JITTA JOURNAL OF INFORMATION THEORY AND APPLICATION

AN ANALYSIS OF

MOHAMMAD M. RAHMAN, North South University School of Business, Banani C/A, Dhaka 1213, Bangladesh, Tel: +880 (181) 776 8484, Fax: +880 (2) 882 3030, : [email protected]

ABSTRACT

Wikipedia is defined by its founders as the “free that anyone can edit.” This property, we argue, makes Wikipedia a public good and hence subject to under-provision. A puzzling feature of Wikipedia however is its enormous size, at roughly seven times that of its commercial counterparts. What is driving this growth? And how can we assess the reliability of this giant encyclopedia arising solely from free-editing? We model contribution to Wikipedia and its reliability. We demonstrate that Wikipedia is indeed subject to free-riding, and offer a novel explanation for the mitigation of under-provision under such circumstances. We also find that the public-good feature of Wikipedia and free-riding introduce a lower-bound in the quality of Wikipedia. This finding is consistent with a previous empirical study that established Wikipedia‟s surprisingly high level of quality. We identify Wikipedia as part of a general phenomenon that we call the Collaborative Net, and that includes features such as citizen journalism and online reviews.

INTRODUCTION content composition by nontechnical users.” , the result of an open-source effort, is a relatively new technology that Perhaps the most profound, and without allows Net surfers to freely create and edit question the most well-known Wiki project is Web page content using any . It is Wikipedia, the “free encyclopedia that anyone remarkably simple technology, and with its can edit.” It is available in several languages text syntax is equally simple to use. In the including Shqip and Walon; the English words of the Wiki community: version started in 2001 and by December 2008 had more than 2.5 million articles. Googling “Like many simple concepts, „open exotic terms will almost certainly yield links to editing‟ has some profound and subtle Wikipedia sites, which may be a sign of its effects on Wiki usage. Allowing everyday quality, and is certainly a sign of its popularity. users to create and edit any page in a Other multilingual free-content projects Web site is exciting in that it encourages include , , and democratic use of the Web and promotes .

Didem Demirhan acted as the senior editor for this paper.

Rahman, M. M., “An Analysis of Wikipedia,” Journal of Theory and Application (JITTA), 9:3 2008, 81-98. Mohammad Rahman

MOTIVATION AND RESEARCH CONTRIBUTION QUESTIONS The primary contribution of this That Wikipedia is offered for free will paper is its explanation for the paradoxical not be surprising to information economists. growth of the public good Wikipedia, a free Indeed, information goods are characterized by encyclopedia that anyone can edit. To our high up-front costs and virtually zero marginal knowledge, our explanation is novel and costs of production. Since competition will contributes to the general literature on drive prices to marginal costs, much of public goods. The paper also offers information on the Internet will be offered for theoretical explanations for the surprising “free,” (or equivalently, sold with zero price empirical findings on the superior quality of tags). Even Britannica, the well-respected the giant encyclopedia arising from free- commercial encyclopedia, had to reduce its editing. This paper should be highly price for its full volume to a fraction of what it interesting to researchers engaged in the had charged consumers for years. economic modeling of information systems But what is surprising about Wikipedia, projects, particularly because of the and other free Wiki efforts is that the high up- uniqueness of Wikipedia and its difference front costs are not as significant. Wikipedia is from (other) Systems. It a collaborative effort that anyone can should also be of interest to practitioners, contribute to. Wiki as a technology reduces given the increasing popularity of publishing costs to virtually zero. A question Wikipedia and Wiki technology. about the articles then immediately follows. Can Net users gather the as a “further information from Wikipedia with a reasonable reading” resource on the topic of same-sex degree of comfort about its reliability? marriage. Sreenath Srinivasan, dean and Wikipedia has received much criticism professor of Journalism at Columbia in the past about the accuracy of its contents University first doubted Wikipedia but soon (CNN.com, 2005). Wikipedia often responded was surprised by its apparent reliability. Jimmy by making changes to its design. In December Wales, Wikipedia‟s founder, intends that 2005 for example, Wikipedia considered Wikipedia should achieve a “Britannica or requiring users to register before creating or better” quality. This may seem almost editing articles. Whereas previously, unrealistically ambitious, as “Encyclopaedia Wikipedia users did not require any formal Britannica” is the oldest English-language registration process to make even the most general encyclopedia, first published in 1768. drastic changes to an article. This was in Recent articles in the popular press and media response to a complaint in an op-ed published however indicated that Wales‟ goal with in USA Today by a prominent journalist, John Wikipedia may very well be achievable. Seigenthaler, also a former administrative CNN.com (2005) citing a study by assistant to Robert Kennedy. An article in (Giles, 2005) claimed that “Wikipedia [was] as Wikipedia had claimed he had been suspected accurate as Britannica.” They referred to the in the assassination of the former attorney Seigenthaler case, calling it “the exception general, and President John F. Kennedy rather than the rule.” (Goodin, 2005). In December 2005, following Wikipedia‟s splendid growth is the Seigenthaler controversy, the New York particularly surprising if it is to be assessed Times banned their reporters from using within a “rational” framework. That Wikipedia Wikipedia as a research tool (Musil 2005). is free makes it a public good. While And yet increasingly, Wikipedia contributors may get some benefit from it, articles are being cited in many other many other users will simply try to free-ride. traditionally trusted outlets such as newspaper Traditional economic theory suggests that columns (c.f. Drost, 2005). A favorite example Wikipedia as a public good will be subject to cited by Wikipedia themselves is their use by the tragedy of under-provision. Such under-

82 An Analysis of Wikipedia provision of public goods is usually mitigated our modeling. Cornes (1993) develops through flavors of commercialization such as Hirshleifer‟s analysis further, studying the privatization, auctioning, or subsidies. The effects of changes in income allocation. Varian case of Wikipedia is however quite surprising. (1994) extends Hirshleifer‟s work by studying Wikipedia when compared to Britannica, its the effects on equilibria when provision commercial counterpart, is much larger. If one involves sequential moves by the agents. The measure is the number of articles, Wikipedia results of the literature above do not apply so was already approximately 7 times larger in readily to the case of Wikipedia since they all 2006 than Britannica which had approximately predict very high levels of free-riding whereas 120,000 articles then. Wikipedia appears to be quite large. Wikipedia would not be the first There have been studies that investigate information systems project that began as a mechanisms in which free-riding is mitigated. public good but resulted in a quality product. Andreoni (1990) and Cornes and Sandler Indeed, many successful open-source software (1984) investigate the changes in results projects, such as Unix, were created ground-up whenever consumers are allowed benefits without the offering of any direct pecuniary directly from their private contribution in compensation. These products today are often addition to the level of the public good. While cited for their supremacy over related we believe that their work is relevant, we commercially-produced products. How is the investigate how Wiki technology in particular case of Wikipedia then any different? is able to mitigate free-riding, perhaps beyond the effects of “warm-glow” feelings suggested To summarize, the main research by Andreoni (1990) and Cornes and Sandler questions we ask in this paper are as follows: (1984).  How can we explain the surprising Free-riding has been studied in a empirical findings that an encyclopedia variety of IT application contexts. Their that anyone can edit is of a high quality? contexts, however, make their results too  How can we explain the surprisingly large specific for insights to extend readily over to size of Wikipedia, when it is a public good the Wikipedia case. Carlton and Chevalier (created by people and used by people)? (2003), for example, investigates free-riding and sales strategies for the Internet. Varian  How is the case of Wikipedia different (2004), as another example, studied free-riding from Open Source Software development, in the provision of (general) information another information systems project that is systems reliability. His study has a a public good and where neither quality probabilistic flavor, emphasizing the likelihood nor provision is compromised? of failure of information systems, and also repeats the standard extreme free-riding result. RELATED LITERATURE Two kinds of equilibria in games of For our analysis, we invoke the solution incomplete information are considered in our concept of Nash (1950) equilibrium, since we paper. First, we consider cheap-talk equilibria model the contribution to Wikipedia as a non- (cf. Gibbons, 1992) in dynamic games of cooperative game. To analyze situations incomplete information when messaging is involving sequential moves, we also consider “cheap” or costless, and hence receivers must Stackelberg equilibria, which in concept are determine the credibility of the messages. the natural applications of the Nash Second, we briefly talk about signaling equilibrium solution to dynamic games. equilibria (cf. Vega-Redondo, 2003) when In addition, the stream of economics players try to signal their types using costly literature related to the private provision of messaging techniques. public goods is relevant. Hirshleifer (1983) Wikipedia itself has been the subject in investigated the variation of public good a variety of studies. Most notably, Nature‟s provision with three different . We (Giles, 2005) study involved 42 articles use his seminal piece extensively as a basis for reviewed by experts to compare the prestigious

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 83 Mohammad Rahman

Britannica to the free giant Wikipedia. Their It is easy to recognize (1) as the results indicated that the average scientific function of agents in a game involving the entry in Wikipedia contained four errors or private provision of a public good. And it is omissions, while Britannica had three. easy to envision Wikipedia in the same Nonetheless, Wikipedia is planning on test- context. Every Internet citizen can potentially launching a reviewing program. Forte and benefit from having Wikipedia. Contributing to Bruckman (2005) investigate why people write Wikipedia however will involve a positive cost for Wikipedia even when the encyclopedia function. Not surprisingly, we can intuitively does not provide bylines to credit authors for expect free-riding as a result. That is, more their hard work by interviewing 22 people will simply use Wikipedia than Wikipedians. They are however unable to contribute to it. We shall now derive that derive economic explanations, and instead standard result. suggest „softer‟ incentives such as engagement First, we need to determine the reaction in desirable activities. Finally, IBM research functions and Nash equilibria for this (c.f. Wattenberg et al., 2007) uses simultaneous contribution game. A reaction sophisticated HCI technology to track the function fx() gives the optimal strategy of contribution by Wikipedians, and the growth ij of Wikipedia articles. They find that while agent i given a choice of x j by agent j , most articles have been vandalized, “vandalism j{0,1}, j i . Let the reaction function of is usually repaired extremely quickly.” agent i be given by fi . We assume that vi and c are twice continuously differentiable for all THE CONTRIBUTION PARADOX OF i WIKIPEDIA i . The first-order condition is given by '' We will begin by modeling Wikipedia vi()() x i x j c i x i . as a public good, and illustrate the standard derivation of the free-rider result, and its If we assume that ci is linear in xi , under-provision property. Suppose that there ci() x i  i x i , where i is a positive constant, are two agents, i {1,2} , and that each can ' and that vi has an inverse, we can define choose to contribute a level xi to Wikipedia. ˆ '1 . This is in very general terms. It may refer to a xvi () i i correction of an error, or the authoring of a If we solve for agent i ‟s contribution major article. Doing so, each agent i receives under the first-order condition, we see that it is a payoff of xxˆij . To derive agent i ‟s reaction function u v()() x  x  c x (1) i i i j i i fi , we only need impose a non-negativity constraint to get where vi is monotone concave function f( x ) max{ xˆ x ,0} . increasing in the total contribution, and ci is i j i j the cost function for that agent, and We can define and account for j{1,2}, j i . differences in the tastes of the agents in terms ˆ Since (1) is key to our analysis, we will of xi . More formally, we say that agent i likes explain its form. First, we are defining Wikipedia better if and only if xxˆˆij . This is

Wikipedia to be xxij , the total contribution, because xˆi can be defined as agent i ‟s as it is created entirely by Internet users. Every standalone contribution: the amount he individual benefits from having such a website, contributes to Wikipedia when the other agent hence the function vi . That function is concave does not contribute at all. to reflect the standard diminishing marginal We may plot the reaction functions f utility assumption. For each individual, the net 1 utility depends also on the cost of his own and f2 of agents 1 and 2 on the same pair of contribution. axes. This is given in figure 1. The x -axis

84 An Analysis of Wikipedia

gives values of x1 whereas the y -axis gives how a growth paradox persists even as the ** number of agents increases. values of x2 . Any point (,)xx12 where the two response function will intersect will Suppose, without loss of generality, correspond to a Nash equilibrium. This is agent 2 likes Wikipedia more than agent 1, that ** ** is xxˆˆ . Then in the unique Nash because at (,)xx12 , f1() x 2 x 1 , and 21 f() x** x which satisfies the definition of a equilibrium, agent 2 provides all of the 2 1 2 articles, and agent 1 free-rides. If xxˆˆ , then Nash equilibrium. When only one such point 21 exists, the Nash equilibrium is unique. Looking a plethora of Nash equilibria exist as the at figure 1, the proposition that follows is then reaction functions will coincide. But as is clear immediate. from the figure, the total size will still be unique in equilibrium. Paradox 1a: If the contribution to Wikipedia is modeled as the standard Paradox 1b: In the two-agent provision private provision game where the utility game of Wikipedia where the utility functions have the form given in (1), there functions have the form given in (1), all exists a unique total size of the contributions to Wikipedia are made by encyclopedia in equilibrium. A Nash the agent(s) who like it most. All other equilibrium always exists, and is unique agents free-ride. when the two agents have different tastes. We now contrast that expected outcome Paradox 1a suggests that Wikipedia against the social optimum. The social problem cannot be expected to grow perpetually, which will solve clearly contradicts the continually growing maxv1 ( x 1  x 2 )  v 2 ( x 1  x 2 )()  c 1 x 1  c 2 () x 2 characteristic of Wikipedia that can be xx12, observed. (Between January 2006 and s. t . x12 0, x 0 December 2008, Wikipedia tripled in size.) While it was assumed that the number of agents was fixed, shortly we will demonstrate

x2

f1(x2)

Sometimes equilibrium w/ sequential moves Nash equilibrium w/ simultaneous moves

f2(x1) x1

Figure 1. Equilibria in the standard contribution game

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 85 Mohammad Rahman

Without loss of generality let us One modification that can be made is to suppose 12 . It is clear then that the social the utility function. In our utility function for optimum is attained when agent 1 contributes individual agents given by (1), each agent everything. The first-order condition then receives utility only from the total level of the becomes. public good. This may be inconsistent with real-life facts. Each agent may receive benefit v( x  0)  v ( x  0) not only from the level of the public good, but 1 1 2 1  , 1 from his individual contribution as well. xx11 Wikipedia provides several reasons why one which can be written simply as may contribute to the public good. Most of these are along the lines of positive feelings v''()() x v x  . 1 1 2 1 1 due to good-Samaritan deeds. For instance, We that since v is concave, Wikipedia users are asked to contribute for the 1 poor child in having no access to ' vx11() is decreasing whereas 1 is a constant. expensive encyclopedia. Yet there are also ' Since vx21( ) 0 for all x1 , then the socially other direct benefits associated with s contributing. Let us consider the evolution of a optimal level of provision, x , is 1 Wikipedian as he contributes to Wikipedia. He xxs ˆ  , is increasingly recognized as a reputable 11 volunteer, and is elevated to a higher status where   0 . A special case would involve such as that of an „administrator‟ and granted distinct privileges.   xˆ2 . This leads us to state formally the The case where agents benefit directly following: from their contribution in addition to the overall level of the public good was Paradox 2: In the two-agent investigated by previous researchers. In contribution game where the utility Andreoni‟s (1990) simple model, an agent‟s function is of the form in (1), when utility function is a function of both his own compared to the socially optimal case, contribution, and the amount of the public Wikipedia will always be under-provided. good. Andreoni‟s (1990) model is very Further, the wrong agent may contribute in general, in that it captures altruism and its the sense that he may like Wikipedia antithesis, egoism, as well as “impure more, but is worse in quality. altruism,” meant to capture concepts such as The case of the wrong contributor i the “warm-glow” felt by agents upon their contribution to charities. Andreoni‟s (1990) will occur whenever xxˆˆ , even though ij results however pertain to the effects of

ij . income re-distribution between agents on the contribution to charity. Cornes and Sandler‟s Our findings thus far are already (1984) result is more relevant. They show that surprising. We expect Wikipedia to be smaller when a single act of contribution is able to in size to the case that is optimally social, as generate utility both directly and indirectly, as Wikipedia can be treated as a public good. community size increases, free riding and its This under-provision should be lacking or at associated inefficiency may decrease. Their least lessened when financial incentives are model is set up as a standard consumer introduced. Indeed, subsidies and taxes are one behavior optimization problem. method of changing equilibria to points that are social optima (Landsburg, 2001). So why is An alternative explanation for it then that a purely commercial counterpart, Wikipedia‟s size when compared to Britannica Britannica, is much smaller in size than is based on the cost structure. Encyclopedia Wikipedia, the privately-provided public fall under a class of goods known as good? At the very least it warrants further information goods. The production of these analysis. goods is characterized by the necessary existence of high up-front (fixed) costs, and

86 An Analysis of Wikipedia virtually zero marginal costs. Britannica‟s the number of agents using it increases. To see fixed costs would consist of two major that, we must analyze the problem in the components. First, Britannica would need to context of an arbitrary number of n agents. invest in signaling expenses, discussed in We make the simplifying assumption that the detail in the next section. Second, Britannica agents are all identical. In particular, vi and ci would incur costs in authoring articles for are all identical in1,..., . First, let us view inclusion in its encyclopedia. Britannica‟s the social optimum as a function of n . As profits would depend on the number of stated above, the whole range of equilibria are articles, as the following indicates. Let FC possible since the tastes are identical, and since stand for fixed cost, Cs for signaling cost, g the response functions fi will intersect in the for a convex cost function increasing in k the n -dimensional space at an infinite number of number of articles, TC for total cost, TR for points. All such equilibria satisfy the following total revenue, and let  denote Britannica‟s Nash requirement, that i profits. Then **ˆ xij x x . FC Cs g() k , ji TC FC 0 , But one equilibrium may be more „intuitive,‟ and somewhat informally Pareto and optimal. Let us assume that in the Nash  TR  TC . equilibrium output, all of the agents exert identical levels of effort. That is In the first-order condition, k* solves **** x12 x ...  xn  x . TR  gk'( ) . k In the Nash equilibrium now, ** Assuming that it exists, k* then is then x xˆ ( n  1) x . the unique number of articles selected by Solving for x* , one sees that Britannica for inclusion in its encyclopedia. As the above system of equations indicates, this * xˆ * x  . k depends on TR , which in turn is of course n determined by the demand and reservation values of the consumers. On the other hand, the social optimum output is of course A noteworthy point is that Britannica‟s choice of k* will not be socially optimal, and nxˆ . it is straightforward to argue this. The socially Let us define  , the relative efficiency as efficient price necessarily equals marginal cost. follows: But in Britannica‟s case, we can safely assume this to be zero. So any non-zero price will xˆ   nxˆ . involve positive amounts of deadweight loss. n Of course, there is no solution to this social 2 inefficiency problem. Whenever a firm has Then  is simply the constant 1 n , decreasing average costs at the socially which has derivative 2 n3 . The following optimal point, as Britannica does, its profits proposition then is immediate. will be negative there. There is no easy way however to compare the differences between Paradox 3: When utility functions are the degrees of suboptimality of the two of the form in (1), and the agents are all different cases. identical, the relative efficiency of Wikipedia decreases rapidly as the Since Wikipedia use appears to be number of users n increases, even when growing, it is of interest how the overall all the agents are contributing. efficiency compares to the social optimum as

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 87 Mohammad Rahman

As mentioned before, Wikipedia by riding completely, x1  0 . For any choice nature is very dynamic. Wikipedia grows not x  0 , he will receive a net benefit of only as new articles are created, but also as 1 extant articles are edited. The game of v1()() xˆ 2 c x 1 , contribution to Wikipedia discussed so far however has been static in the sense that all as agent 2 will always provide the remainder of moves were simultaneous. It would be the positive good. In free-riding completely interesting to investigate the change in the however, agent 1 can receive higher net equilibrium outcome if agents moved benefits as doing so will cost him nothing. sequentially. Varian (1994) investigated the That is, free-riding will yield a net benefit of general theory of sequential contribution to vx12()ˆ . public goods. Our discussion below is based on Varian (1994), albeit using a simpler The second case is more complicated, version of his elegant model. and more interesting. The first-mover, agent 1, likes the good more. That is xxˆˆ . As in the Now the two agents move sequentially, 12 first case, if agent 1 chooses to free-ride so the game of contribution is dynamic. completely, he can ensure a net-benefit of at Suppose, without loss of generality, agent 1 least vx()ˆ . Although this is less than vx()ˆ , moves first. Choosing x , he receives a utility 12 11 1 agent 1 may still free-ride completely as a of positive contribution by agent 1 entails costs

u1 v 1()() x 1  x 2  c 1 x 1 that he will incur, and the net benefit he will derive is given by when agent 2 subsequently chooses x2 . Using v()() xˆˆ c x the reaction function of 2, we can write the 1 1 1 1 . right-hand-side equivalently as If this net benefit v1()() xˆˆ 1 c 1 x 1 is u v( x  f ( x ))  c ( x ) 1 1 1 2 1 1 1 greater than vx12()ˆ , agent 1 will provide all of or the good himself, whereas if it is smaller, agent 1 will free-ride entirely. This is quite surprising

u1 v 1( x 1  max{ xˆ 2  x 1 })  c 1 ( x 1 ) as a result when we recall that agent 1 likes the good better. It is interesting to highlight the The reaction function can be used to cases when free-riding by agent 1 will occur, split agent 1‟s utility into the following system even when he likes the good better. One case of two equations, may be when tastes are similar. Indeed, if xˆ2 is

u1()()() x 1 v 1 x 1 c 1 x 1 if xx12 ˆ less than xˆ1 but xˆ2 is large enough, then agent 1 will free-ride. u1()()() x 1 v 1 xˆ 2 c 1 x 1 if xx12 ˆ , The analysis above may explain a

since for any level of contribution x1 seemingly strange behavior by the by agent 1, agent 2 will always contribute x administrators of Wikipedia. On Wikipedia‟s 2 website, the administrators encourage all users at least and just enough so that the total to be “bold” and make changes to any of Wikipedia‟s articles, even the same article with x1 x 2 xˆ 2 . that message itself. Where the stability and Two cases will arise, depending on the reliability of the articles is a concern, one difference in preferences of the two agents. In would perhaps expect some form of mandatory the first case, xxˆˆ12 , that is agent 1 likes registration process, or at least a message of a Wikipedia less than agent 2. In that case, agent much different tone, such as the following 1 will always choose to free-ride on agent 2 perhaps: and contribute nothing to Wikipedia. To see “Please author an article only if you are that, first note agent 1‟s choice between a completely sure of its contents. Please do strictly positive contribution, x1  0 , or free-

88 An Analysis of Wikipedia

not make changes to an article unless you signal their higher “quality.” We contend are completely certain of its faults.” however that such contributions to Wikipedia cannot constitute a signaling activity, and Our analysis shows however that provide an intuitive explanation. Users cannot when moves are sequential, it may be effectively signal their “quality” because advantageous to have the agent who likes the reward structures based on such signals cannot good least move first as doing so will result in be justified. Simply put, if better articles were a higher level of contribution. This is because rewarded for, then agents could easily acquire the other agent will not have any option of the information at nominal costs from other free-riding, and will always provide all of the sources, such as Britannica, and the bases for good, and hence a „higher‟ level of the good rewards would be unfounded. will result. When ask users to be “bold” and make changes, it may An Explanation for Wikipedia’s Size act as a signal to the high-level contributors So far, we have been able to reproduce that their moves are all that remain. Similarity only the extreme free-riding result that is of preferences was mentioned above as one standard in the public goods economics case when we will see free-riding by agent 1 literature. Clearly though, the abstraction in the even when he likes the good better. In model is far too rigid to be true in practice. Wikipedia, the similarity in tastes will Instead of extreme free-riding, what we can probably feature prominently as the number of readily observe in Wikipedia is a variety of users is large, and preference may actually be a contribution levels. The empirical study by continuous variable. Nature (Giles, 2005) suggests that there is We end our discussion related to the some free-riding with only about 10% of the contribution to Wikipedia by considering the scientists it surveyed contributing to articles. case of Open-Source Software (OSS), which is Most articles seem to be the result of generally another category of “public-good” projects in cooperative effort with partial contributions Information Technology that also exhibits the from a large number of users. Some paradoxical growth and high-quality. In doing contributors seem to be highly excited by their so we shall highlight what distinguishes topics of interest while being indifferent to Wikipedia from OSS, in order to demonstrate other topics. Finally, some articles seem to be both the novelty and the validity of our work. reactive to others and quite large, such as the article on the late scientist Lisa Meitner who Open-Source development projects as was failed to be recognized for her work in public-goods are driven in growth by the with the Nobel laureate Otto seemingly altruistic efforts of a variety of Hahn. individuals. As with Wikipedia, of wonder has been the effect of voluntary provision on both In this section, we modify our model the quality and amounts of such open-source and offer an explanation for Wikipedia‟s size. efforts (cf. Lerner and Tirole, 2000). And as We introduce a new property of agents known with Wikipedia, open-source projects are as “type.” Suppose agent i has type ti  0 . In surprisingly impressive in quality, and found in contributing x the agent receives a payoff of abundance. A considerable amount of research i has been conducted to investigate this apparent 2 ui v i( x i  x j (1  ( t i  t j ) ))  c i ( x i ) (2) contradiction to the traditional findings related to the private provision of public goods. The where vi is again a monotone concave theoretical explanation that seems most function, and cx  is the cost function for feasible (Lerner and Tirole, 2002) is that i i i that agent. The payoff model above is participation in open-source projects allows straightforward and intuitive. From the other developers to effectively signal their skills to agent‟s contribution, an agent receives utility ensure higher levels of future returns. One may that is moderated by the degree of similarity be tempted to suggest that contribution to between the two agents. For example, an Wikipedia may be explained away in a similar economist may care little about a psychology manner, that individuals are editing articles to article, and at the very extreme, a liberal may

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 89 Mohammad Rahman actually receive disutility from the presence of We can state the most important result: a conservative‟s article on say abortion. The Proposition 1a: In the two-agent first-order condition is given by contribution game with the utility function '2 of the agents having the form given in (2), vi( x i x j (1  ( t i  t j ) ))   i as the difference between the preferences Once again, we can define xˆ as 2 i of the agents ()ttij increases, the free-

'1 rider problem of Wikipedia as a public xvˆ  () i i i good is mitigated. assuming linear costs and the existence of the From the figure, we see that the exact ' inverse of vi . Now suppose agent j Nash equilibrium outcome will depend on the ˆ 2 contributes xi . Some algebra shows that agent magnitude of ()ttij . The dashed lines are i „s best response is to provide the different response functions of the two 2 2 agents with different values of ()ttij . The xˆi( t i t j ) 0 points of intersection highlighted as Nash whenever ttij , and quite surprisingly, equilibria correspond to pairs of response functions with the same values of ()tt 2 . ˆˆ2 ij xi() t i t j x i 2 When ()ttij is small enough, then complete 2 whenever (ttij ) 1 . So even though agent free-riding will result, as long as one agent j is contributing the entire amount that agent prefers Wikipedia more than the other. At an intermediate level of ()tt 2 , the two agents i would have contributed himself, agent i ij cannot simply free-ride as agent j ‟s offer their standalone contributions. Now even preferences are different. The results are more though agent 1 is offering his original contribution, agent 2 is not free riding clear if we plot the response functions fxij(). This is given in Figure 2.

x 2 2 (tt12 ) 1

f1(x2)

Nash Equilibria

f2(x1) x1

Figure 2 Equilibria in the contribution game with different preferences

90 An Analysis of Wikipedia

2 Wikipedia more. Suppose the article to be anymore. Finally, if ()ttij is very large, created is to profile a prominent conservative then the Nash equilibrium is the outermost politician. If our two agents are both point, where both agents are reactively 2 contributing very large amounts. We state that supporters of the politician, and so ()ttij is more formally below. fairly small and in region 1, then the agent who likes Wikipedia more will author the article Proposition 1b: Suppose, without entirely. Suppose instead that one agent likes loss of generality, xxˆˆ , and that ji the politician‟s stance on opposing outsourcing 2   xˆi , four regions of ()ttij can be labor, whereas the other agent likes his stance 2 associated with four different kinds of on the environment. Then ()ttij is in region equilibria: 2, and agent 1 will not contribute everything. This is probably most reflective of Wikipedia‟s xxˆˆ 2 ji editing scenario, where free-editing allows  If 0 (ttij  )  , agent i will xˆ j individuals to contribute what they value most free-ride entirely on agent j as in in the form of small edits. Suppose one agent equilibrium x  0 . In addition, supports the politician as a union member i strongly opposed to outsourcing, whereas the ˆ . xxjj other agent supports him as an environmental activist. Then ()tt 2 is in region 3, and each xxˆˆ ij  If ji(tt  )2  1, agent i will xˆ ij agent will write their version of the article j being indifferent to each other‟s contribution. free-ride partially on agent j as in 2 Finally, if one agent is liberal, then ()ttij is equilibrium 0 xxˆ . ii in region 4, and we may expect two different 2 articles, one with a liberal focus and another  If (tt ) 1, then agent i will not ij with a conservative focus. free-ride at all, being indifferent to agent j „s contribution. The outcome is RELIABILITY OF WIKIPEDIA (,)xxˆˆ which can often be socially ij In this section, we extend our model of efficient. the contribution game to account for reliability. 2 In a general setting involving n potential  If (ttij ) 1, then both agents contributors, let the contribution by agent i be contribute at levels that are high, but described by q  0 , where q is the quality of which can often be socially inefficient. i i that contribution. The quality of Wikipedia Proof: {Sketch} To derive region 1, first from then is a function of q, q ,..., q . One figure 2 it is clear that agent i will stop free 12 n particular function that is well suited as a riding as soon as fx(ˆ ) 0 . We note that ij definition of quality for Wikipedia is the

fxij(ˆ ) 0 is given by geometric mean given by

2 n 1/n xi xˆˆ i  x j(1  ( t i  t j ) ).  Qq  i . In that case, a little algebra can show i1 2 that the condition on ()ttij is that it should Although this definition may appear xxˆˆ somewhat arbitrary, or even strange as a be larger than ji. Deriving the rest of the choice, it is well suited as it captures the idea ˆ x j that “weaker-links” are more significant. regions is straightforward, and we omit it. Weaker-links in the context of public goods have been studied by Cornes (1993), albeit We can demonstrate the meaning of the within the setting of a general model. A closely ranges by means of an example. Suppose we related concept is that of the Cobb-Douglas have two contributors, where one agent likes function in the context of public goods (cf.

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 91 Mohammad Rahman

Varian, 1984). It is clear that this definition We may model the weakest-link captures the essence of “weaker-links” when concept by redefining quality as we take its derivative with respect to qi , Q min{ q1 ,..., qn } (3) QQ  . To solve for the equilibrium qii nq contribution qualities, we first need to derive the reaction functions. Suppose v and c are Clearly, the marginal effects on total i i functions as before but accepting qi as the reliability Q are higher whenever qi is lower. In terms of the reliability of Wikipedia, input parameter instead. Also let n  2 . Agent “weaker-links” will determine whether or not i will receive the following in net benefit by

Wikipedia can be trusted in general as a contributing qi : source. If it is known a priori only that a few articles are inaccurate, without knowing which ui v i(min{ q i , q j }) c i ( q i ) ones exactly, then potentially all articles Let us capture differences in tastes by should be approached with caution, or at least the constants qˆ and qˆ , which are the verified using other sources. To simplify our 1 2 analysis, we may consider the special case of maximum levels of qualities that agent 1 and “weaker-links,” which is the case when agent 2 would care for Wikipedia to have reliability is determined by the “weakest-link.” respectively. It is then straightforward to show In that case, if it is known a priori only that a that for agent i , it is optimal to match the single article is inaccurate, without knowing other agent‟s contribution if it is less than qˆ1 or exactly which one, then without verification provide qˆ1 otherwise. So the reaction potentially any article may be the inaccurate functions are given by one and the reliability of the entire project is in question. fi( q j ) min{ q j , qˆ i }

q2

f1(q2)

f (q ) 2 1

A Nash equilibrium w/ simultaneous moves.

Always unique equilibrium w/ sequential moves

q1

Figure 3 Reliability equilibria in the contribution game

92 An Analysis of Wikipedia

Without loss of generality suppose qqˆˆ12 . socially optimal quality level, then reliability Plotting the reaction functions in figure 3, we will be compromised. If on the other hand can clearly see that there exists a plethora of qq1  s even though reliability is at the Nash equilibria. We may select the one that socially optimum level, social welfare can still

Pareto dominates the other as it may perhaps be improved since c2 (.) is increasing in q and be the most likely outcome. In that Nash agent 2 can increase his private benefits by equilibrium the reliability of Wikipedia is compromising the quality of his contribution. given by min{qˆ1 , q ˆ 2 }  q ˆ 1 . So the socially optimal point is the single level of quality, say q , in contribution that solves An interesting extension of the result s above is that uniqueness of Nash equilibria can maxU s easily be established if moves are assumed to q be sequential and hence the game dynamic. Although qs is hard to solve, we can The uniqueness result for the general model still draw insights from analyzing various was argued by Hirshleifer (1983) and cases. Suppose the choice of q is between qˆ established by Varian (2004). The argument s 1 and qˆ where qˆ < qˆ . It is already clear that for uniqueness is as follows. Let agent 1, 2 1 2 without loss of generality have the first move. either one may be more optimal in equilibrium, depending on v and c . To allow for further Agent 1 will choose min{qqˆˆ12 , } . Choosing i i any amount larger will result in forgone analysis, let us simplify the matter and make benefits and useless costs when the subsequent all vi „s identical, and as before ci „s linear choice will be less. Choosing any amount functions. Since the Nash equilibrium outcome smaller is not the best option. is expected to be a choice of qˆ1 , let us first

Proposition 2a: When reliability consider otherwise. In choosing qˆ2 , agent one of Wikipedia is defined as in (3) in the will need to make a suboptimal choice that will sequential two-agent game, the unique decrease his net utility by equilibrium level of reliability of ˆˆ Wikipedia is the least of the minimum v()()() q1 v q 2  1  q levels desired by contributors. where q  qˆˆ21  q . On the other hand, agent This result above appears „mixed,‟ in 2‟s loss from agent 1 selecting qˆ1 is given by that its optimality is not clear. At first glance, it is reassuring to realize that the equilibrium v()()() qˆˆ2 v q 1  2  q reliability will most likely be at least above a bare minimum threshold. But two questions We see that agent 2 will choose qˆ1 in arise subsequently. How does this compare the socially optimal case whenever with the reliability that is socially optimal? 2[v ( qˆˆ ) v ( q )] And is such a threshold level of reliability q 21. „good-enough,‟ per se? 12 To determine Wikipedia‟s equilibrium The above analysis leads us to state the reliability to the socially optimal case, we note following proposition without proof. that the social objective is to maximize the following social utility function, by choosing Proposition 2b: The reliability of Wikipedia, when defined by (3) in the q and q accordingly. 1 2 two-agent game, will be compromised when compared to the socially optimal Uvs 1(min{ qq 1 , 2 })  v 2 (min{ qq 1 , 2 })  cqcq 1 ( 1 )  2 ( 2 ) case if quality preferences are close In the social optimum, level, all agents enough. If quality preferences are far need to be contributing articles of the same apart, then Wikipedia will have the quality. This is easy to argue using socially optimal quality level. contradiction. Suppose that qq . Without 12 Of course, in the analysis thus far, we loss of generality, let qq12 . If qq1  s , the assumed that no individual would be interested

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 93 Mohammad Rahman

in deliberately destroying the reliability of fv of the vandal, as that is easier. For each Wikipedia. That is, we considered only value of x , the vandal needs to choose situations when individuals make the choice between a positive contribution d  0 or solely between benevolent contributions or abstaining from vandalism. A positive free-riding. Wikipedia however is subject to contribution will be better if and only if “vandalism” in that perfect articles can be v cd and dx . The optimal positive edited arbitrarily by individuals interested in * deliberately undermining Wikipedia‟s contribution d will be infinitesimally larger reliability. To incorporate vandalism into the than x . To derive the full response function model, one needs only to introduce agents with fc of the contributor, we note that the choice the appropriate structure of the utility function. is between a positive contribution x  0 and At this point, we suggest no normative no contribution. For x  0 , there is always a guidelines for mitigating this problem. Instead, unique positive x* that solves we highlight that self-regulation will be possible insofar as there are agents who endure maxv ( x )  cx x significant disutility from vandalism actions. At the very least, these agents can always So the choice is between x* and x  0 . change an article back to its original state. The condition for reliability to be maintained Obviously, at any point in time an article may in equilibrium is of course that x*  v . This be the subject of vandalism, and that fact may c not be clear to the casual user. It may be leads us to state the following. worthwhile for users to check the time-stamped Proposition 2c: In the two-agent history of the article to determine whether they (a vandal and a contributor) game of can reliably use it for references. Wikipedia where the utility functions are We can still model the concept of of the form in (4) and (5) articles in vandalism and demonstrate equilibrium equilibrium will not sway back and forth outputs as follows. Suppose there are two between vandals and contributors. To agents, a vandal and one other who is a prevent vandalism of an article in the benefactor whom we call the contributor. unique equilibrium outcome, the least Suppose the vandal has the following utility quality preference among those of the function editors should be at least equal to the benefit derived from vandalism. v c() d if d x uv   (4) Although never due to vandalism, there c() d if d x  is one situation when articles may sway back when he contributes an amount d of damage and forth through editing. When readers are to Wikipedia, while x is the positive unsure of the contents of an article, and have no way of verifying their accuracy, the article contribution of the benefactor. may be subject to repeated editing by polarised In that function v is the benefit the editors. The situation may be exacerbated by vandal derives whenever the reliability of the fact that editing is not a „costly‟ activity. Wikipedia is compromised, and c is the cost Consequently, we may use the solution concept function increasing in d . Suppose the of cheap-talk equilibria (cf. Gibbons, 1992) contributor has the following utility function that investigate credibility in environments sustaining costless messaging. v() x x if x d uc   (5) Suppose chance draws an editor‟s type x if x d  to be either a „lying‟ or „honest‟ individual. where v is again increasing monotone, The editor behaves according to his type and concave in x , and   0 is a cost constant. edits an article. The users of Wikipedia then have the option of believing or disbelieving the We now need to derive the response contents of the article, but have no idea about functions. We start with the response function the true type of the editor. Whether believing

94 An Analysis of Wikipedia or disbelieving occurs in equilibrium will THE COLLABORATIVE NET depend on the fulfilment of three conditions, and eventually on the payoffs to the editor and Today, a striking Internet phenomenon users. The first condition is that the users‟ can easily be spotted. We call this preferred actions will need to depend on the phenomenon the “Collaborative Net,” and it is type of the editor. This condition is trivially a culmination of an information pool created fulfilled; users will prefer to believe honest mostly by most of its users. The simplest editors and disbelieve others. The second technological introductions are enabling this condition is that editors must have different phenomenon, which in turn is drastically preferences across the users‟ strategies. This redefining properties of the Internet. In condition fails to be fulfilled. Both types of addition to wiki, are such a technological editors would like users to believe them. innovation and the blogosphere is a Although the third condition does not need to Collaborative Net feature. be stated, we do so anyway for the sake of One direct consequence of the dynamic completeness. That condition requires that the blogosphere is a concept known as “citizen editors‟ and users‟ preferences not be journalism.” Other terms used to describe the completely opposed. This condition is also not same concept include “grassroots reporting,” fulfilled with Wikipedia. Specifically, users or “media-of-the-masses.” Citizen journalism prefer to believe when editors are honest and as a topic has been investigated in journalism disbelieve otherwise. But lying editors prefer studies (cf. Andrews, 2003; Blood, 2003; that users believe, and hence communication Regan, 2004). Lasica (2003) for example cannot occur. defines it as “individuals playing an active role That many Wikipedia articles cannot or in the process of collecting, reporting, sorting, will not be believed by users is not a result that analysing and disseminating news and is destructive to the value of the project. information, a task once reserved almost Rather, we contend that it is a major strength. exclusively to the news media,” and contends In particular, the polarization result of free- that the transparency of blogging has editing in Wikipedia will act as a perfect contributed to increase the accessibility of signalling device to users for highlighting news entities. While traditional periodic situations when they should disbelieve articles sources of information involved professional that may be highly opinionated and less activities, such as television news programs or factual. This is one explanation for the magazines and other periodicals, citizen common saying about Wikipedia that even journalism is providing Internet surfers amidst discourse and vandalism, the actual alternative sources. Features remarkable about discourse itself may be informative. This citizen journalism are its vast size and its communication feature of Wikipedia may be a provision by ordinary citizens. These features great strength in the face of its commercial become strikingly apparent particularly when counterparts, such as Britannica. First, users of citizen journalism is compared to the Britannica may not be able to discern mainstream media industry, as the latter can be opinionated articles that are further from truth characterized by its composition of a limited from those that are more factually correct. set of players. Of concern is the credibility of Further, these articles will often be believed the information reported through citizen because the three conditions of cheap-talk journalism channels; is the information equilibria highlighted above may often be provided through citizen journalism reliable? fulfilled even after critique by a review In contrast, many mainstream media players committee. have well-established reputations, with famous journalists possessing enviable credentials. An In terms of the design mechanism, we understanding of the credibility of information may be interested in seeing what the effect will reported becomes even more important with be of punishing vandals. Suppose, for example, new practices by Internet news aggregators. In that vandals‟ IP addresses are logged and then a recent article titled “Can You Tell Blogs future activities blocked. From „Real‟ News?” in , Dicarlo (2005) observes that blogs and other user-generated

Journal of Information Technology Theory and Application (JITTA), 9:3, 2008. 95 Mohammad Rahman content will soon show up on Yahoo!, blurring The first characteristic of Wikipedia we the lines between professional media and investigated was its sheer size. Since citizen journalism. Wikipedia can be considered a public-good, we demonstrated how traditional theory would The results established in this paper suggest that the standard free-rider problem have implications for the Collaborative Net would emerge. In equilibrium, only a few feature of citizen journalism. By means of our volunteers would contribute. But this result main result, we have established that when would obviously contradict the empirical preferences are sufficiently different, the observation that Wikipedia is roughly seven underprovision problem of public goods times as large as its commercial counterpart. resulting is mitigated as extreme free-riding is Consequently, we investigated mechanisms in no longer feasible. This result, and our analysis which extreme free-riding was being mitigated. in general will extend over easily to citizen Our main result in this paper was an journalism. The popularity of citizen explanation for the size of Wikipedia based on journalism comprising blogs is often attributed equilibrium contributions depending on the to the failure of traditional media outlets to differences in types. Free-editing allows for a cover a wide enough variety of articles. In variety of expressions; expressions that reflect 2005 for example, bloggers championed the differences in type. In addition, using well- case of a missing woman which did not receive grounded principles from information national media attention as that of Laci economics, we explained why Wikipedia‟s Peterson. According to the bloggers, the commercial counterpart could be much smaller missing woman was poor and African in size. American, and deemed unworthy of media attention unlike the attractive Peterson The second characteristic of the (Farivar, 2005). Our analysis showed that Wikipedia we investigated was its reliability. traditional print media (such as Britannica) This characteristic is currently a topic of much will be unable to cover all of these articles. debate. Indeed, while many critics of Citizen journalism however may not be as Wikipedia are highly skeptical about the accurate as Wikipedia when readers will have reliability of this free-encyclopedia that anyone no way to verify the content. We have already can edit, surprising results are emerging mentioned that in games of incomplete regarding Wikipedia‟s reliability. Our results information, under three conditions cheap-talk were important as we are able to establish both equilibria are possible when information lower and upper bounds for the reliability of cannot be verified. Further, unlike Wikipedia, Wikipedia. Qualitatively, Wikipedia‟s the publisher of a has full control over the definition as a public good, combined with contents of an article. Consequently, highly free-riding and free-editing helps to maintain opinionated articles can easily prevail. An the reliability of Wikipedia. example of this was the appearance of We identified Wikipedia as part of a numerous faceless blogs that successfully general Internet phenomenon that we call the defended G. W. Bush during the 2004 Collaborative Net. The effect that the simple elections when his service record was in technologies enabling the Collaborative Net question. inspires awe. Increasingly, users are adopting more active roles. Previously, Net users were DISCUSSION frequently called “browsers.” And they were Wikipedia is attracting both crowds and exactly that, being unable to edit most of the criticism. Users are drawn to Wikipedia not information online. Today, more and more Net only by its tempting free-offering, but also users are actually the contributors to a vast because it contains articles on almost every pool of information as bloggers or contributors conceivable topic. Why is Wikipedia so large, to Wiki projects. This pool of information is even as a public good? And can we trust characteristically dynamic with changes being articles that “anyone can edit?” made to it constantly.

96 An Analysis of Wikipedia

The primary contribution of this paper sufficient for that purpose, particularly since is its novel explanation for the paradoxical they are the standard in studying provisions to growth of Wikipedia, the free encyclopedia public goods (c.f. Varian, 1994). Second, in that anyone can edit. To our knowledge, our many cases richer games are a collection of explanation is novel and contributes to the smaller games, and in Wikipedia, the general literature on public goods. The paper contribution game will often be reduced to the also offers theoretical explanations for the final two individuals who like it most. Third, surprising empirical findings on the superior mathematically, many of our results will still quality of the giant encyclopedia arising from hold when considering n -dimensional vectors. free-editing. Our findings have implications for While Wikipedia offers many areas of the much-debated topic of credibility in the future research such as the social and legal new Collaborative Net environment. We also aspects of a free-to-edit information source, we highlight the uniqueness of Wikipedia when would particularly suggest studying the compared to (other) Open Source Systems. specific design features of wiki-based Our study features prominently as we information systems. One may investigate, for are able to assess contribution and reliability instance, incentives to remain neutral with within the traditional economic paradigm, in varying levels of policing. Such studies would contrast to other studies. Benkler (2006) for further highlight the suitability of Wikipedia example examines the contribution to blogs and other wiki-based projects as reliable, and wiki projects from a social-capital unbiased information systems for use in perspective. In additional to its theoretical effective knowledge-management. This area is appeal, our study is also of practical relevance particularly promising as commercial as wiki projects will feature as options applications of wiki technology are emerging. alternative to traditional knowledge pool- Many online retailers including Amazon.com models. Knowledge-management, for example, are implementing wiki-based review systems, can be implemented in organizations very and ShopWiki.com is an entire online business efficiently by the use of information systems based on user-generated reviews published that are designed similar to Wikipedia. using wiki. A blogger recently reported that he was offered a contract by a PR The main limitation of our study was associate to edit a Wikipedia article the the use of two-person games to model associate felt was biased against Microsoft contributions to Wikipedia when in reality technology (Jelliffe, 2007). While the associate Wikipedia involves the contributions of maintained that it was only intended to be thousands of individuals. We believe however compensation for using a neutral voice, several that the insights generated are still valid for at interesting questions arise that relate to least three reasons. First, our aim was not to conflicts of interest, and the effects of derive accurate numerical results, but instead pecuniary compensation on the overall to gain an understanding of the behavior. We neutrality of wiki articles. are convinced that two-person games are

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AUTHOR Dr. Mohammad in business administration. Consequently his Rahman teaches in research efforts are inter-disciplinary and offer the School of key insights to managers. Dr. Rahman teaches Business at North technology, operations and strategic South University in management in the MBA program. He Bangladesh. Dr. received a Ph.D. in Business Administration Rahman‟s research from the University of Kansas, with a involves the concentration in decision sciences. application of rigorous techniques in explaining puzzling phenomena and „real-life‟ problems that arise

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