Order 1079275: Entrepreneurship - opportunity analysis video game industry in Australia
Journal of Management Information Systems / Fall 2007, Vol. 24, No. 2, pp. 195–219.
© 2007 M.E. Sharpe, Inc.
0742–1222 / 2007 $9.50 + 0.00.
DOI 10.2753/MIS0742-1222240208
Digital Consumer Networks and Producer–Consumer Collaboration: Innovation and Product Development in the Video Game Industry
REINA Y. ARAKJI AND KARL R. LANG
REINA Y. ARAKJI is a Ph.D. candidate in Information Systems at the Zicklin School of Business, Baruch College, CUNY. She holds a B.A. in Economics and an MBA in Finance. Her research interests include information economics, innovation, social networks, virtual communities, and the digital entertainment industry.
KARL R. LANG is an Associate Professor in Information Systems at the Zicklin School of Business, Baruch College, CUNY. He holds a Ph.D. in Management Science from the University of Texas at Austin. Dr. Lang’s research interests include decision tech- nologies, management of digital businesses, knowledge-based products and services, and issues related to the newly arising informational society. He held previous posi- tions at the Free University of Berlin in Germany and the Hong Kong University of Science and Technology (HKUST). He has also taught in the MBA program at the Wharton School, University of Pennsylvania, in Philadelphia. His findings have been published in diverse journals, including Journal of Management Information Systems, Communications of the ACM, Decision Support Systems, Computational Economics, and Annals of Operations Research. He is an associate editor of Decision Support Systems and Electronic Commerce Research and Applications.
ABSTRACT: This paper examines new forms of collaboration between producers and consumers that are emerging in the digital entertainment space. Taking the case of the video game industry, we show how some firms have opened a portion of their proprietary content for transformation by consumers and allowed the development of consumer-designed and consumer-implemented derivative products. By reap- propriating these derivatives, video game firms are successfully outsourcing parts of their game design and development process to digital consumer networks. Applying economic analysis, we explore the potential benefits and risks associated with outsourc- ing to networks of consumers. We also derive the optimal combination of copyright enforcement and consumer compensation. Our results suggest that profit-maximizing producers of video games have incentive to partially open game content to their users and to remunerate the most innovative ones, under the condition that the derivatives constitute complements to, and not substitutes for, the original product. We discuss the implications on firm strategy for innovation.
KEY WORDS AND PHRASES: digital entertainment, innovation, outsourcing, producer– consumer collaboration, user-generated content, video games.
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TRADITIONALLY, FIRMS DESIGN NEW GOODS and produce and distribute them. Consumers, on the other hand, are supposed to maximize their utility by buying these products, subject to a budget constraint, without directly taking part in the design, production, or distribution process. Input from consumers is largely limited to participating in market research and providing feedback to the design process. A core assumption of classical economics is therefore a strict dichotomy between producers and consumers. The only forms of collaboration considered in this traditional setting are producer–producer partnerships, including joint ventures for research and development [21].
As information technology (IT) is permeating the various dimensions of new prod- uct development, the innovating firm’s relationship with its customers is changing [38, 46], allowing us to relax the conventional assumption of complete separation between producers and consumers. Technology is, in fact, enabling valuable new forms of producer–consumer collaboration in the product development process. This phenomenon has already been observed in special settings where trendsetters have innovated in surgical instruments and sports equipment [51], but only recently did this type of outsourcing shift with unprecedented scale and scope to the digital realm, first to open source software projects where companies such as IBM and Red Hat encour- age consumer innovation as part of their business strategy [9, 32] and now also to the digital entertainment industry [35]. Unlike the open source software phenomenon that has received widespread attention in the literature, outsourcing innovation to consum- ers in digital entertainment has yet to be systematically studied. The present paper addresses this gap and provides a first in-depth study on outsourcing innovation to consumers in digital entertainment, with a specific focus on the video game industry. We investigate whether the conventional wisdom that strong copyright enforcement is good business strategy for firms that own and distribute digital content also applies to firms that innovate new content.
Background Discussion
Changing Consumer Needs
PRODUCER–CONSUMER COLLABORATION IN THE INNOVATION and product development pro- cess is driven by the changing consumption patterns of individuals engendered by the falling cost of communication and information transfer [11, 36]. Only a decade or two ago, people lived within a mass culture where stable and predictable consumption patterns allowed for mass production of cultural artifacts [23, 43]. But people today increasingly live in an ever-shifting world of networks redefining their lifestyles and fragmenting culture [12]. Firms are finding it difficult and costly to understand their customers and it is becoming a challenge to develop the products that meet hyper- differentiated consumer demands [16]. Some pioneering companies are no longer attempting to grasp the details of consumer needs and are reassigning the design aspect of product development to external sources of ideas [26], including their own customers [52], giving rise to a new business model where firms are outsourcing product innovation and development to their consumers.
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Digital Consumer Networks
While many companies have already put lead users at the center of the design process to develop new products, some digital entertainment firms have gone further and have outsourced part or all of the innovation process to digital consumer networks. Accord- ing to Von Hippel [50], lead users are consumers who experience needs for particular products ahead of the general users who will develop these needs later on. The lead users thus constitute “need-forecasting” agents to the firms and may also help provide new product designs when they seek new solutions to their needs. We define digital consumer networks, on the other hand, as online communities of consumers who share similar interests in certain product genres and who take advantage of Internet connec- tivity as well as the powerful and easy-to-use digital technology to not only discuss products but also engage in the design, development, and distribution of new digital products. By adopting strategies of opening a portion of their proprietary digital con- tent for transformation by the public, the firms are, in fact, allowing digital consumer networks to generate new derivatives that can possibly be reintegrated into the firms’ innovation process. This partial opening of proprietary content requires the transfer of some rights from the copyright-owning firm to the community in return for stimulating user-generated new product designs that provide a new source of intellectual property for the firm.
Intellectual Property Environment and Strategic Enforcement of Copyrights
As norms evolve over time, so does the law that defines the permissible roles and behaviors within the context of these norms. With the increasing diffusion of the In- ternet and the explosion of digital entertainment, cyberspace laws are adapting to new practices such as user-generated content creation and multimedia mashups. Different stakeholders advocate different regulatory changes. They argue, from different per- spectives, for what constitutes the best balance between keeping the Internet an open platform that generates creativity, innovation, and growth and securing cyberspace against security threats and business risks that arise from the openness of the Internet to third-party actors [34, 55].
In terms of copyright protection and consumer access rights to digital works, the established digital entertainment industry is generally calling for additional protec- tions to ensure that creators have incentive to keep creating new works in the future and that businesses can protect their intellectual property rights and safely distribute digital products to online consumers [54]. At the same time, we find a collectivist trend among the proponents of participatory culture inviting consumers to stop being just passive receivers and to become active, collaborative contributors [5, 42].
In the current study, we do not engage in the debate regarding Internet law and op- timal copyright regulation in a changing technological environment [20]. We assume that the current regulatory framework is restrictive and examine if a profit-maximiz-
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ing firm should implement policies that are less restrictive (or more open) than the regulatory policy currently in effect.
Research Questions
A pioneer of producer–consumer collaboration for innovation and strategic copyright policy is the video game industry, which has taken the lead in partially opening its digital content and encouraging consumers to participate in designing products on a wide scale. The video game industry, in fact, has a specific structure that allows firms to safely and successfully explore producer–consumer collaborative efforts. First, the games are digital information goods, which support the usage of IT-based toolkits to alter games and design new ones. As important is the fact that most games are now played online by multiple players, facilitating the formation of digital consumer net- works. Finally, numerous consumers of video games are technologically proficient and hence have not only the motivation but also the necessary ability to reinvent the way a game is played by digitally manipulating and transforming it.
In this paper, we first investigate newly emerging forms of collaboration between producers and networks of consumers in the context of massively multiplayer online games (MMOGs) and the particular case of Valve LLC and its game Half-Life. We find that this collaborative arrangement is beneficial only when the consumer-designed derivatives constitute complements to, and not substitutes for, the original product. We also present a simple economic model that formally answers the following specific questions. Please note that although we state 1 and 2 separately for the sake of clarity, they are not solved independently:
1. Copyright enforcement at the firm level: Should producers enforce their full copyright protection rights? Or should they open some of their content for external development of derivative products?
2. Compensation level: Should producers compensate the consumers that create innovative product designs?
3. What are the trade-offs between copyright enforcement and compensation level and what is their optimal combination?
Our results indicate that it is in the interest of a profit-maximizing game developer to both compensate its most innovative consumers and to partially open its propri- etary content to the public. The optimal combination of consumer compensation and copyright enforcement depends on the company’s strategic positioning.
The Video Game Industry and Its Evolving Modding Strategy
FROM ITS MODEST BEGINNINGS IN UNIVERSITY LABS in the 1950s and 1960s, video games have grown into a multibillion dollar industry. Video games are divided into PC games and console games. The former are played on regular home computers, whereas the latter need specialized hardware such as PlayStation (Sony), Xbox (Microsoft), or Wii (Nintendo) in addition to a TV or display screen. Video game industry global
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sales reached $21 billion in 2003 and are estimated to surpass the global recorded music industry by 2009 [39]. In the U.S. video game industry, revenues have already exceeded those of the movie box office and have continued to grow strongly, reaching around $13.5 billion in 2006 [2].
Game toolkits are industry-specific applications that were originally developed for use by professional developers. By releasing toolkits to the public, some video game firms enable their customers to create and test customized product designs. When compared to the traditional producer innovation and design process, digital consumer networks equipped with toolkits can reduce the costs of transferring sticky information between producers and consumers [52]. Users of video games know which design features resonate with them, and why. But this information about consumer wants is hard to transfer to firms, thus limiting exchange channels and creating informa- tion-processing constraints for firms. The information becomes sticky, leading to an escalation in costs, as developers try through trial and error to get the new game right. Toolkits thus have the potential to significantly reduce costs and development time by decentralizing information processing and decision making [48] and invit- ing networks of consumers to become responsible for improving existing games and designing new ones.
In the context of the MMOG industry, transmutability—that is, the digital manipu- lation of content that is represented as bits [24]—enables the creation of mods by consumers. Mods are direct modifications of an original game and may be classified into two general types, according to the extent of alteration of the game elements:
1. Partial conversion mods add new content to the underlying game and refer to mere game variations and extensions. They are created by altering and adding to a game’s media files, resulting in changed game scenery and music as well as modified or additional game characters and objects. Partial conversions may alternatively manipulate a game’s map files, which control character and object positions and movement, allowing the modification of existing playing levels or the addition of new ones.
2. Total conversion mods create entirely new games. They consist of the concurrent modification of media and map files, as well as other game functionalities, to create complete departures from the original game theme. In that sense, total conversions present new, derivative game products.
Both types of mods are freely distributed on the Internet, where online feedback mechanisms [17] within a social network [3] create large-scale “word-of-mouth” effects that can propel the best-quality mods into stardom. Some mods have found larger audiences and have become more popular than the original games they were derived from.
The Case of Half-Life and Counter-Strike
The game developer Valve LLC produced Half-Life, a successful game that has sold over 8 million units since its release in 1998. Half-Life is an example of a single- person game—that is, a game that is played by one person alone. Valve made the
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decision to partially open the game to allow and encourage the creation of mods by the user community while retaining full copyrights over the game.1 About 80 percent of Half-Life’s code, representing the content of the game, has been made available for transformation while the other 20 percent, representing the game engine, which serves as a platform on which Half-Life content runs, remains closed. In addition, toolkits for modding the game are supplied with the product. Mods are distributed and shared on dedicated Half-Life modding Web sites and on Steam (www.steampowered.com), Valve’s content delivery and digital rights management platform.
Valve’s choice of opening Half-Life’s game content while protecting its underlying engine code achieved two business goals. It successfully stimulated the game user community to engage in designing mods derived from Half-Life that ranged from minor variations of the original to entirely different games. It also successfully protected its revenue stream by designing the architecture of Half-Life such that all mods created with the supplied toolkit can only run on the engine of the original game. Mods in that sense are complementary to the original game. As Figure 1 illustrates, the engine is the fundamental code of the game, providing essential functionalities such as graphics rendering, artificial intelligence, and other core features. Consumers who download mods but are not interested in playing Half-Life still need to purchase the original game to access its engine in order to run the mods.
The approach of not entirely opening Half-Life did not inhibit modding activities in the user community. Many mods of varying quality and success have been derived from Half-Life. Less than one year after the publication of Half-Life, two students, Minh Le and Jess Cliffe, wrote the mod Counter-Strike, which resonated particularly strongly with the game player community. A total conversion of Half-Life, Counter- Strike is a multiplayer shooting game between teams of terrorists and counterterrorists, which represents a different genre from the original Half-Life in which a single player fights against alien invaders. The popularity of Counter-Strike soon exceeded that of Half-Life and players of Counter-Strike (the mod) generated more sales than players of Half-Life (the original) for Valve. Eventually, the company fully reappropriated Counter-Strike and acquired the game in 1999 from the modder team. It also recruited Le and Cliffe to continue the development of the mod, which was later released as a stand-alone retail product for the PC, PlayStation, and other hardware platforms.
Online Modder Community and Value Creation and Appropriation
The game user community is a digital consumer network that comprises game play- ers and modders. The development toolkits are bundled with the original game and can be accessed by all consumers in the network. Most consumers, of course, do not experiment with toolkits and remain passive consumers who are content with just playing the game. The rest form the modding community of the game, a substructure that is embedded in the larger user community. Its members are users who have the motivation and the creative and technical skills to develop fully functional mods. Whereas players perform important tasks in terms of market research and testing, it is the modders that contribute product innovations.
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We divide the mods that are generated by the modding community into three seg- ments. Mods belonging to the first segment, M1, are amateurish in nature and present relatively minor changes to the original game. They are essentially game personaliza- tions and are primarily intended for private use. The second segment, M2, refers to professional quality mods that are distributed within the network. M2 mods can be partial conversions that substantially extend or improve a game, or total conversions that radically modify the original game. M3 mods are cherry-picked from among the best M2 mods and offer outstanding quality that is already tested in the market. Firms reappropriate these M3 mods and develop them further into commercial products that are released as new stand-alone games. In the process, the firm can de facto outsource market research, innovation of game ideas and designs, as well as product develop- ment, to the digital consumer network of game users.
M2 mods benefit the producer by potentially increasing game revenues. As comple- mentary products, they do not cannibalize sales of the original games, although there is a possibility of some cannibalization effects on future and other existing games if consumers prefer playing free M2 mods over officially released games. However, the available data show that while an MMOG has an average shelf life of eight to 12 months, it can be significantly extended when professional quality mods (M2) are made available to players. Half-Life sales, for instance, increased from 2 million units in the first year to 3.5 million units in the second year (an increase of 75 percent). Sales further increased by 8.6 percent in the third year, reaching 3.8 million units. Doug Lombardi, the Director of Marketing at Valve, attributes most of this increase to the three most popular mods: Day of Defeat, Team Fortress, and, of course, Counter-Strike [27]. Even though originally released in 1998 and no longer a best-selling game [1], Half-Life still tops the charts in terms of online usage level, as shown in Table 1, as gamers need the original game to be able to run the newly released M2 mods. Aside from Valve, there are a number of other game developers—such as id Software, Bethesda Softworks, Epic Games, and others (www.moddb.com)—that explicitly encourage modding activities because they have observed a positive impact on sales.
Valve further exploits M2 mods by managing them as if they constituted a competi- tive market of game innovation and design ideas. Table 1 shows the number of M2 modding projects (both partial and total conversions) for the 25 most popular (original)
Figure 1. Mod as a Complement to the Original Game
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Table 1. Video Game Online Activity Ranking and Mod Statistics
Total number Number M2 mod Online of M2 of completion activity mod released rate rank Game title projects M2 mods (percent)
1 Half-Life 406 213 52.5 2 Counter-Strike Source N/A N/A N/A 3 Battlefield 2 137 18 13.1 4 Wolfenstein: Enemy Territory 8 4 50.0 5 Call of Duty 2 25 4 16.0 6 Call of Duty 22 3 13.6 7 America’s Army N/A N/A N/A 8 Battlefield 1942 48 17 35.4 9 Quake 3 Arena 69 26 37.7 10 Jedi Academy N/A N/A N/A 11 FEAR 1 1 100.0 12 Unreal Tournament 2004 166 47 28.3 13 Jedi Knight 2 N/A N/A N/A 14 Soldier of Fortune 2 10 6 60.0 15 Battlefield Vietnam 38 11 28.9 16 Call of Duty: United Offensive 10 1 10 17 Day of Defeat: Source N/A N/A N/A 18 Medal of Honor: Spearhead N/A N/A N/A 19 Medal of Honor: Allied Assault N/A N/A N/A 20 Return to Castle Wolfenstein 8 4 50.0 21 Vietcong N/A N/A N/A 22 Half-Life 2 1,365 49 3.6 23 Half-Life (Old Protocol) N/A N/A N/A 24 StarWars: Battlefront 2 2 0 0.0 25 HALO 22 12 54.5 Average 34.6
Sources: Adapted from Mod Database (www.moddb.com) and Server Spy (www.serverspy.com).
games. For example, Half-Life has spawned a total of 406 mods, of which 213 have been completed and released to the public. Monitoring the online feedback and word of mouth [17] propagating through its digital consumer network, the firm is able to identify and select from the pool of M2 mods the best candidates for reappropriation. The mods thus chosen, which are typically total conversions, are then further devel- oped and differentiated for commercial release. One of these is Counter-Strike, which became a new original that ranked second in online usage (Table 1). In addition, Valve reappropriated other popular mods such as Day of Defeat and Team Fortress and also released them as stand-alone products.
Beyond savings in new product development time and costs, releasing an appro- priated mod instead of publishing a producer-designed video game can also greatly
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reduce investment risk. As with all companies operating in the entertainment industry, game publishing companies are uncertain about the demand for new games while they are still under development [30]. In conventional production methods, focus groups and prescreenings, which are expensive to organize and evaluate, are employed to decrease investment risk. Focus groups and prescreenings occur in stylized settings and are limited to only a small fraction of targeted consumers and, hence, often fail to accurately gauge the demand for a new product. Monitoring the online word of mouth, community discussions, and how many times a mod is downloaded and how much it is played, on the other hand, allows the firm, at low cost, to find new quality game products, already tested in the market, that can be commercially exploited.
Risks Associated with Outsourcing to Consumers
The risks inherent to producer–consumer collaborations on product innovation are similar to those found in producer–producer research joint ventures [37], albeit in different magnitudes. The scale of the risks involved differs depending on whether one is outsourcing to partner firms or to a network of consumers. By default, sharing information and copyrighted content with a few limited, trusted partners implies less risk than sharing the same information with large online user communities.
The first risk entails poaching, or the act of using information divulged in a collabo- ration process for private gains outside the contractual agreement [15]. Even though keeping the game engine separate from the public content files and development tools provides some level of protection, ideas and methods expressed in the game content portion that is shared with the modding community are vulnerable to poaching risk. Modders may transfer knowledge to other projects that may benefit competitors to the firm that owns the original game. Game publishers may also fear the emergence of independent user-created games that could cannibalize their own game products and potentially destabilize the concentrated game development industry, as well as the possibility of having competitor firms masquerading as users to access proprietary code.
From a resource-based value perspective, the returns from an innovation that can be easily reproduced, but that needs complements (or cospecialized assets) to make it useful and valuable, will accrue to the owners of the cospecialized assets [14, 45]. In Half-Life, the game is the mod’s cospecialized asset, and there is no value in addi- tional characters or levels without the original game. The game developing company, in fact, promotes efficiency in the mod market in order to extract rents in the original game market [19].
A second serious risk that firms may face is “two-stage entry” risk, the possibility of having a partner move from innovating in the complement product to innovating in the basic product [19]. Blizzard Entertainment, the software firm behind the tremendously popular MMOG World of Warcraft, for instance, had to face BnetD, an open source program that lets gamers set up their own private servers to play the game instead of using Blizzard’s fee-based Battle.net servers [10].
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Finally, a third risk concerns firms’ loss of control over the content that modders develop based on their products. For example, mods promoting norms and values that conflict with those of the original can significantly damage the value of the original game. Copyright owners of the games typically include cease-and-desist clauses in their end-user license agreements (EULAs) in order to reduce this form of risk.
Stimulating Consumer-Driven Innovations
Opening Proprietary Content for Transmutation by Consumers
PARTIAL OPENING OF A GAME’S PROPRIETARY CONTENT suggests that it is not always neces- sary to strictly choose between the private (full control) and collective (public access) ownership models. In fact, a combination of both, or a private–collective innovation model [53] could inspire both private investors and innovative consumer communities [41]. We reiterate that while many economists and legal experts adopt various positions on copyright law aiming to strike the proper balance between control and access [25, 31], we take the current intellectual property regulations as given and only discuss firm strategy with respect to its copyright enforcement decision. Given all the value that can be extracted from the modding community and the additional risks that must be born by the firm when outsourcing to networks of consumers, the choice of whether to fully enforce their copyrights or how much proprietary content to make available to the public constitutes a powerful strategic tool for the innovating firm.
We therefore suggest our first theoretical proposition:
Proposition 1: In the presence of complementarity between mods and the under- lying original game, the optimal strategy for profit-maximizing game developers will include partially opening proprietary content to modders.
Compensation of Innovative Consumers
By issuing an M3 mod as a stand-alone retail product, the game developers can real- ize significant profits while the innovative network of consumers absorbs most of the product design and development costs. For the digital consumer network to continue generating innovative ideas, though, the interests and incentives of both producers and consumers should be aligned. It is often argued that consumers that are intrinsi- cally motivated actively participate in and contribute to online community network tasks because they enjoy topical challenges, gain status and reputation, get ego grati- fication, and may even land future job offers [33]. Full development of an M3 mod, however, necessitates an average of three years of continuous laborious effort [28]. Based on the data presented in Table 1, the modding community only completes about 35 percent of all the M2 projects it starts, which raises the questions of whether the intrinsic rewards alone provide enough incentive for modders to continue supplying superior mods in the long run, and whether it might be in the game developing firm’s
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interest to provide extrinsic motivation and share some of the value drawn from M3 mods with their creators.
The literature suggests that financial remuneration may possibly create social bar- riers, and discourage cooperation [49] or crowd out existing intrinsic motivation [29, 40] in some settings. Overall, extrinsic motivation can undermine, enhance, or have no effect on intrinsic motivation [7]. Similar to Hars and Ou [22], we assume, for our case, dominance of extrinsic motivation—that is, productivity gains from extrinsic rewards are not (fully) offset by losses from diminished intrinsic rewards. This is due to the long-term commitment to the modding project that is necessary to fully develop new game ideas, and also for the fact that the video game firms typically retain owner- ship of the modder-generated products.
Producers may therefore have incentive to cooperate more deeply with the modders and share the rents with them. Not compensating the modders might decrease the firm’s costs and increase its efficiency ex post, but it could hamper ex ante efficiency by dampening the users’ motivation to create superior mods in the future [19]. Likewise, since MMOGs exhibit network effects and the game publishing firm is a monopolist in each game it produces, the firm has incentive to subsidize the innovative consumer network [18]. In fact, the upholding of network effects necessitates a high output of free mods that can be played online in a multiplayer setting. Encouraging consum- ers, through competitions or explicit ex post remuneration, to generate superior mods would ensure that game complement output remains at a high level. Furthermore, even if modding consumers cannot obtain copyrights for their designs, a game developing firm ought to willingly offer value-sharing contracts with high-performing modders to help ensure that they do not sell their ideas to a competitor [4]. This is especially the case for total conversion mods that could technically be ported to any other game that has a flexible engine supporting transmutation.
We therefore suggest our second theoretical proposition:
Proposition 2: Assuming dominance of extrinsic motivation, the optimal strategy for profit-maximizing game developers that open content for modding will include monetary compensation to the best modders.
A Simple Economic Model
TRADITIONALLY, CONTENT DEVELOPERS KEPT THEIR SOURCES closed and compensation was meaningless as there were, without access to content, no legitimate modders. As dis- cussed above, some firms have begun experimenting with opening content to various extents, although current industry practice among those firms is to not offer any direct financial compensation. While the case analysis, given in the second section, discusses the risks and benefits of modding to the firm in its entire complexity, we now present some initial formal analysis that focuses specifically on managing modder-contributed innovation in terms of the quality of M3 mods. The two principle questions concern- ing producer–consumer collaboration for innovation are (1) if game developing firms should make proprietary content available for transmutation by consumers given the
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additional risks involved in the process, and, if so, (2) if firms should compensate their innovating consumers to ensure a continuous supply of superior M3 mods.
We next present a simple economic model that aims to derive the optimal compensa- tion rate and the optimal content openness level for profit-maximizing firms that are turning user-generated derivatives (M3 mods) into new retail products. We exclude M1 and M2 mods from our basic model because only M3 mods present new product innovation that is reintegrated into the firm’s product portfolio.
Following work in cultural economics that emphasizes quality when modeling artistic output [47], and because quality is the selection criterion for picking the M3 from the pool of M2 mods, we develop a production function for consumer-designed video games (i.e., appropriated M3 mods). The function’s output is quality, Q, and its inputs are labor, intellectual capital, and human capital.
Q = f (L, S, H). (1)
Labor, L, is the time that modders invest in the creation effort. The firm’s effort is captured in S, which represents the source material that it makes available to the modding community. For modders engaging in transmutation of video games, in- tellectual capital is the proprietary digital content, S, that the firm chooses to make public. Human capital, H, refers to a modder’s expertise in using the toolkits and his or her creative talent.
Q represents the quality of the produced mod and is positively related to L, S, and H—that is, the partial derivatives Q
L , Q
S , and Q
H > 0. S may best be understood as
the proportion of the original game content that the firm makes accessible to modders and S hence varies between 0 and 1. For S = 0, the creators of the original video game fully enforce their copyrights to prevent the external creation of derivative products, whereas for S = 1, the original game content is offered in a complete open source setting. Any value of S between 0 and 1 denotes a partial opening of digital content.2 Similarly, copyright enforcement means the degree to which content remains closed and, in our case, is 1 – S. H varies between 0 and 1 as well, where H = 0 means users with neither expertise nor talent and H = 1 indicates perfect proficiency in using the toolkits and superior creativity. Because we are modeling the quality of the very best mods, M3, it is reasonable that we set H = 1.
As in other sectors in the entertainment industry, game providers essentially behave like price takers. We observe little price differentiation in the current market. Most standard games sell for about $40 to $50 per copy. Although this situation may, and perhaps should, change in the future, we assume in our model, in line with current industry practice, that the retail price of a video game, regardless of quality, is fixed by market forces at price point P. We further assume that the sales Y of a consumer- created video game is directly proportional to the quality of the M3 mod on which it is based, or Y = αQ. Compensation for creators of superior mods, C, is royalty based, with the creators obtaining a percentage of revenues after the superior mod is appropriated and issued as a stand-alone product. C = r P Y, where r is the royalty rate that varies between 0 and 1. In the extreme cases, r = 0 denotes no monetary compensation for
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consumer innovators and r = 1 implies that creators of superior mods appropriate all the revenues from the release of the mod as an independent video game.
It is normally assumed that, unlike regular labor, artists are mainly driven by non- pecuniary motivations [8]. But while video game production involves artistic inspira- tion, it also requires substantial amounts of professional labor to fully develop game ideas. We posit that in addition to internal rewards derived from the expression of artistic ideas, modders respond to financial incentives when developing fully functional mods. We hence assume that the effort and time invested in the creation of a superior mod are positively related to the royalty rate, or L
r > 0.
Absolute Profit Maximization with Highest-Quality M3 Mods
A video game–producing firm that needs to decide how much game code to open to the community and what royalty rate to offer to M3 modders is interested in maximizing its absolute profits π, where
π = revenues – compensation of innovating consumers – additional costs.
Similar to literature on firm innovation that generally formulates research and devel- opment costs as a quadratic cost function [21], the additional costs in our model, tS2, are quadratic in source openness and represent losses arising from the risks of opening content to consumers and exposing the firm to piracy, poaching, and two-stage entry risks. The marginal cost of making additional content public is 2tS, with the marginal cost increasing as more source code is opened. This gives a full statement of the profit function to be maximized:
max (r, S)
π = PαQ – rPαQ – tS2. (2)
The optimum levels of modder compensation and copyright enforcement are obtained by simultaneously solving the first-order conditions and assuming that the second-order conditions are met. As shown in the Appendix, the optimal royalty payments are
r
e L
e L
L r
L r * ,=
+1 (3)
where eL is the labor elasticity of quality and Lr is royalty elasticity of labor. The r* function is strictly greater than 0 and reaches a value of 1 at the limit. Therefore, r* suggests offering creators of superior mods financial compensation. This analytic result supports Proposition 1.
As firms in the video game industry are moving away from traditional production models, where compensating innovative consumers is irrelevant, and are increasingly incorporating user-contributed innovation, they may need to offer direct compensation to modders, which is in contrast to the current industry practice of r = 0.
Optimal copyright enforcement is 1 – S*, where
208 ARAKJI AND LANG
S PYe
t e L
S
L r * =
+( )2 1
(4)
and eS is the source-openness elasticity of quality. Under the condition
t PYe
e L
S
L r >
+( )2 1 ,
which indicates that the potential financial losses arising from opening content need to be substantial,3 S* is bounded between 0 and 1. This limitation is consistent with our previous discussion and our assumption that there are significant risks to opening content. Thus, we derive from our analysis that it is optimal for the firm to open some content, which supports Proposition 2. In addition, the higher the magnitude of t or the risks involved in opening proprietary content, the higher the optimal copyright enforcement level.
It is important to note that 1 – S* and r* represent the optimal combination of copyright enforcement and royalty payment that would yield the highest possible M3 quality level Q* that maximizes absolute profits π*. The quality of M3 mods may not always meet the Q* level when, for technical or strategic reasons, producing firms cannot attain the levels of S* and r*. There is, however, an optimal combination of r and S that would minimize costs, and hence maximize profits, for each given mod quality level.
Profit Maximization for Varying M3 Mod Quality Levels
Assuming that the quality production function Q (L, S, H) follows the generalized Cobb–Douglas or the generalized constant elasticity of substitution forms, its isoquants will be convex to the origin. Under some conditions and parameter restrictions, a quadratic or a transcendental form would result in convex to the origin isoquants as well [6].
An isoquant is a curve depicting all possible combinations of two inputs for the production of a given quantity of output. In our modding case, the expertise and creativity level H is fixed at 1, leaving only L and S as variable inputs. The convex- ity implies that as one moves along the isoquant of any given M3 mod quality level, there is a trade-off between L and S. In other words, if the firm wishes to decrease its royalty rate, which would decrease labor time and effort invested in the development of the mod, it has to decrease its copyright enforcement level and make more content available for transmutation to maintain the same mod quality level (Figure 2). Alter- natively, a firm that prefers to be strict in enforcing its copyrights needs to increase its royalty rate to give modders the incentive to devote the required effort needed to produce, with less intellectual capital (i.e., available transmutable content) to work with, the same quality mod.
Even though different combinations of r and S may be used to produce a given mod quality, there is only one combination that would minimize the costs and hence maxi-
DIGITAL CONSUMER NETWORKS AND PRODUCER–CONSUMER COLLABORATION 209
mize profits at that quality level. The optimal combination of r and S is found by solving the constrained minimization of input costs, IC, at the particular quality level.
min (r,S)
IC = rPαQ + tS2 (5)
subject to
q – Q(L, S, H) = 0.
The optimal combination of S and r (derived in the Appendix, and assuming that the second-order condition holds) satisfies the following equation:
r tS e L
e PQ
L r
S =
2 2
α .
(6)
This equation corresponds to the expansion path of a video game firm, which is the curve shown in Figure 2, that illustrates the least-cost combination of S and r for ev- ery level of desired quality q, where q3 > q2 > q1. We also note that r* and S*, which were derived above and were associated with the highest mod quality Q* and absolute profits π*, must satisfy Equation (6) as well.
Some Implications for Firm Strategy
We do not have much empirical data on the precise values of the levels of r and S and their interrelationship. But current industry practice has only some firms experiment- ing with opening content (i.e., some firms set S = 0 while others set S > 0) and gener- ally does not offer any direct compensation rate to modders (i.e., at present, r = 0),
Figure 2. Quality Isoquants and the Royalty Rate/Content Opening Optimal Path
r tS e L
e PQ
L r
S =
2 2
α
210 ARAKJI AND LANG
whereas our theoretical analysis suggests that optimal modding strategies would set S > 0 and r > 0. Drawing on the convexity of the isoquants in addition to the expan- sion path for the optimal combination of royalty rate and copyright enforcement, we can formulate theoretical profit-maximizing strategies for firms that are engaging in producer–consumer collaboration. By choosing r and S, firms can induce behavioral modifications among modders and the quality of their output. Of course, this is not
Figure 3. Firm Strategies When the Royalty Rate or Copyright Enforcement Is Higher Than Optimal
Figure 4. Firm Strategies When the Royalty Rate or Copyright Enforcement Is Lower Than Optimal
r tS e L
e PQ
L r
S =
2 2
α
r tS e L
e PQ
L r
S =
2 2
α
DIGITAL CONSUMER NETWORKS AND PRODUCER–CONSUMER COLLABORATION 211
going to retroactively have any impact on existing mods and their quality, but affects only new mod development going forward.
We distinguish two suboptimal positions, points A and B in Figures 3 and 4, respec- tively, where a hypothetical company has arbitrarily set r > 0 and S > 0. In both cases, there are three viable strategies that the firm can pursue to reach a profit-maximizing situation for each of the three quality levels (high, medium, and low) shown in Figure 2 that represent the strategic positioning of the firm.
1. Position A (r > r* or S < S*): For a firm whose chosen royalty rate r and copy- right enforcement level 1 – S are higher than optimal—for example, at point A on isoquant q2 in Figure 3—there are three options, each corresponding to a different quality and hence revenue level, for moving toward an optimal combination of S and r.
• The firm may follow strategy a1, which entails maintaining its royalty rate and decreasing its copyright enforcement. Making additional proprietary content publicly available will allow modders to design better quality derivatives in future projects. The firm will move up to isoquant q3, which will generate higher revenues.
• Technical reasons may make it infeasible for the firm to open any additional content, lest it compromise the complementarity condition. For the game Half-Life, for example, if the optimal S* were above 80 percent, part of the game engine would be open, risking that the created mods may run without the original product. In that case, the firm may have no choice but to adopt strategy a2, decrease its royalty rate for new modding acquisitions, and move to a lower quality level.
• The firm may implement strategy a3 by simultaneously decreasing its roy- alty rate and copyright enforcement level. This strategy will minimize costs while maintaining the quality level and revenues of isoquant q2. With a3, the company will implement a more efficient production of quality q2 than at point A.
2. Position B (r < r* or S > S*): When the chosen royalty rate r or copyright en- forcement 1 – S are lower than optimal—for example, at point B on isoquant q2 in Figure 4—the three alternative profit-maximizing strategies are:
• The firm may adhere to strategy b1 by keeping its copyright enforcement level unchanged while increasing its royalty rate. This strategy will move the firm up to isoquant q3, boosting its revenues.
• If the firm is concerned about losing control over its proprietary content, it may follow strategy b2 and increase its copyright enforcement level. This strategy will decrease the quality of mods from q2 to q1 and will hence have a negative effect on the firm’s revenues.
• In the presence of production inefficiencies, the firm may opt for strategy b3 and simultaneously increase its royalty rate and copyright enforcement level. This strategy keeps the firm on isoquant q2, maintaining its revenues but minimizing costs as well.
212 ARAKJI AND LANG
Conclusion
THIS PAPER HAS EXPLORED PRODUCER–CONSUMER collaboration efforts in the context of product innovation in the video game industry. The success of this new form of collaboration depends on the presence of a market in which consumer demand is heterogeneous and changes rapidly, on the absence of high product performance and resource requirements, and, as the present analysis concluded, also on the presence of complementarity among the derivative and the original product.
Separating game content from the game engine that serves as a platform on which the original game content as well as all the derived mods need to run greatly reduces the risk of outsourcing innovation and development of new game designs to digital consumer networks. Allowing the core product—the game—to be developed by a network of consumers would increase the risk of poaching and the risk of competitor firms masquerading as users and likely cause wealth transfer away from the creator of the original game. In such a case, it would probably be more prudent to collaborate with just a few lead users or some trusted partner firms that would help in the design of the core product, under strict confidentiality. In fact, some game developers have remained successful in the market without allowing substantial modding.
We suggest that the absence of complementarity between derivatives and original works explains why the movie and music industries have been less receptive to opening content to their user communities. A remixed song or movie plays just as well, whether or not you have the original piece, which may lead to a complete transfer of rents from the firms to consumers. However, remixing of limited content such as trailer clips has been allowed by some movie studios [44] since trailers do exhibit complementarity and do not replace the original movies. They only support promotion strategies.
Exploiting the complementarity property in game design, developers may take the right to enforce partial rather than full content protection and thus partial rather than full revenue transfer to the modder. Enforcement of copyright protection afforded by law is therefore not just a mere legal restraint on the development of derivative products by consumers but can also be considered a powerful strategic tool that enables the firm to retain most of the value of consumer-designed derivatives. Our model sug- gests that producers have incentive to partially open their content for transformation by consumers and to compensate the creators of superior derivatives.
There are a number of questions and issues that arise from the present study that need to be addressed in the future. We need to ask whether game players are better off now because their preferences are better reflected by the new supply of games that incorporate modding. The formal analysis could be extended to incorporate, for example, the impact of M2 mods on original game sales and to explicitly link M1 and M2 to quality of M3 mods. It would also be desirable to refine the representation of risk in the model to better capture the complex and multifaceted benefit–risk trade- offs that exist. Finally, we would like to suggest a simulation methodology [3] as an alternative to analytical modeling, which could allow us more adequate modeling of the complex dynamics of modder behavior, once better data become available.
DIGITAL CONSUMER NETWORKS AND PRODUCER–CONSUMER COLLABORATION 213
NOTES 1. SteamTM Subscriber Agreement, Valve Corporation, Bellevue, WA (available at www.
steampowered.com/v/index.php?area=subscriber_agreement). 2. In the case of Half-Life, for example, the game developer Valve set S = 0.8 by choosing
to open the 80 percent of source code that represents the game content while keeping the engine (the remaining 20 percent) closed.
3. For example, let us suppose that all elasticities were equal to 1. In this case, any value for t that represents a quarter of total sales or more would indicate substantial risk and would bound S*.
REFERENCES 1. 2006 sales, demographic and usage data. Technical Report, Entertainment Software
Association. Washington, DC, 2006 (available at http://www.theesa.com/archives/files/ Essential%20Facts%202006.pdf).
2. 2006 U.S. video game and PC game retail sales reach $13.5 billion exceeding previous record set in 2002 by over $1.7 billion. Press Release, NPD Group, Port Washington, New York, January 2007.
3. Abrahamson, E., and Rosenkopf, L. Social network effects on the extent of innovation diffusion: A computer simulation. Organization Science, 8, 3 (1997), 289–309.
4. Anton, J.J., and Yao, D.A. Expropriation and inventions: Appropriable rents in the absence of property rights. American Economic Review, 84, 1 (1994), 190–209.
5. Barlow, J.P. The economy of ideas. Wired Magazine, 2.03 (March 1994) (available at www.wired.com/wired/archive/2.03/economy.ideas.html).
6. Beattie, B.R., and Taylor, C.R. The Economics of Production. New York: John Wiley & Sons, 1985.
7. Benabou, R., and Tirole, J. Incentives and prosocial behavior. American Economic Review, 96, 5 (December 2006), 1652–1678.
8. Benhamou, F. Artists’ labour markets. In R. Towse (ed.), A Handbook of Cultural Eco- nomics. Cheltenham, UK: Edward Elgar, 2003, pp. 69–75.
9. Benkler, Y. Coase’s penguin, or, Linux and the nature of the firm. Yale Law Journal, 112, 3 (2002), 369–447.
10. Blizzard v. BNetD. Electronic Frontier Foundation, San Francisco (available at www.eff. org/IP/Emulation/Blizzard_v_bnetd/).
11. Castells, M. The Rise of the Network Society. Oxford: Blackwell, 1996. 12. Castells, M. Materials for an exploratory theory of the network society. British Journal
of Sociology, 51, 1 (January–March 2000), 5–24. 13. Chiang, A.C. Fundamental Methods of Mathematical Economics. New York: McGraw-
Hill, 1967. 14. Clemons, E.K. Corporate strategies for information technology: A resource-based ap-
proach. IEEE Computer, 24, 11 (November 1991), 23–32. 15. Clemons, E.K, and Hitt, L.M. Poaching and the misappropriation of information: Transac-
tion risks of information exchange. Journal of Management Information Systems, 21, 2 (Fall 2004), 87–107.
16. Clemons, E.K.; Gu, B.; and Spitler, R. Hyper-differentiation strategies: Delivering value, retaining profits. In R.H. Sprague Jr. (ed.), Proceedings of the Thirty-Fifth Annual Hawaii International Conference on System Sciences. Los Alamitos, CA: IEEE Computer Society Press, 2003 (available at http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/ dl/proceedings/&toc=comp/proceedings/hicss/2003/1874/08/1874toc.xml&DOI=10.1109/ HICSS.2003.1174592).
17. Dellarocas, C. The digitization of word of mouth: Promise and challenges of online feedback mechanisms. Management Science, 49, 10 (October 2003), 1407–1424.
18. Economides, N. The economics of networks. International Journal of Industrial Orga- nization, 14, 6 (1996), 675–699.
214 ARAKJI AND LANG
19. Farrell, J., and Katz, M.L. Innovation, rent extraction, and integration in systems markets. Journal of Industrial Economics, 48, 4 (December 2000), 413–432.
20. Farrell, J., and Shapiro, C. Intellectual property, competition, and information technology. In H.R. Varian, J. Farrel, and C. Shapiro (eds.), The Economics of Information Technology: An Introduction. Cambridge: Cambridge University Press, 2004, pp. 49–85.
21. Greenlee, P. Endogenous formation of competitive research sharing joint ventures. Journal of Industrial Economics, 53, 3 (September 2005), 355–391.
22. Hars, A., and Ou, S. Working for free? Motivations for participating in open-source projects. International Journal of Electronic Commerce, 6, 3 (Spring 2002), 25–39.
23. Hughes, J.K., and Lang, K.R. If I had a song: The culture of digital community networks and its impact on the music industry. Journal of Media Management, 5, 3 (2003), 180–189.
24. Hughes, J.K., and Lang, K.R. Transmutability: Digital decontextualization, manipula- tion, and recontextualization as a new source of value in the production and consumption of culture products. In R.H. Sprague Jr. (ed.), Proceedings of the Thirty-Ninth Annual Hawaii International Conference on System Sciences. Los Alamitos, CA: IEEE Computer Society Press, 2006 (available at http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/ dl/proceedings/&toc=comp/proceedings/hicss/2006/2507/08/25078toc.xml&DOI=10.1109/ HICSS.2006.511).
25. Hunter, D. Cyberspace as place and the tragedy of the digital anticommons. California Law Review, 91, 2 (March 2003), 442–519.
26. Huston, L., and Sakkab, N. Connect and develop: Inside Procter and Gamble’s new model for innovation. Harvard Business Review, 84, 3 (March 2006), 58–66.
27. Hyman, P. Video game companies encourage “modders.” Hollywood Reporter, Los Angeles, April 9, 2004 (available at www.hollywoodreporter.com/hr/search/article_display. jsp?vnu_content_id=1000484956).
28. Jeppesen, L.B. Profiting from innovative user communities: How firms organize the production of user modifications in the computer games industry. Working Paper Series IVS/ CBS 2004–3, Department of Industrial Economics and Strategy, Copenhagen Business School, Copenhagen, Denmark, 2004.
29. Kunreuther, H., and Easterling, D. Are risk–benefit tradeoffs possible in siting hazardous facilities? American Economic Review, 80, 2 (May 1990), 252–286.
30. Landes, W., and Posner, R. An economic analysis of copyright law. Journal of Legal Studies, 18, 2 (June 1989), 325–363.
31. Landes, W., and Posner, R. The Economic Structure of Intellectual Property Law. Cam- bridge: Belknap Press, 2003.
32. Lee, G.K., and Cole, R.E. From a firm-based to a community-based model of knowl- edge creation: The case of the Linux kernel development. Organization Science, 14, 6 (2003), 633–649.
33. Lerner, J., and Tirole, J. Some economics of open source. Journal of Industrial Econom- ics, 50, 2 (2002), 197–234.
34. Lessig, L. The Future of Ideas. New York: Random House, 2001. 35. Lessig, L. Free Culture: How Big Media Uses Technology and the Law to Lock Down
Culture and Control Creativity. New York: Penguin Press, 2004. 36. Malone, T.W. The Future of Work: How the New Order of Business Will Shape Your
Organization, Your Management Style, and Your Life. Boston: Harvard Business School Press, 2004.
37. Nahm, J. Open architecture and R&D incentives. Journal of Industrial Economics, 52, 4 (2004), 547–568.
38. Nambisan, S. Information systems as a reference discipline for new product development. MIS Quarterly, 27, 1 (2003), 1–18.
39. Organization for Economic Cooperation and Development. Digital broadband content: The online computer and video game industry. Committee for Information, Computer and Com- munication Policy, Paris, May 12, 2005 (available at www.oecd.org/dataoecd/19/5/34884414. pdf).
40. Osterloh, M., and Frey, B. Motivation, knowledge transfer and organizational form. Organization Science, 11, 5 (2000), 538–550.
41. Parker, G., and Van Alstyne, M. Mechanism design to promote free market and open source software innovation. In R.H. Sprague Jr. (ed.), Proceedings of the Thirty-Eighth Annual Hawaii
DIGITAL CONSUMER NETWORKS AND PRODUCER–CONSUMER COLLABORATION 215
International Conference on System Sciences. Los Alamitos, CA: IEEE Computer Society Press, 2005 (available at http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/ dl/proceedings/&toc=comp/proceedings/hicss/2005/2268/08/2268toc.xml&DOI=10.1109/ HICSS.2005.406).
42. Perelman, M. Steal This Idea: Intellectual Property Rights and the Corporate Confisca- tion of Creativity. New York: Palgrave Macmillan, 2002.
43. Stevenson, N. Understanding Media Cultures: Social Theory and Mass Communication. Thousand Oaks, CA: Sage, 2002.
44. Sullivan, L. Video social networking enables movie-mashup contest. InformationWeek (May 17, 2006) (available at http://www.informationweek.com/industries/showArticle. jhtml?articleID=187900395).
45. Teece, D. The Competitive Challenge: Strategies for Industrial Innovation and Renewal. New York: Harper & Row, 1987.
46. Thomke, S., and Von Hippel, E. Customers as innovators: A new way to create value. Harvard Business Review, 80, 4 (April 2002), 5–11.
47. Throsby, D. An artistic production function: Theory and an application to Australian visual artists. Journal of Cultural Economics, 30, 1 (2006), 1–14.
48. Van Zandt, T. Decentralized information processing in the theory of organizations. In M. Sertel (ed.), Contemporary Economic Issues, vol. 4: Economic Design and Behavior. London: Macmillan, 1999, pp. 125–160.
49. Vohs, K.D.; Mead, N.; and Goode, M. The psychological consequences of money. Science (November 17, 2006), 1154–1156.
50. Von Hippel, E. Lead users: A source of novel product concepts. Management Science, 32, 7 (1986), 791–805.
51. Von Hippel, E. Democratizing Innovation. Cambridge, MA: MIT Press, 2005. 52. Von Hippel, E., and Katz, R. Shifting innovation to users via toolkits. Management Sci-
ence, 48, 7 (2002), 821–833. 53. Von Hippel, E., and Von Krogh, G. Open source software and the “private collective” inno-
vation model: Issues for organization science. Organization Science, 14, 2 (2003), 209–223. 54. Zittrain, J.L. Technological Complements to Copyright. New York: Foundation Press,
2005. 55. Zittrain, J.L. The generative Internet. Harvard Law Review, 119, 7 (2006), 1975–2040.
Appendix: Mathematical Derivations
max (r, S)
π = PαQ – rPαQ– tS2.
First-Order Conditions
1. ∂ ∂
= π r
0
∂ ∂
= ∂ ∂
∂ ∂
− − ∂ ∂
∂ ∂
= π
α α α r
P Q
L
L
r P Q Pr
Q
L
L
r 0
∂ ∂
∂ ∂
− − ∂ ∂
∂ ∂
= Q
L
L
r Q r
Q
L
L
r 0
r
Q
L
L
r
Q
L
L
r Q
∂ ∂
∂ ∂
= ∂ ∂
∂ ∂
−
216 ARAKJI AND LANG
r
Q
L
L
r Q
Q
L
L
r
* =
∂ ∂
∂ ∂
−
∂ ∂
∂ ∂
r Q
Q
L
L
r
* = − ∂ ∂
∂ ∂
1
r Q
L
Q Q
L
L
Q
L
r
* = − ∂ ∂
∂ ∂
1
r L
e L
r
e Q
L
L
QL L* ,= −
∂ ∂
= ∂ ∂
1 where
r L
r
L
e L
r
r
L L
*
*
* = −
∂ ∂
1
r
r
e L L
L
r
r
LL r r*
* *
,= − = ∂ ∂
1 where
r
e L
e L
L r
L r * =
+1
2.
∂ ∂
= π S
0
∂ ∂
= ∂ ∂
− ∂ ∂
− = π
α α S
P Q
S P r
Q
S tS2 0
2tS P Q
S r
Q
S =
∂ ∂
− ∂ ∂
α
S
P Q
S r
t * =
∂ ∂
−( )α 1 2
S P
Q
S
S
Q r
t S
Q
*
*
* =
∂ ∂
−( )α 1
2
DIGITAL CONSUMER NETWORKS AND PRODUCER–CONSUMER COLLABORATION 217
S
P Qe r
tS e
Q
S
S
Q
S S*
*
*
,= −( )
= ∂ ∂
α 1 2
where
S
PYe r
t Y Q
S * ,=
−( ) =
1
2 where α
S PYe
t e L r
e L
e L
S
L r
L r
L r * ,=
+( ) =
+2 1 1 where
Second-Order Conditions
1. π rr < 0
αP L
r r
L
r
Q
L r
Q
L
Q
L r −
∂ ∂
+ − +( ) ∂ ∂
∂ ∂
− − +( ) ∂ ∂
∂ ∂ ∂
<2 1 1 0
2
2
2
2. π rr π
SS – (π
rS )2 > 0
α αP t P r Q
S
L
r r
L
r
Q
L − − − +( ) ∂
∂
−
∂ ∂
+ − +( ) ∂ ∂
∂ ∂
− −2 1 2 1 1 2
2
2
2 ++( ) ∂
∂ ∂ ∂ ∂
− ∂ ∂
+ − +( ) ∂ ∂ ∂
>
r L
r
Q
L r
P Q
S r
Q
r S
2
2 2
1α 00
min (r,S)
IC = rPαQ + tS2 subject to q – Q(L, S, H) = 0
Forming the Lagrangean function to transform the constrained minimization into an unconstrained one [13]:
LIC = rPαQ + tS2 – λ[q – Q(L, S, H)]
First-Order Conditions
1.
∂ ∂
= LIC
λ 0
∂ ∂
= − ( ) =LIC q Q L S H λ
, , 0
2.
∂ ∂
= LIC
r 0
218 ARAKJI AND LANG
∂ ∂
= + ∂ ∂
∂ ∂
− ∂ ∂
∂ ∂
= LIC
r P Q rP
Q
L
L
r
Q
L
L
r α α λ 0
λ α α
∂ ∂
∂ ∂
= + ∂ ∂
∂ ∂
Q
L
L
r P Q rP
Q
L
L
r
λ α
α= ∂ ∂
∂ ∂
+ P Q Q
L
L
r
rP
3.
∂ ∂
= LIC
S 0
∂ ∂
= ∂ ∂
+ − ∂ ∂
= LIC
S rP
Q
S tS
Q
S α λ2 0
λ α
∂ ∂
= ∂ ∂
+ Q
S rP
Q
S tS2
λ α= + ∂ ∂
rP tS Q
S
2
Equating the value of λ in the second and third first-order conditions yields:
P Q Q
L
L
r
rP rP tS Q
S
α α α
∂ ∂
∂ ∂
+ = + ∂ ∂
2
P Q Q
L
L
r
tS Q
S
α ∂ ∂
∂ ∂
= ∂ ∂
2
P Q L
Q Q
L
L
Q
L
r
tS Q
S
α
∂ ∂
∂ ∂
= ∂ ∂
2
P L
e L
r
tS Q
S
e Q
L
L
QL Lα
∂ ∂
= ∂ ∂
= ∂ ∂
2 , where
P L r
L
e L
r
r
L
tS Q
S L
α
∂ ∂
= ∂ ∂
2
DIGITAL CONSUMER NETWORKS AND PRODUCER–CONSUMER COLLABORATION 219
P r
e L
tS Q
S
L L
r
r
LL r rα =
∂ ∂
= ∂ ∂
2 , where
P r
e L
tS S
Q Q
S
S
Q
L r
α =
∂ ∂
2
P r
e L
tS
e Q e
Q
S
S
QL r S Sα = =
∂ ∂
2 2 , where
r tS e L
e PQ
L r
S =
2 2
α
Second-Order Condition
�H
LIC LIC
r
LIC
S
LIC
r
LIC
r
LIC
r S
L
=
∂ ∂
∂ ∂ ∂
∂ ∂ ∂
∂ ∂ ∂
∂ ∂
∂ ∂ ∂
∂
2
2
2 2
2 2
2
2
2
λ λ λ
λ IIC
S
LIC
r S
LIC
S∂ ∂ ∂ ∂ ∂
∂ ∂
<
λ
2 2
2
0
0
2 2
− ∂ ∂
∂ ∂
− ∂ ∂
− ∂ ∂
∂ ∂
∂ ∂
∂ ∂
+ −( ) ∂ ∂ ∂
∂ ∂
+ ∂ ∂
Q
L
L
r
Q
S
Q
L
L
r P
Q
L
L
r Pr
Q
L r
L
r
Q α α λ
LL
L
r P
Q
S Pr
Q
r S
Q
S P
Q
S Pr
Q
∂ ∂
∂ ∂
+ −( ) ∂ ∂ ∂
− ∂ ∂
∂ ∂
+ −( ) ∂ ∂
2
2
2
2
α α λ
α α λ rr S
t Pr Q
S∂ + −( ) ∂
∂
<
2
0
2
2 α λ