnatons s astronomcal. 1 The frm faces an nformaton problem. If the frm knew n advance whch use-products consumers would actually use, t could feasbly test only those combnatons. Large markets reveal aggregate demand, but even large markets do not reveal ths nformaton. In effect, a frm may sell mllons of copes of a complex software product and nevertheless face a myrad of small markets for dfferent use-products, each wth ts own demand. But the transacton or barganng costs become prohbtve to obtan ths demand nformaton for thousands of tny markets. Hence frms must offer fewer features, cut product qualty, or both. Property rghts fal to nternalze the publc good externalty wth complex products. On the other hand, wth open source software, ndvdual agents who both produce and consume can use ther prvate nformaton to advantage. Agents who place suffcently hgh value on the software wll test, debug and enhance ther own use-product. In a market wth both commercal software and open source developers, as product complexty rses, the market share addressed by open source developers also rses. For hghly complex products, even monopoly frms wll fal to provde software, but open source provson stll occurs. Despte losses assocated wth free-rdng, self-selecton can generate more complete provson than wth propretary software, resolvng the apparent paradox. But open source development s ncompatble wth some property rghts, n partcular, wth patents. Patent-holders have ncentves to block entry by open source developers and patent lcensng s ncompatble wth open source lcensng. Thus strong property rghts do not unambguously mprove the provson of complex publc goods. Lerner and Trole [2000] present a model of open source that explores the role of reputaton n motvatng software developers. Harhoff et al [2000] consder other ncentves for open source. Johnson [2000] presents another model that explores the possble falure of open source development that can arse f developers wat to see f other developers create the product frst. Ths paper complements these n that the focus here s not on the orgnal development of a new product, but rather on enhancng, testng, and debuggng. Testng and debuggng are less lkely than codng to mprove an engneer s reputaton and watng problems are less severe wth complex 1 If a product had 100 ndependent features and each combnaton took only one second to test, then the job could not be fnshed before the sun s predcted to swallow the earth even f every human currently alve spent every second untl then testng.

4 3 - Open Source Software: - Bessen - 5/01 products. Testng and debuggng requre codng, of course, but they typcally account for most of the development cost and hence most of the free-rdng problem. The provson of complex nformaton goods s a general problem, however, ths paper specfcally explores just the case of complex software. Software has several dfferent possble property rghts (trade secrets, copyrght, and patents) and several dfferent forms of provson (commercal packaged software, custom programmng, self-development, and open source development). The paper frst develops a model of a smple good provded n these dfferent ways. Then I extend ths model to complex products, lookng both at the extent of provson and strategc nteracton between dfferent types of provders. II. Background Software products are afforded four man types of ntellectual property protecton: 1. Trade secrecy. Software developers wrte source code that s compled nto bnary object code to produce an operable product. Snce reverse-engneerng object code s mpractcal, commercal frms keep the source code prvate and dstrbute only the object code. Employee confdentalty agreements, non-dsclosure agreements, common law and, n some cases, copy-protecton devces all support ths trade secrecy, makng the object code excludable. 2. User lcenses. Software developers requre customers to sgn lcense agreements that prohbt or control the re-dstrbuton of the product. 3. Copyrght. Commercal software s copyrghted, preventng drect duplcaton. After legal developments of the 1980 s, copyrght allows compettors to ntroduce smlar products that are not complete mtatons. 4. Patents. Snce the md-1980 s, software deas have been patentable n the U.S. Patents prevent the use of competng products that contan nfrngng deas. Commercal software products use trade secrecy, user lcenses, copyrght, and sometmes patents to protect ther products. Open source software can co-exst wth commercal software that s protected by user lcenses, copyrght and trade secrecy. However, I assume that patent protecton

5 4 - Open Source Software: - Bessen - 5/01 prevents open source provson a patent-holder can elmnate competng open source products. And patent lcensng s ncompatble wth open source lcensng. 2 Open source developers do not use trade secrecy they reveal ther source code, hence open source. Open source developers do, however, nsst on user lcenses. A common user lcense s the GNU General Publc Lcense (GPL) developed by Rchard Stallman [GNU Project]. Ths lcense permts the free dstrbuton of source code, guaranteeng users access to the product at no drect cost. But t also nssts that modfcatons and enhancements to the source code should also be freely dstrbuted. Ths type of lcense s called vral because t nfects modfcatons and enhancements, ensurng that they, too, are free. Other open source lcenses do not requre free re-dstrbuton of all modfcatons (e.g., the Apache lcense), however, strong communty norms ensure that almost all modfcatons to base products are made freely avalable. 3 Ths vral feature s sgnfcant, because open source advocates clam that ths provdes a substantal advantage n developng complex software products of hgh qualty. In fact, packaged software products have become much more complex over tme. Competng software frms, attemptng to reach ever-larger markets, engage n feature wars, addng large numbers of new features to product revsons, encouragng upgrades and hopng to ncrease market share. The result s an ntense pressure to add new features. Ths growng complexty s evdent n fve Mcrosoft product upgrades that occurred durng the late 80 s and early 90 s [Cusumano and Selby, 1995, p. 224 and 246]. The number of lnes of source code n each product grew substantally from one verson to the next, the ncreases rangng from 31% to 109%. As noted above, a product wth many features has combnatoral possbltes that tax the testng and debuggng processes [see Cusumano and Selby, 1995, p. 310 for Mcrosoft s verson of ths complexty problem]. In response, software frms try to strctly lmt features. Products are bult usng structured code and object-orented regmens that help reduce bugs and also make them easer to locate once they are observed. Frms also use a wde varety of testng technques, ncludng automated testng [Cusumano and Selby, 1995, chapter 5]. And they provde partally debugged code to lmted groups of customers for beta testng [Cusumano and Selby, 1995, p. 310] (although beta tests can also be used to pre-empt competton and for marketng purposes). 2 In practce, software patents have not been extensvely used to blockade markets, although ths use appears to be ncreasng. See Bessen and Maskn [2000]. There are cases where open source developers have been prevented from dstrbutng ther products under threat of patent nfrngement suts. 3 Communty norms also regulate other forms of behavor, for example, avodng forkng a product nto two, slghtly dfferent products wth dfferent groups of developers.

6 5 - Open Source Software: - Bessen - 5/01 Also, they do not test exhaustvely, rather products are released when bug dscovery rates fall below a specfed level. Nevertheless, complexty nsures that most of the cost of software arses from testng, debuggng and customer mantenance (that s, fxng bugs or provdng work-arounds after product release), not from the orgnal desgn and codng. One study found that testng, debuggng and mantenance account for 82% of the cost of software [Cusumano, 1991, p. 65]. In 1995, Mcrosoft employed 3,900 engneers for testng and customer support [Cusumano and Selby, 1995, p. 51]. Yet t only employed 1,850 software desgn engneers and these splt ther tme between ntal codng and debuggng. Open source advocates clam to have found a better way to manage ths complexty [Raymond]. Rchard Stallman, Lnus Torvalds and others developed a new methodology of software development that utlzed rapd communcaton over the Internet [Moody, 2001]. They released beta software very early, very frequently (sometmes daly releases) and nvolved a large number of other developers n debuggng and enhancng the product. Erc Raymond ctes ths as a key advantage: Gven a large enough beta-tester and co-developer base, almost every problem wll be characterzed quckly and the fx obvous to someone. Or, less formally, Gven enough eyeballs, all bugs are shallow. No closed-source developer can match the pool of talent the Lnux communty can brng to bear on a problem. Raymond goes on to cte the actual magntude of the contrbuton made by other developers to Fetchmal, the open source software he orgnally created. By 1999, 600 developers had made contrbutons to 115 versons of a program that was then 17,000 lnes of code (a relatvely small program) [Raymond, Johnson, 2000, p. 3]. That s, the rato of developers per lne of code for ths project was one to two orders of magntude greater than for commercal software development! Although many developers undoubtedly contrbuted only mnor changes, these mnor changes helped elmnate bugs and mprove product qualty. There s some evdence that products developed under open source may, n fact, acheve better qualty. A Unversty of Wsconsn study comparng Unx products found that open source products were notceably more relable than ther commercal counterparts, even though the latter had been around much longer [Martn et al, 1995]. A Datapro survey ranked Lnux hghest n customer satsfacton among operatng systems [Economst, 1998]. Several open source software products have rapdly captured substantal market share from commercal compettors, even for large, complex programs such as operatng systems. In 1999, the Internet Operatng System

7 6 - Open Source Software: - Bessen - 5/01 Counter found 31% of servers used Lnux [1999]; the Netcraft survey reports that as of January 2001, 59% of publcly-accessble web servers use the Apache open source product [Netcraft]. 4 Ths performance suggests that open source development of complex programs may have advantages that offset effcency losses assocated wth free-rdng. III. Smple Goods A. Modelng assumptons Software developers can provde ther products to customers n a varety of relatonshps. Software may be provded commercally (for sale to other partes), prvately (for the developer s own use), or for both prvate use and resale to other partes. Commercal software may be provded as a product va a market transacton or as a servce under contract to ndvdual customers (custom programmng). Self-developed software may be resold commercally or t may be made avalable to others under an open source lcense. Ths secton evaluates the provson of smple software under dfferent customer relatonshps and dfferent property rghts. Let there be N agents who are both consumers and developers. Ths assumpton smplfes the exposton, but as I note below, t mples an mportant qualfcaton. Each agent can potentally develop the product at a cost of c > 0. For smplcty, I assume ths cost s the same for all agents and ts value s common knowledge. The margnal producton cost of software s zero. Each of these agents also consumes the product. The value of consumpton, v, vares from agent to agent and these values are dstrbuted accordng to the cumulatve dstrbuton functon, F(v), v 0. The th agent s value, v, s prvate knowledge to that agent, but the dstrbuton F ( ) s common knowledge. It s also contnuous, twce dfferentable and the correspondng revenue functon (below) s concave. Also, F ( 0) = 0. Let there also be an nfnte number of frms that do not consume the product. These frms can also develop the product at cost c. I explore dfferent modes of software provson n a two-stage game. Durng the frst stage, one or more frms or agents smultaneously decdes whether to enter, that s, whether to develop the software and provde t n a partcular way. In the second stage, the software s sold or s 4 These surveys only count servers drectly on the publcly accessble Internet. They exclude servers used nternally by organzaton that are behnd so-called frewalls. Ths affects the nterpretaton of the results, nevertheless, these open source products have rapdly acheved substantal market share n the publcly accessble market segment.

8 7 - Open Source Software: - Bessen - 5/01 dstrbuted under an open source lcense. If the software s sold, sellers compete on prce durng ths stage. The solutons to the games are perfect equlbra. In many of these games, multple agents may enter n the frst stage and the advantage to enterng depends on the number of other agents who choose to enter. I explctly model agents belefs about the lkelhood that other agents wll enter. I assume these belefs are consstent and symmetrcal, that s, the soluton to the frst stage of the game s a symmetrc Bayesan equlbrum. I consder games where agents provde software va dfferent market relatonshps, frst commercal software, then custom programmng/self-development, and then open source provson. B. Commercal software In ths form of provson, frms develop software and then sell t to consumers n a market relatonshp. Snce ths s a smple product, frms do not prce dscrmnate, rather they sell to all consumers at the same prce (prce dscrmnaton s consdered below wth a more complex product). Frst, consder the case where a sngle frm has a patent monopoly. If the frm offers the product to consumers at market prce p, then consumers wll purchase as long as v > p. The frm does not know each agent s consumpton value, but the frm s rsk neutral and knows the dstrbuton functon F ( ). The frm s expected proft s thus (1) π p) p N ( 1 F( p) ) c (. The frm wll choose p to maxmze expected profts: (2) pˆ = arg max π( p). p Snce c s constant, ths s the revenue maxmzng prce as well. I assume that the revenue functon, R( p) pn( 1 F( p) ) s concave, so that pˆ s a unque global maxmum. Note also that pˆ s ndependent of c and N; t depends only on F ( ). Ths means that the frm can proftably offer the product as long as the market s suffcently large, specfcally, as long as (3) ˆ c N > N. pˆ ( 1 F( pˆ) ) Conversely, for small markets (N less than or equal to Nˆ ), the frm wll not provde the software commercally va a market transacton.

9 8 - Open Source Software: - Bessen - 5/01 Now, suppose that nstead of patent protecton, frms can only obtan trade secret and copyrght protecton. That s, more than one frm can enter and compete. When more than one frm enters durng the frst stage, Bertrand competton arses durng the second stage, yeldng zero profts to all frms. Each frm wll want to avod ths stuaton, so a frm s entry decson depends on ts belefs about the lkelhood that other frms wll enter. The frctons mplct n ths case can be modeled several dfferent ways. The frms mght engage n a pre-empton game to determne whch can enter. And f multple frms enter, they mght engage n a war of attrton game to determne who survves. In these dynamc games, effcency losses arse from tme delays and from possble duplcaton of development costs. 5 Here, to keep thngs smple, ths neffcency s captured by a probablty that the software wll not be developed at all n a sngle perod. Followng Justn Johnson [2000], I consder a smple Bayesan game n the frst stage. Let ψ desgnate the th frm s decson varable ( ψ = 0 means do not develop, ψ = 1 means develop ). Let q desgnate that frm s belef on the probablty that any other sngle frm wll develop. Suppose, for the moment, that there are f frms (ths number wll be taken to the lmt below). Then the frm beleves that the probablty that no other frm develops s P f 1 0 ( q ) (1 q ). The th frm s expected proft s then π = ψ ( ( q ) R( pˆ) c) + (1 ψ ) 0 P. 0 I restrct the soluton to one wth symmetrc belefs, that s, q = q q * for all and j. j = By nspecton, f N Nˆ, then q* = 0. If N > Nˆ, then a soluton wth q* > 0 s possble, however, consstency requres that q* < 1; f q* = 1, then any frm s best choce would be ψ = 0, whch would be nconsstent. An nteror soluton must occur at the pont where a frm s ndfferent between enterng or not, namely (solvng d π d ψ = 0 ), 1 f 1 c q * = 1. R( pˆ) The correspondng probablty that at least one frm wll provde the software s 5 For example, Blss and Nalebuff [1984] develop such a dynamc game for the provson of a publc good (correspondng to the open source example below). Note also that smlar neffcences also arse wth patents n standard patent race models. I gnore the process that allows a frm to obtan a patent, hence I ntroduce a somewhat artfcal asymmetry between the patent and compettve commercal models.

10 9 - Open Source Software: - Bessen - 5/01 f f 1 f c Q C = 1 (1 q*) = 1 and lm R( pˆ) f Q C c = 1. R( pˆ) So the soluton n the lmt for an nfnte number of frms s a probablty of provson of Q C 0 N Nˆ = c. 1 N > N ˆ R( pˆ) To summarze, Proposton 1. Commercal provson of smple software. Commercal frms provde smple software n large markets ( N > Nˆ ). Wth patent protecton provson s certan; wth only copyrght and trade secret protecton provson occurs wth postve probablty, 0 Q < 1. In small markets, however, commercal provson of smple software fals. < C Fgure 1 shows the probablty of provson for frms wth and wthout patents. The superor provson under patent protecton compared to copyrght and trade secret protecton corresponds to a standard argument about the mportance of patent protecton. Ths argument s lmted to smple products n large markets, however. Note also, that as N becomes asymptotcally large, Q C converges to one. Note that the falure of commercal provson n small markets corresponds to observatons about the development of the software market. Durng the frst decades of electronc computers, most software was provded through self-development or contract programmng. Commercal software was lmted and largely conssted of software bundled wth computer hardware. Only wth the dramatc expanson of the personal computer market dd commercal software become a large porton of the total software market. In large markets, commercal provson s effcent because the frm aggregates demand from many consumers. In small markets, commercal provson fals because the frm has only lmted knowledge of customers preferences. Although some customers mght be wllng to pay enough to cover development costs, the frm does not know ths for sure, and so s unwllng to take the chance. Ths contrasts wth a custom-programmng relatonshp (and self-development), where the provder obtans nformaton about ndvdual preferences.

11 10 - Open Source Software: - Bessen - 5/01 C. Custom programmng / self-development Custom programmng and self-development both nvolve a greater degree of self-selecton than commercal provson. Wth custom programs, agents wth potentally hgh value, v, may choose to contract for the development of the software, perhaps at a prce above pˆ. Such agents mght also be wllng to develop the software themselves. Once developed, the software may then be resold to other consumers under both forms of provson. Ths self-selecton permts the development of software n small markets wth some postve probablty. In the current settng, all consumers are also potental developers. Snce agents preferences are prvate nformaton, custom programmng entals barganng and ths mples transacton costs. Custom programmng (f t s to be proftable) thus costs an agent more than selfdevelopment. Hence no agent would ratonally contract wth a thrd party to develop software she could develop herself. Thus the model here apples to self-development. Wth slght modfcaton, however, ths model can be extended to a world where some consumers cannot develop and nstead contract for custom programmng. In the frst stage of the game, each of the N agents decdes whether to develop the software. 6 There are no patents to blockade entry. In the second stage, any agents who develop software then offer the product to the remander, competng on prce. If only one agent enters, she wll want to charge pˆ. If more than one agent enters, Bertrand competton wll drve prces to zero. Now f p ˆ > c, ths game s unrealstc because no agent n stage 2 would choose to purchase software at a prce exceedng the cost of self-development. In ths case, development wll always occur. I restrct consderaton to the regon of hgher cost, pˆ c. In the frst stage, each agent s decson depends on that agent s belefs about whether other agents wll develop the software. If an agent does develop, then profts from resale depend on whether other agents also develop. If an agent does not develop, she may stll be able to buy the software n the second stage, thus there may be an ncentve to wat. Let q desgnate that agent s belef on the probablty that any other sngle agent wll develop. Then the probablty that no other agent develops s P N 1 0 ( q ) (1 q ) and the probablty that exactly one other agent develops s P N 2 1 ( q ) ( N 1) q (1 q ). If the agent develops, she gets the beneft and cost of developng 6 For brevty, I do not consder self-developers who mght obtan patents.

12 11 - Open Source Software: - Bessen - 5/01 and she also profts from resale, provdng no other agents enter. If she does not develop, but one other agent does, she can pay pˆ, f she wants. If more than one other agent develops, the prce s zero. For an agent wth (4) U S v ( ψ ) pˆ, the expected utlty s = ψ A smlar expresson derves n the regon where ( v c + P0 ( q ) R( pˆ) ) + (1 ψ ) ((1 P ( q )) v P ( q ) pˆ ) v 0 < pˆ (see Appendx). The soluton to the game takes the form of a Bayesan Nash equlbrum. An agent can maxmze utlty by choosng to develop when d U S d ψ > 0 and not developng otherwse. Ths dervatve depends on v and q. Clearly, an agent wll be ndfferent between developng and not developng when ths dervatve equals zero. Solvng v out of ths ndfference condton yelds d U S (5) v * ( q ) v such that = 0 d ψ Snce. U S s an ncreasng functon of v, an agent wll develop as long as v > v * ( q ). Hence the probablty that the th agent develops s just F( v * ( q )) one wth symmetrcal belefs. Then consstency requres that 1 1 (6) q * 1 F( v * ( q*) ), q = q*, = 1, 2,... N =.. I restrct the soluton to The probablty that solves ths equaton corresponds to a symmetrc Nash equlbrum. The. probablty that any agent wll develop software s then Q *) N S = 1 (1 q. The followng result s obtaned n the Appendx: ˆ), then selfdevelopment wthout patents wll occur wth postve probablty less than one, 0 Q < 1. Proposton 2. Self-provson of smple software. As long as F ( c R( p ) < 1 < S Thus self-development occurs n both small and large markets as long as development costs are not too hgh. The ntuton that self-selecton provdes an advantage n small markets s correct. Fgure 1 shows the provson under self-development when F s a unform dstrbuton. Compared to commercal packaged software provson, self-development (wthout patents) s superor to compettve commercal provson, and s superor to monopolstc provson (under patents) n small markets, but not n large markets.

13 12 - Open Source Software: - Bessen - 5/01 D. Open source provson Under open source provson, assumng no patents, agents develop software themselves and then lcense t at no charge to other agents. Ths s very smlar to self-development, but here the agent does not stand to gan from resales. The correspondng expected utlty (smlar to Johnson s [2000]) s: U ( ψ ) = ψ v c + (1 ψ ) (1 P0 ( q )) v. (7) O ( ) Ths has a smlar soluton to self-development, yeldng a probablty of development general, f F ( c) < 1, then the probablty of provson s postve, 0 Q < 1. < O Q O. In Note, however, that n a world wth smple products covered by copyrght and trade secret protecton, agents motvated by narrow self-nterest wll prefer self-development to open source development: An agent developng software herself can make out better by resellng the software to other agents. Hence open source development s domnated by self-development. Ths s also evdent n the example n Fgure 1. Of course, real lfe open source development may be about a dfferent set of crcumstances than ths. Altrusm or reputaton may motvate agents (see Lerner and Trole [2000]). Also, as I argue below, even agents motvated by narrow self-nterest may undertake open source development of enhancements or modfcatons to complex open source products. E. Free-rdng and property rghts In ths model of a smple software product, do property rghts prevent neffcences assocated wth free-rdng? The propretary regmes above can be contrasted to a regme wthout copyrght and trade secret protecton (assumng no excludablty). In fact, the latter corresponds to the open source model above n both, only the frst agent faces any cost for usng the software. The probablty that software wll be developed under open source thus corresponds to the probablty that software would be developed wthout copyrght and trade secret protecton. Comparng (4) and (7), (ths result also holds where v < pˆ ), d U d ψ S > d U d ψ O for N > 1, ndcatng that the ncentve to develop s greater under self-development and so v* wll be lower. Snce 1 q * = F( v*) and F( ) s a non-decreasng functon, t follows that the probablty of development wll be at least as hgh under self-development wth copyrght and trade

14 13 - Open Source Software: - Bessen - 5/01 secret protecton, O S Q Q. If F ( ) s a strctly ncreasng functon and F ( v * (0)) < 1, selfdevelopment s strctly superor. Also, n large markets wth patents, commercal provson occurs wth probablty one. Ths permts a verson of the free-rdng hypothess: Proposton 3. Free-rdng. For smple software products, copyrght and trade secret protecton weakly mprove the probablty that software wll be developed; patents strctly ncrease the probablty of development n large markets. The ntuton here s that the profts of sellng software to other partes provde greater ncentve to development, assumng agents are motvated by narrow self-nterest. Open source suffers from free-rdng n two dfferent ways. Frst, f development costs exceed ndvdual consumpton values, open source developers cannot advantageously provde software, whle commercal provders can proftably aggregate demand from many consumers. Second, even when costs are not hgh, strategc watng may reduce the probablty of provson under open source. Note, however, that results concernng socal welfare are ambguous even n ths smple settng. When software s provded at a postve prce, some consumers wll forego consumpton; these same consumers would gan postve value under open source provson. Hence, the lower coverage of open source development may be offset by the greater consumpton value. On the other hand, any form of provson other than patents may have effcency losses arsng from wasteful duplcaton of development effort. 7 IV. Complex Goods A. Modelng assumptons Ths framework readly extends to complex products. Suppose that the product now has M possble features, ths number beng common knowledge. For example, a basc desktop publshng product mght be capable of producng low-resoluton black-and-whte newsletters. But a fully featured product mght also be capable of color, hgh-resoluton output and book pagnaton. I assume M s an exogenously fxed number, but below I dscuss the possblty that t may be endogenous and also change over tme as new feature possbltes are dscovered. 7 However, ths may arse from the unrealstc aspect of smultaneous entry n ths game. Where agents have even a slght reputatonal gan from open source development, they beneft from reportng projects they ntend to develop, thus avodng duplcaton. In fact, onlne regstres exst where open source developers do just that.

15 14 - Open Source Software: - Bessen - 5/01 Suppose all agents derve consumpton value u for the base product. Each of the addtonal capabltes s a feature that adds value for some, but not all, consumers. Some consumers mght fnd a feature rrelevant or costly to learn, so they wll not use t even f t s ncluded n the product they purchase. Suppose that w percent of consumers receve postve value from any gven feature 1 and < w < 1. 8 The th consumer n ths group receves utlty v > 0 from the jth feature. The 2 remanng 1 w percent of consumers do not want the feature. For smplcty, the value an agent receves from each feature s ndependent of the value she receves from other features and the total value she receves s the sum of the values of the features she uses. Thus a consumer who uses the frst m features and pays prce p receves utlty of j u m + v j =1 j p. Now the vj could be assgned a probablty dstrbuton as above. However, to smplfy the exposton, I assume that all consumers who use a feature receve a consumpton value of v. That s, v j = v for all users and all features condtonal on the th agent usng the jth feature (wth probablty w). Ths s a strong smplfyng assumpton; n realty, features may be complements or substtutes and there may be dmnshng returns to the value of features. The basc results below could be obtaned wth a more general specfcaton, but ths smple lnear assumpton smplfes the exposton. Wth ths assumpton, the consumer who uses the frst m features and pays prce p receves utlty of (8) u + m v p. features s The probablty that any gven user wll want a partcular use-product that ncludes m (9) y m M m ( m) = w (1 w). Each such combnaton must be tested and debugged separately, because the dfferent features nteract. Ths test and debug actvty s not free, however. Let c now desgnate the cost of codng a feature (and the base product) and let d desgnate the cost of testng and debuggng a 8 The lower bound ensures that only popular features are consdered. Ths smplfes the analyss.

16 15 - Open Source Software: - Bessen - 5/01 sngle combnaton of features used, a sngle use-product. 9 I assume that the cost of debuggng a sngle use-product s ndependent of the total complexty. Debuggng costs per use-product may actually be slghtly hgher n hghly complex products some bugs may be harder to locate. But as long as debuggng costs do not rse too rapdly, constant d approxmates realty. M Thus the cost of codng and debuggng all possble use-products s ( M + 1) c + 2 d. Clearly, even f d << c, total development cost largely conssts of debuggng cost for complex products. Even f advanced programmng methods (e.g., object-orented code) can elmnate 99% of the bugs, the exponental growth of debuggng costs ensures that debuggng costs are substantal. To smplfy matters, I assume that consumers only purchase commercal software that has defntely been debugged for ther use-product (they have the knowledge to determne ths). 10 Frms need not, however, debug use-products for consumers who wll not purchase the product (e.g., f they are prced out of the market). Fnally, debuggng cost d also refers to the cost of enhancng the product. That s, the dstncton between fxng a bug and enhancng s one of degree. A feature that s poorly mplemented s a bug; an unmplemented feature s just a serous bug. Snce d can refer to an average cost of testng and debuggng, ths actvty ncludes enhancements. The basc problem wth complex software s that even wth a modest number of features, 2 M >> N. Ths means that very few of the possble use-products are actually used, even though debuggng them s costly. The basc ntuton below s that n ths stuaton, the self-selecton benefts of open source can outwegh the losses due to free-rdng. As above, I consder dfferent types of software provson, frst separately and then n combnaton. Now the game has three stages: frst, frms or agents decde to enter or not; then they decde whch features to develop and they code these; fnally, they compete on prce, debuggng those use-products that wll actually be used at the chosen prce. 9 One mght thnk that testng the combnaton where all features are used would debug all possble nteractons. But just because hgh resoluton prntng works wth color documents does not mean that t also works wth black and whte documents. Both uses must be tested. 10 Under a more realstc scenaro, consumers do not know n advance whether ther partcular use-product has been debugged and the software frm thus faces a reputatonal game. Such consderatons do not change the basc ntuton developed below, so I avod them for smplcty of exposton.

17 16 - Open Source Software: - Bessen - 5/01 B. Commercal provson Frst consder a monopolst wth a patent. Nothng n ths model prohbts a monopolst from prce dscrmnatng by offerng dfferent use-products at dfferent prces. That s, the monopolst could develop all M features and then offer crppled versons of software that have dfferent combnatons of features dsabled. In ths case, a verson that ncludes m features can be prced at p = m v + u and the monopolst can then extract the maxmum possble value. Of course, n a more realstc settng, frms face costs of ntroducng dfferent product versons and these costs make such fnely graned prce dscrmnaton uneconomcal. Nevertheless, ths extreme form of prce dscrmnaton s useful exactly because t permts the hghest possble proft and the best possble performance for the commercal provson of software. If commercal frms fal to provde software wth ths advantage, then they surely wll also fal to provde t under less favorable crcumstances. The expected margnal proft from a use-product wth m features s then (10) z( m) ( m v + u) y( m) N d. Ths s an ncreasng functon of m snce w > 1 2. The frm wll only want to offer use-products that have non-negatve margnal proft and t can exclude unproftable use-products by chargng suffcently hgh prces. Defne m as the smallest number of features that s stll margnally M proftable (such that z ( m) 0 ). Then, snce there are m features, the frm s total expected proft s M M (11) π = z( m) ( M + 1) c. m m = m dfferent use-products wth m Now note that as M grows larger, m also ncreases because y (m) decreases wth M. As consumers are afforded more choces, the number of consumers selectng any partcular choce declnes. So for hghly complex software, commercal frms wth patents wll not offer some useproducts. If the product s even more complex, then the use-product wth all features wll be unproftable, z ( M ) < 0. Then all other use-products wll also be unproftable, or, n effect, m > M. In ths case, commercal provson of the full product wll not occur at all. Instead, a monopolst can make out proftably by developng only a subset of the possble features. More

18 17 - Open Source Software: - Bessen - 5/01 generally, straghtforward calculatons shows that π s concave n M. So the monopolst can maxmze profts by choosng an optmal value for M ˆ arg max π, and f M > Mˆ, the monopolst wll only offer a subset of features n the product. Proposton 4. Commercal provson of hghly complex software under patent protecton. If the product s suffcently complex such that m > 0, then a commercal provder wth a patent wll fal to provde software for use-products where m < m. If the potental product s even more complex, such that M > M ˆ, then a patent holdng frm wll not offer an ntegrated product wth all M features. M When a monopolst chooses to lmt the features n a product, the monopolst (or, perhaps, other frms) can then offer other products based on other subsets of M. Ths sort of dfferentaton provdes a natural explanaton for the appearance of software layers n hghly complex envronments. Groups of features that are used by a varety of programs are bundled nto varous layers an applcaton layer, an operatng system layer, a prnt management layer, a network layer, etc. Each layer provdes a gven number of features and a standard nterface for use by other software programs. Thus each layer has only lmted complexty, allowng proftable development. By combnng products n dfferent layers, users may realze dfferent combnatons of features. However, nteractons between dfferent components of a system are not necessarly debugged. Indeed, the dvson of complex software nto layers gves rse to system ntegrators who provde sem-standardzed software and perform custom debuggng and enhancement under contract n order to get the dfferent layers to work together for a partcular customer s applcaton. Strctly speakng, ths s not commercal provson of packaged software an ntegrated product s not offered. Rather, ths type of provson s a verson of hgh end custom programmng (see below). In a compettve envronment, thngs can get more complcated. Frms may choose dfferent standards, defne layers dfferently (e.g., ncludng an Internet browser n the operatng system layer) and compete on these dfferences. A large lterature exsts on standards and systems competton and such matters are beyond the scope of ths paper. Rather than specfyng the process that determnes these software layers, I assume that the number of features n the gven layer s determned exogenously. To keep thngs smple, let M refer to just the number of features n the layer beng studed. I assume that all potental competton takes place between frms offerng subsets of these features (and not features found n other layers). Note that the selecton of

19 18 - Open Source Software: - Bessen - 5/01 the M features s an economc as well as techncal decson, and that dfferent forms of software provson may thus generate very dfferent software layers and standards. In partcular, I suggest below that the dvson of software generated by commercal frms may not necessarly constran open source developers. Assume for the moment that a sngle frm can proftably develop all M features. In the Appendx, I show that n the second stage of the game wth multple frms, n Nash equlbra, one frm codes all M features and the remanng frms code no features and make no profts. As n the case of a smple commodty above, ths structure mples a war of attrton once frms have entered. I assume that the market s large enough so that the probablty of provson s close to one. That s, belefs about other players exert only a second order effect and n reduced form the soluton s one where a sngle frm enters n the frst stage and t develops all M features n the second stage. In a more elaborate settng, frms mght race to develop a product wth the full set of features n a preempton game. Frms mght also lack a pror nformaton about the popularty of features, and learn whch are valuable through sequental tral-and-error. Indeed, commercal software competton often takes the form of feature wars where frms sequentally develop versons wth new features hopng to frst fnd the feature set that can domnate the market. Ths wnner-take-all aspect dffers from the results of vertcal dfferentaton models of Gabszewcz and Thsse [1979, 1980] and Shaked and Sutton [1982, 1983] where, under some condtons, a natural olgopoly may arse. For example, a frm offerng a low qualty product may co-exst wth a frm offerng a hgh qualty product. Gven suffcent complexty, ths result does not occur here, however development costs exceed duopoly revenues for the low qualty product. 11 C. Open source provson To model open source provson, I assume that open source developers have coded the base product, but they have not coded enhancements or debugged any use-products. That s, I presume an ntal development effort motvated by altrusm or reputaton that provdes a core of software for free. Ths ntal product s made avalable under a vral GNU General Publc Lcense, so that avalable from author). 11 Ths s also true for models where v takes a unform dstrbuton as n the vertcal dfferentaton lterature (calculatons

20 19 - Open Source Software: - Bessen - 5/01 all enhancements, modfcatons and bug fxes are also free. 12 Agan, I assume that no patents prevent such use. An agent wll consder debuggng a partcular use-product wth m features f u + m v > d. An agent wll consder codng a feature and debuggng a use-product when u + m v > d + c. Snce the analyss s essentally the same n ether case, I consder just the former case. In ths case, the agent takes nto account the possblty that other agents mght debug the use-product. Suppose that n << N other agents want ths partcular use-product. 13 Then the probablty that no other agent wll debug the use-product s P ) n 0 ( q ) = (1 q, and the agent s expected utlty s (12) U ( ) = ψ ( m v + u d ) + (1 ψ ) (1 P0 ( q )) ( m v u) ψ. O + In general, the soluton yelds a postve probablty of open source provson, Q > 0, f m v + u > d and no provson ( Q = 0 ) f mv + u d. That s, agents only debug the software O under open source wth postve probablty when the prvate value of the software exceeds the debuggng cost. Moreover, when the expected number of agents wantng the same use-product s small, then Q O wll be close to one. In ths case the falure to debug a use-product because of strategc watng s only a second-order effect. 14 Fnally, note that these condtons on the provson of open source software are ndependent of M. Ths mples that wth complex products, open source software wll be provded n stuatons where commercal software s not offered. If M s suffcently large, then m > ( d u) v, so that open source software wll be provded for the range of use-products O where ( d u) v m < m. Moreover, n the case where M s so large that a monopolst wll not offer a product wth all M features, open source provders may stll offer such a product. That s, open source developers are not constraned by the commercal dvson of software nto layers. 12 The lcense does not commt users to make enhancements avalable to others f these enhancements are for ther own prvate use the lcense requres only that future dstrbutons nclude the enhancements. However, as a practcal matter, users wll want to take advantage of mprovements made by others n the contnually-updated code. To avod havng to repeatedly merge ther enhancements nto updated code, they wll want to have ther changes ncluded n the dstrbuted code. 13 In fact, the agent does not know exactly how many other agents mght want the same use-product but does know the probablty that a gven number wll want t (based on w). The agent s expected utlty must therefore be calculated over ths dstrbuton. The exposton s smplfed by treatng only a sngle nstance, and the general results are no dfferent. 14 Furthermore, n a more elaborate game where expectatons about other agents are modeled as a war of attrton, strategc watng may only play a mnor role for another reason. Bugs are usually detected only when a product s used. So dfferent agents are lkely to dscover a bug at very dfferent tmes. In a war of attrton model, ths asynchroncty reduces the motvaton to wat for another agent to do the debuggng.

21 20 - Open Source Software: - Bessen - 5/01 D. Self-development and hgh end solutons In a complex settng, the self-developer s hardly dstngushable from the commercal software frm the agent s own consumpton value s now a very small part of the overall calculaton. For ths reason, I do not treat self-development separately. On the other hand, a form of custom programmng may actually be more applcable n complex envronments. Consder a hgh end software frm that ntally codes a product wth M features, but does no debuggng. The frm then offers to sell ths product to consumers along wth a servce and support contract that ncludes debuggng for ther ndvdual use-products. Much of what goes on under the rubrc of customer servce s, n fact, debuggng and feature enhancement. Ths s smlar to the system ntegrator scenaro above. But n these cases, frms only do what agents could do themselves, at lower cost, as open source developers. Open source provson thus domnates these forms of custom provson, at least n a world where all consumers are also potental software developers. E. Commercal software vs. open source provson Now consder strategc nteracton between dfferent types of provders n a world wth trade secret and copyrght protecton (no patents). Snce custom provson s domnated, I only consder strategc nteracton between commercal frms and open source developers. As above, I assume that open source developers have prevously coded the product. Consder the thrd stage of the game for a partcular use-product wth m features. If no frm has entered, then an agent s expected utlty s U O as n (12), and the agent develops wth postve probablty when m v + u > d. If a frm enters and offers a prce p < d, then no agent wll develop under open source because t s less expensve to purchase the product. In the regon where m v + u < d, the frm wll offer p = m v + u and agents wll purchase. So a frm wll offer use-products as long as m m. Now consder the range where m v + u p d. If the frm charges more than d, each agent wll choose nstead to debug ther own use-product. So f the frm enters, t charges d (or a har less). Then t s only proftable for the frm to offer the use-product when y ( m) N 1. To summarze,

22 21 - Open Source Software: - Bessen - 5/01 Lemma 1. Provson of Complex Software. Under competton between open source developers and commercal frms wth copyrght and trade secret protecton, debugged software may be provded under two sets of necessary condtons: 1. If y ( m) N > 1 and m m, a sngle frm may provde use-products and charge a prce mn d, m v + u ; these use-products are not provded by open source. equal to ( ) 2. If y ( m) N 1 and m v + u > d, then open source provson occurs wth postve probablty and no commercal frm provdes these use-products. Furthermore Q 1 n much of ths range where y(m) N << 1 because the expected number of other agents who want the same use-product s small (see Appendx). These regons are llustrated for three examples (treatng the varables as contnuous) n Fgures 2 4. Fgure 2 shows an nstance wth relatvely few features (small M) and relatvely low O value / cost. The fgure shows two curves, one for y( m) N and one for ( m v + u) d, plotted aganst m on the x-axs. In ths case, the frst curve reaches one frst and open source provson does not occur for any use-products. Ths s smlar to the provson of a smple product. Fgure 3 shows an nstance wth more features correspondng to greater value / cost. Here, the lne for ( m v + u) d reaches one frst (at pont A), and open source provson occurs between ths pont and the pont where y( m) N equals one (pont B). Commercal provson occurs between B and m = M. Fgure 4 shows a hghly complex product where y ( M ) N < 1. In ths case, commercal provson of a product wth M features does not occur at all and only open source provson occurs. When a commercal frm has a patent monopoly, that frm can offer a product wth fewer than M features, as above. However, a commercal frm n competton wth open source developers does not have ths opton open source developers wll delver fully featured products (wth postve probablty), makng products wth fewer features unproftable. Note that when both forms of provson occur, open source development delvers the smpler use-products, some of whch would be provded commercally n the absence of open source developers and some of whch would not. 15 Open source, n effect, provdes use-products that are more closely talored to smpler needs. Ths echoes a complant heard among open source 15 Ths s a consequence of the assumpton that w > ½. In a more general settng, open source provdes use-products that are both more and less complex than commercal use-products.