1 Introduction

Over the past three decades, peer-produced online information goods such as open source software and Wikipedia have become extremely popular. Wikipedia recruited over 30 million volunteers to produce hundreds of millions of encyclopedic entries in 314 languages. As Wikipedia has become one of the most popular information sources on the web and the destination most internet users turn to when they seek information [1], the quality of its articles has been the topic of public debate. Wikipedia is based on wiki technology: a web-based collaborative authoring tool that allows contributors to add new content, append existing content, and delete or overwrite prior contributions [2]. Thus, Wikipedia articles evolve through the continuous additions, deletions, and shaping of existing content (rewriting, reorganizing, and integrating).

The success of online production communities, such as Wikipedia, has attracted much interest within the scholarly community, given that the organization of such communities seem to defy traditional organizational logic [3–7]. Broadly speaking, two key issues have been investigated. The first pertains to contributors’ characteristics and their interactions during the collaborative production [8–12]. Namely, given that most communities do not have formal procedures to select, train and assign contributors to a task, it is not clear how work effectively gets done and how high-quality goods are co-produced. This issue is particularly interesting since communities are often heterogeneous and members vary greatly in terms of their motivation, affiliation with the community and identification with its goals, and their activity profiles. The second key issue is community governance [13–15]. Specifically, communities need to balance openness and freedom of action so as to allow contributors to self-select and self-organize, while controlling uncooperative behavior, such as manipulations and vandalism. In other words, there is a fundamental tension between emergent behavior and regulation in peer production [16]. Successful communities, thus, had to devise “light” governance mechanism [15] that would strike a fine balance between these two opposing objectives. Extensive research in the area over the last three decades has been able to shed light on many aspects of peer production; still, fundamental questions remain unclear, specifically regarding the way in which governance shapes individual-level interactions. Hence, the overarching objective of our study is to investigate the interplay between the community’s governance and contributors’ cooperation-competition dynamics in peer production (and specifically, in Wikipedia).

Large and complex socio-technical systems, such as Wikipedia and other large-scale peer production projects, are difficult to study in a holistic manner, and by and large, scholarly investigations have focused on a particular angle, for example contributors’ motivations [11, 17], coordination [9], or conflict management [8]. One particularly relevant approach for studying such complex systems is through modeling. A model, by definition, presents a simplified depiction of the complex reality, formalizing key salient features of the system, while ignoring other less critical aspects. Models have the potential to reveal deep insights about the phenomenon being investigated. Moreover, when the model-based predictions are validated with empirical data, credence is lent to the model’s results. In this study we employ game-theory to study the interplay between the community’s governance and contributors’ individual-level interactions.

Game theory, “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers” [18], is well suited for studying competitive and cooperative dynamics and thus may reveal insights into peer production. Despite its demonstrated utility in studying cooperation and competition, the use of game theory in peer production research has been rather limited [19]. In this study, we employ game-theoretic modeling in order to study the interplay between the community’s governance and contributors’ individual-level interactions. More specifically, we develop a two-step leader-follower game-theoretic model [20, 21] that captures both cooperation-competition dynamics among the contributors to the article’s collective authorship (i.e., “follower”), as well as the community’s governance efforts to enforce neutrality (i.e., “leader”). We briefly detail the key elements of our model, beginning with the former: the dynamics of contributors’ interactions.

The “follower” level of our model assumes a heterogeneous community, where contributors are characterized by two important traits. First, we assume that each contributor combines self-interest (e.g., promoting one’s viewpoints and enhancing their own reputation [22, 23]) with others-oriented interests (e.g., helping the community co-create high-quality goods) [24]. The self-interest is linked to a competitive behavior and others-orientation to a more cooperative conduct [25]. A contributor is driven by a combination of cooperative and competitive goals, and we refer to this trait as the contributor’s cooperative/competitive orientation.

A second important characteristic that we model is contributors’ activity profile. Despite the freedom to select the particular ways in which one contributes (for example, in Wikipedia: adding new content or shaping others’ previous contributions), members of online production communities are typically characterized by highly stable activity patterns (aka “emergent roles”; [26]). Building on prior studies in the area [27, 28], we distinguish between the roles of a creator (in Wikipedia, mostly adding new content) and a curator (refining, shaping and reorganizing existing content), modeling each individual’s activity profile as some combination of creation and curation activities. It should be noted that in the context of Wikipedia, the creator/curator distinction applies to activity in the primary area (referred to as the Main namespace): co-producing encyclopedic entries; other areas (namespaces) within Wikipedia are dedicated to coordination work. For example, each article is coupled with a TalkPage where discussions regarding the article take place. Our model assumes that these two characteristics, i.e., contributors’ cooperative/competitive orientation and their creator/curator profile are stable traits (at least within the timeframe of our analysis).

We further presume that the contributor’s decision variable is the the amount of work to be done (i.e., number of content elements, e.g., sentences, to be edited), reflecting their individual motivation and availability. This decision is influenced by the utility function, i.e., the balance of costs and benefits. We assume that contributors derive both competitive benefits (namely, shaping a Wikipedia article to align with one’s personal viewpoint, thus coming to “own” portions of that article) and cooperative benefits (i.e., co-producing a comprehensive encyclopedic entry). Similarly, the costs of editing the focal article are influenced by one’s activity profile (creator/curator, and hence are applicable to both cooperative and competitive contributors), the amount of coordination work required (more applicable to cooperatively-oriented contributors) and the effort of handling the community’s governance (more applicable to competitively-oriented contributors). When many contributors participating in a collective authoring effort attempt to promote their reputation and perspectives, competition between them is inevitable [25].

Contributors’ dynamics does not occur in a void. The interactions among the contributors are influenced by the community’s governance (i.e., the “leader” in the two-stage game-theoretic model). Wikipedia’s governance mechanisms have been investigated in prior studies, e.g., [13–15]. These studies describe Wikipedia’s extensive mechanisms for ensuring that the co-produced content is of high quality, including instruments such as norms, policies, as well as technical tools for facilitating collaboration, resolving conflicts and fighting vandalism [29]. In particular, Wikipedia emphasizes objectivity (Neutral Point of View; NPOV) as a central pillar of the community (http://en.wikipedia.org/wiki/Wikipedia:FivePillars) and lists “susceptibility to editorial and systemic bias” as one of the key aspects of its quality assurance work [25, 30, 31], http://en.wikipedia.org/wiki/ReliabilityofWikipedia. Of particular relevance to our investigation are studies of governance mechanisms that are intended to ensure neutrality by countering attempts toward bias in Wikipedia articles [32, 33].

To recap, contributors are characterized by their cooperative/competitive orientation and by their typical activity pattern (creators or curators of content). A contributor’s decision regarding the amount of content to be edited is based on that individual’s utility function, and is also influenced by the strategies used by other contributors, which in turn are affected by adherence to governance (i.e., the principles of neutrality). Contributors’ optimal strategies are calculated using the Nash equilibrium of the game.

To lend greater credence to our model’s predictions, we validated the findings with empirical data. We performed a computationally-heavy empirical analysis of 219811 distinct contributors co-producing 864 Wikipedia articles (articles’ lifespan ranges from 129 to 4078 days; mean = 2681 days). We performed the empirical validation for the entire period covered by our data set (2001–2012), as well as for each yearly interval independently. We estimated contributors’ cooperative/competitive orientation based on their role in the community (those closer to the community’s core are assumed to be more cooperative) and estimated their position on the creator-curator continuum based on the average size of their edits (i.e., larger edits within a sentence are typical of content creators) [34–37].

To verify the validity of the “creator”/“curator” labels, we performed an analysis on the dataset from [38], calculating each contributor’s average edit size and profiling the types of activities that she makes. We found that: (a) the larger the relative proportion of the “Add Content” and “Structural Changes” edit types in a contributor’s profile, the larger is the contributor’s average edit size; and (b) the larger the proportion of “Corrections” and “Add References” edit types, the smaller is the contributor’s average edit size. Together, these patterns suggest that contributors with a large edit size are the “creators” who structure and article and add much of the content, whereas those making small edit size are “curators” that mostly engage in refining existing content.

We used a sentence as our basic content unit, and our estimate of the cost of editing a sentence, i.e., the effort contributors invest, is approximated as a linear function of contributors’ average edit size per sentence [39, 40]. We estimated contributors’ competitive benefit based on the portion of the article that they own, employing the “content ownership” algorithm from a prior study [38], and their cooperative benefit from the comprehensiveness of the co-produced article (estimated through the article’s length).

The key results of our game-theoretic analysis are (a) the factors that determine who ends up owning content are contributor’s characteristics: their cooperative/competitive orientation and their creator/curator activity profile, and (b) governance levels should be limited, so as not to overburden contributors.

2 Background and related work

This section reviews prior work on Wikipedia, addressing the following issues: (a) contributors’ cooperation and competition (Section 2.1); (b) the activities involved in Wikipedia’s collaborative authoring process (Section 2.2); and (c) community-based governance of Wikipedia’s peer production (Section 2.3).

3 Research question

Notwithstanding the value of prior research, the scholarly literature on peer production has not investigated the interplay between individuals’ cooperative/competitive dynamics and the socio-technical governance mechanisms. Our goal in this paper is, thus, to investigate Wikipedians’ cooperative content production and the competition over content ownership, as well as to explore the way in which this competitive dynamic is shaped by the governance community’s effort to ensure an NPOV. We recall that contributors derive benefits from both the collective production of a high-quality article (more applicable to those with a cooperative orientation) and from the ownership of content (more applicable to competitively-oriented contributors). Contributors also incur costs in producing content (effort is a function of one’s activity profile: creator or curator), coordinating and organizing work (largely applicable to cooperative contributors) and in complying with Wikipedia’s neutrality-enforcement mechanisms (primarily for competitive contributors). Hence, we pose the following two research questions, which we investigate to answer in this research.

RQ1: What is the optimal strategy for a contributor who is attempting to balance the costs and benefits of peer production? Namely, how many sentences within an article should be owned by a contributor that is characterized by a certain cooperative/competitive orientation and a particular creator/curator activity profile?

RQ2: How does the community governance mechanism, particularly the attempt to ensure a NPOV, affect the dynamics underlying Wikipedia’s co-production process?

4 A game theoretic model of Wikipedia’s collaborative production and governance

A game-theoretic model should capture essential features of the modeled system. Below we present our model in a descriptive manner, and then introduce the formal notations in the following subsections. Socio-technical systems such as Wikipedia exhibit both cooperative and competitive dynamics. Our game-theoretic model aims to represent (a) contributors’ cooperation in the production of high-quality articles as well as their competition to “own” articles” contents and (b) the community’s attempt to ensure that articles present a neutral and balanced perspective. In other words, our model assumes contributors may be driven by two goals: the first is to contribute towards the creation of comprehensive encyclopedic entries and the second goal is to maximize ownership of article sections, such that content “owned” by that contributor survives multiple rounds of revisions of the article. Our model also assumes that the objective of Wikipedia’s governance mechanisms enacted by the community is to ensure the neutrality of content, such that no single contributor takes ownership of large portions of an article. Wikipedia’s governance has the broader goal of regulating behavior, such that the community thrives and the peer-produced content is of high quality. Our focus here is on one important dimension of governance: that of combatting the attempts to “color” the article according to one particular viewpoint, that is, to ensure objectivity and the lack of bias in Wikipedia’s content [8]. Beyond the importance of this particular dimension of Wikipedia’s governance (as evident by the NPOV pillar), objectivity is particularly relevant for our conceptualization, as it is directly impacted by contributors’ effort to “own” content.

We model the interactions between the governance mechanisms and contributors’ co-production as a Stackelberg (leader-follower) game [20, 21], where the community is the leader that determines a level of governance that increases the neutrality of an article. Given a set level of governance, contributors’ interactions are modeled as a non-cooperative game, where each contributor’s objective is to maximize both the article’s comprehensiveness and the contributor’s content ownership. A high level schematic of the interactive model between the community’s goal of ensuring neutrality and contributors’ cooperation/competition is presented in Fig 1.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. A high level schematic of the interactive model between Wikipedia’s governance to ensure neutral point of view (NPOV) and the interactions between contributors.

https://doi.org/10.1371/journal.pone.0281725.g001

Peer production on Wikipedia is a complex socio-technical process and contributions occur asynchronously over time. Our strategy for capturing these dynamics is temporal bracketing: recording a series of yearly “snapshots” of the process over a finite time horizon [71]. We use a static game-theoretic model to study these interactions, and test the model against empirical data for each of the yearly snapshots. Please note that modeling such a complex process requires some simplifying assumptions. We assume that contributors’ activity profiles, namely, their position on the creator-curator continuum and their cooperative/competitive orientation, are stable over time (at least within a yearly snapshot). This assumption is in line with prior research that demonstrated that the changes in contributors’ activity profiles are infrequent [16]. We also assume that Wikipedia’s governance structure, and in particular the goals of ensuring neutrality, are stable over time (as changes in policies are relatively infrequent). It should be stressed that while our model provides an approximation to the complexities of peer production, we also validated it using empirical data that captures Wikipedia’s actual collaborative-authoring dynamics.

We model the net utility as the difference between the utility (the contributor’s fractional ownership and the benefit derived from the co-production of high-quality articles) and the cost (a measure of all the efforts expended by the contributor). The optimal strategies are determined through the Nash equilibrium of the non-cooperative game that models the interactions between contributors. We analyze the conditions for the existence and uniqueness of a Nash equilibrium for the game and discuss its implications.

As noted, we model the interactions between the governance mechanism—namely, enforcing a neutral point of view- and contributors’ co-production as a Stackelberg (leader-follower) game. The role of the neutrality-enforcing mechanism is to choose the optimal level of enforcement, t, defined in our model in terms of the effort involved in complying with governance (i.e., when editing a sentence). The response of the N contributors in the particular article is to make unilateral contributions that maximize their net utility (the difference between the benefit obtained from their content ownership as well as co-producing a comprehensive article and the efforts expended to make edits, maintain the quality of the article and comply with governance). A contributor may choose to make any number of contributions (i.e., sentences owned in an article). Our objective is then to determine for each contributor, the optimal levels of activity, so that each contributor’s net utility is maximized. Please refer to Tables 1 and 2 for the list of notations/variables that are used in our analysis.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. List of notations used to set up the game theoretic model.

https://doi.org/10.1371/journal.pone.0281725.t001

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. List of notations used to evaluate the Nash equilibrium of the game.

https://doi.org/10.1371/journal.pone.0281725.t002

4.2 Neutrality enforcement and its effect on co-production

The community governance factor in our model is the result of contributors’ aggregate governance effort. The level of governance, t, should be chosen so as to maximize the effectiveness of peer production. Our model assumes that the main objective of Wikipedia’s governance is to reduce bias and ensure that all points of view are reflected in an article. Assuming a sufficiently large sample, the set of contributors working on an article would sample a range of viewpoints. The more one contributor (or a small subset of the contributors) is able to dominate the discussion (i.e. take ownership of large portions of the article), the more likely the article is to reflect a single side. In contrast, when content ownership within an article is more equally distributed and when multiple contributors own sections of the article, a more NPOV is expected. Thus, our notion of article neutrality reflects equal ownership of an article’s contents. We are less interested here in the particular biases that may be present in the content added by each contributor.

Building on information theory [73], we use the metric of entropy to estimate the amount of bias in the distribution of content ownership. We note that the entropy metric was employed in prior studies in organization science [74], and in particular in estimating the distribution of work in Wikipedia [8]. In information theoretical terms, if a source emits N possible symbols, with probability distribution, p_i, i.e., the source emits symbol, W_i, with probability, p_i ≥ 0, , then the entropy of the source, H is defined as [75] (9) In any Wikipedia article, the fractional ownership of all contributors, are all non-negative and satisfy the condition, . Therefore, a page can be viewed as as an information source with the N contributors playing the role of the N possible symbols and the fractional content ownership of each contributor, , playing the role of p_i. The entropy of the page can then be written as (10) In Eq (10), the entropy, H(t), may depend on other factors, e.g., the optimal contributions, 1 ≤ i ≤ N, obtained from Eq (4), which in turn, depend on β and . However, we represent the entropy as H(t) because the neutrality enforcement, t, is the only parameter in H that represents the action taken by Wikipedia’s governance mechanisms. Our model’s optimization function for neutrality enforcement (maximizing entropy in contributors’ ownership) is normalized (each article’s entropy is calculated in relation to the maximum entropy of any article, which is 1).

It was shown in information theory [75] that the expression of entropy, H(t), in Eq (10) is maximized when , ∀ i. i.e., when all contributors make equal contribution, which corresponds to the scenario when there is complete neutrality. Therefore, we use the entropy in Eq (10) as the objective function for determining the optimal level of neutrality enforcement for the Stackelberg game. Namely, the objective function for neutrality enforcement in our model is to maximize the entropy in content ownership within an article.

The optimal level of neutrality enforcement, t, is the value of z that maximizes H(z) in Eq (10), which is obtained by replacing t with z in Eq (6). Then, (11)

From Eqs (6), (10) and (11), the optimal value of t that maximizes the entropy is the value of t that makes , ∀ i, i.e., t → ∞. See Appendix-2 in the S2 File for details. Our analysis indicates that while neutrality enforcement levels remain moderate, our prior results from the non-cooperative game remain unchanged, such that those with a cooperative orientation who are content creators (i.e., make above-average-size contributions) end up not owning content. However, when neutrality enforcement levels exceed a certain threshold the non-cooperative model collapses, ownership becomes a direct function of neutrality enforcement (rather than contributors’ efforts). Namely, from Eq (6), when (i.e. when the amount of effort a contributor has to exert to overcome neutrality enforcement is significantly- typically one order of magnitude- larger than the aggregate effort that all contributors exert in making unit contributions to the article), . In other words, ALL contributors end up owning an insignificant but equal portion of the article’s contents. Therefore, the optimal value of t is obtained by solving (12) where z* represents the maximum level of neutrality enforcement allowed in order to maintain the neutrality of an article above a required threshold. The resulting Stackelberg game model is depicted in Fig 2.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. The comprehensive Stackelberg game depicting the complete interaction between Wikipedia’s governance to ensure neutrality and cooperation/competition peer production dynamics.

https://doi.org/10.1371/journal.pone.0281725.g002

The complete model for the leader-follower game between the governance mechanism and the competitive self-interested contributors suggests that at the Stackelberg equilibrium, the governance mechanism operates in such a manner to result in an implicit outcome that keeps the entropy high, i.e., the difference between maximum and minimum fractional content ownership is kept low, thus ensuring the article’s objectivity. Further, our model limits governance levels to an upper threshold.

5 Verification of the analysis with empirical data

To verify the game theoretic analysis, we compared its predictions against data from Wikipedia. In line with prior studies in the area [26], we employed a double-stratified sampling procedure, randomly selecting 1000 articles from the January 2012 dump of the English Wikipedia. Our strata were based on: (I) the number of revisions the article has gone through (i.e., article maturity) and (II) the article’s topical domains. This sampling strategy is important given that collaboration patterns could differ across articles in different phases of their life cycle across topical domains. Given the power law distributions in the number of articles’ revisions [76], we used the following four maturity strata: (a) 1–10 revisions; (b) 11–100; (c) 101–1000; and (d) more than 1000 revisions. The topical strata were based on Wikipedia’s categorization system, using the main topics scheme. The English Wikipedia main topic categorization scheme is developed by the community and is subject to frequent changes; see http://en.wikipedia.org/wiki/Category:Main_topic_classifications. With 4 maturity strata and 25 topical categories, we have 100 cells with 10 randomly selected articles in each (i.e. 250 articles in each maturity stratum and 40 articles in each topical category). Altogether, this sample contained: 1000 articles and 721,806 editing activities (i.e. article revisions), made by 222,119 contributors. In line with prior works in the area [8], we assume that for non-registered contributors, a unique IP address corresponds to a distinct contributor. About half of the contributors in our sample are non-registered. After excluding articles with a single contributor, we were left with 864 multi-contributor articles, which make up the sample of our analysis.

We began by counting the number of distinct contributors (N) and the total number of edits made by each contributor, across all articles and the total number of sentences edited by the i^th contributor (1 ≤ i ≤ N), ζ_i, across all of the articles in our sample. Next, we calculated the average amount of effort expended by the contributor when editing a sentence. A contributor’s average edit size, Lβ_i, was calculated based on his activity profile across all articles within the sample to which he contributed. The contributor’s position on the creator-curator continuum, β_i, was estimated based on the average size of edits per sentence, calculated using the Levenshtein distance [77]. The Levenshtein distance is a string metric used in information theory and computer science for measuring the difference between two sequences (or between two text segments) and is defined as the minimum number of single-character edits (i.e. insertions, deletions or substitutions) required to change one word into another [78]. This metric has been commonly used in the study of Wikipedia to estimate the scope of editing activities [79]. Based on this calculation, we were able to approximate the size of all edits made by the i^th contributor (1 ≤ i ≤ N), e_i, to all articles in our sample. We then computed the average edit size of contributor i per sentence, Lβ_i, . Note that β_i is a trait of the contributor, reflecting her activity profile (whether a creator or a curator of content) such that it remains the same across all articles that we analyzed.

In order to approximate a contributor’s cooperative/competitive orientation, we relied on their functional roles within Wikipedia, as reflected by their access privileges. Wikipedia community has developed a comprehensive and detailed set of procedures for governing the collaborative editing process, including a well-defined scheme of access privileges [80]. Very broadly speaking, these roles could be organized in four strata, reflecting contributors’ commitment and involvement within the community: unregistered members, registered members, privileged members (holding a special privilege), and core members (i.e. administrators) [81] Data regarding contributors’ functional roles were accessed through Wikipedia’s API. We relied on these strata in order to estimate the extent to which one is competitive (i.e. w_i) within the community: the greater one’s rights and responsibilities within the Wikipedia community, the more one is considered to have a cooperative orientation. Specifically, we assigned the values of 0.1, 0.4, 0.6, and 0.9 to the different strata (e.g., an administrator is assigned w₁ = 0.1, reflecting the least competitive and most cooperative orientation).

We measured contributors’ self-interest benefit (i.e. ownership of articles’ contents) and costs (namely, the effort in making an edit) by calculating the fractional ownership for each contributor in each article of our sample using the algorithm in [38]. The content ownership algorithm tracks the evolution of content, recording the number of sentences owned by each contributor at each revision, until the study’s end date. The algorithm uses a sentence as the unit of analysis, where each full sentence is initially owned by the contributor who first added it; as content on a wiki page evolves, a contributor loses a sentence when more than 50% of that sentence’s content (i.e. the words in the original sentence) is deleted or revised by others (thus, a contributor making a major revision to an existing sentence can take ownership of that sentence). If no single contributor “owns” more than 50% of a sentence, that sentence becomes ownerless. The output of the algorithm indicates the number of sentences (and the fraction of sentences within the focal Wikipedia article) originated by each contributor that persisted in the most recent version of the article. We defined as the number of sentences owned by contributor i. A contributor’s fractional ownership in a particular article is obtained as .

The number of contributors in the 864−article sample was found to follow a uniform distribution with the average number of contributors being 124.6 and a standard deviation, 71.9. We also found that contributors are more likely to make smaller edits per sentence than larger edits, with the distribution of Lβ_i resembling an exponential probability density function. The average Lβ_i was 6.8 (measured in Levenshtein distance) and the standard deviation was 6.2. The average content ownership in an article for users, , was found to have a mean of 8% and a standard deviation of 0.55.

Employing the β_i’s and w_i’s thus obtained, we used the expression in Eq (6) to determine our model’s prediction for a contributor’s fractional ownership in a particular Wikipedia page. Eq (6) provides us with a contributor’s expected fractional ownership. We repeated this analysis for all Wikipedia articles in our sample and for all contributors in each article. Our empirical analysis suggests that a contributor’s creator/curator activity profile (β_i) and cooperative/competitive orientation (w_i) are two distinct variables, as the correlation between their estimators is quite low (Pearson correlation = 0.167).

We empirically tested our model’s predictions regarding the relation between contributors’ average edit size (i.e. a proxy for the effort typically exerted by a contributor when making an edit, reflecting their position on the creator-curator continuum), their cooperative/competitive orientation and their resulting content ownership. In trying to gain a better understanding of the temporal dynamics underlying the co-production competition over an article’s content, we applied a temporal bracketing technique by breaking each article into yearly brackets (i.e. Year 1 since inception, Year 2, etc.). We then created subsets by yearly periods, capturing the states of all articles after their first year of operation, second year etc., and calculated contributors’ average effort (i.e. their creator-curator profile), cooperative/competitive orientation and fractional ownership at the end of each year in an article’s life. Next, for each of these yearly subsets, we repeated the analysis described above, comparing the model’s prediction to actual fractional ownership. Our analytical results indicate that the number of sentences owned by a contributor, x_i, hinges on both w_i and β_i. Naturally, it is expected that correlates with these two variables. The correlation between and w_i is 0.678 (i.e. contributors that have a competitive orientation tend to own more sentences). The correlation between and β_i is −0.571 (i.e., curators tend to own more sentences).

Our findings show that the model’s predictions regarding contributors’ fractional ownership are almost identical to the empirical findings. Please see Fig 3 for the results for the entire study period. Looking at the temporal brackets, we observe that already at the end of the year of inception (Year 1), the process converges and our model’s predictions closely match the empirical data (see Fig 4). Fig 5 shows that from Year 2 onward, the results are almost identical to the findings for the entire period. These results suggest that as articles mature and the co-production process stabilizes, our empirical results become more aligned with the model’s prediction.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. The percentage ownership obtained from the data and that obtained from Eq (6) for 864 multi-contributor articles in our sample, for the entire period of study.

Results represent the aggregated solution for the 864 games (each game solved with the appropriate number of editors). Contributors are indexed according to the decreasing order of ’s.

https://doi.org/10.1371/journal.pone.0281725.g003

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. The percentage ownership obtained from the data and that obtained from Eq (6) for 864 multi-contributor articles in our sample, for the first year of inception.

Results represent the aggregated solution for the 864 games (each game solved with the appropriate number of editors). Contributors are indexed according to the decreasing order of ’s.

https://doi.org/10.1371/journal.pone.0281725.g004

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. The percentage ownership obtained from the data and that obtained from Eq (6) for 864 multi-contributor articles in our sample, for the second year of inception.

Results represent the aggregated solution for the 864 games (each game solved with the appropriate number of editors). Contributors are indexed according to the decreasing order of ’s.

https://doi.org/10.1371/journal.pone.0281725.g005

We measured the Pearson’s correlation coefficient value between the fractional ownership obtained by the game theoretic analysis and that obtained from the measured data (2 years from inception, and onward), and found it to be 0.789, thus demonstrating that the data closely follow our model’s predictions. The stability of our findings across various stages of an article’s life cycle solidifies the validity of our model, demonstrating that despite simplifying assumptions and using a static model, we were able to capture the temporal dynamic underlying cooperation and competition in Wikipedia’s co-production of articles. In order to further test for the effect of articles’ maturity, we analyzed the alignment between the model’s prediction and the empirical findings by the number of contributors per article. We found that the alignment increases as the number of contributors per article grows (stabilizing at roughly 30 contributors per article). In order to verify the robustness of our model, we re-ran our analysis, this time excluding non-human editors (i.e. “bots”). Our findings indicate that the pattern of results for both the entire-period and the temporal bracketing analyses remains the same.

Trying to get a better sense of the (small) discrepancies in ownership values between the model’s prediction and the empirical data, we explored whether the differences could be offset by establishing a linear fit function mapping. Let (representing the ownership of the contributors obtained by the game theoretic analysis) and (representing the ownership of the contributors obtained from the empirical data). For each Wikipedia article, we fit a function (13) where the parameters, ρ and δ, are obtained by the method of least squares [82]. We randomly selected 300 articles as training data in supervised learning to determine the linear regression coefficients, repeating the training/testing split 1000 times. The average error for the training data was 7.6%. We then ran a linear regression on the remaining 564 pages and tested the linear fit as well as its significance by measuring the p−value. The error was found to be between 18–23% and the linear regression was statistically significant at p < 0.05. The implication of this result is that the game theoretic analysis models the contributors’ interactions in Wikipedia accurately up to a linear scaling factor.

We further employed a combination of the game theoretic analysis and findings from the empirical data to determine how governance levels influence the trade off between articles’ neutrality and their comprehensiveness Fig 6 depicts the impact of governance level, t, on the neutrality of an article (measured by its entropy) and the comprehensiveness of the article (measured in terms of the article size). The entropy was measured from empirical data and the article size was obtained analytically using in Eq (4). Fig 6 shows that reasonably low levels of governance t ≈ 6 ensure neutrality (large amount of entropy >0.9), while maintaining an article’s comprehensiveness (high value for ). However, when the governance, t, becomes larger (closer to 100), the comprehensiveness of the article (article size) is reduced significantly yet the gain in neutrality (i.e. entropy) is marginal. This result suggests that that low levels of governance are sufficient for curbing much of the competition over content ownership, ensuring a relatively even distribution of ownership, while resulting in only a very minor reduction in activity levels, thus having a minimal impact on articles’ comprehensiveness.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. The effect of governance level,t, on the article size, obtained analytically using in Eq (4) and the entropy, H(t) obtained from empirical data.

For H(t) we just measured the entropy of each article using Eq (10) but with the values of from the data. The articles were indexed in the same order for which the normalized number of sentences were calculated.

https://doi.org/10.1371/journal.pone.0281725.g006

6 Discussion and conclusion

Whereas most research in the area has emphasized the cooperative aspects in Wikipedia’s co-production, answering the call to shift the focus of online collaboration research to issues of scarcity and competition [83], the focus of the current study is on the interplay between contributors’ competition and cooperation. In particular, in this paper we developed a game-theoretic model of cooperation and competition in Wikipedia, under constraints of governance. We corroborated the model through an empirical study. We stress that we did not intend our game-theoretic model to be comprehensive; socio-technical systems such as Wikipedia are much too complex to be fully captured through a game-theoretic model. Instead, we attempted to model a few essential features of Wikipedia’s co-production process, namely contributors’ cooperation in producing high-quality and comprehensive articles, and their competition over content ownership, while taking into account the community’s efforts to ensure that articles represent a balanced perspective.

The key results of our game-theoretic analysis are as follows:

• Analytically, we found that the contributor’s characteristics, or more specifically, the ratio between the contributor’s position on the creator-curator continuum and the contributor’s cooperative/competitive orientation is the factor that determines who ends up owning content. When this ratio is smaller than the group’s average, the contributor maintains ownership over portions of the article. Namely, under the governance mechanisms, the fractional content that is eventually owned by a contributor is higher for curators (i.e., with a typical small-size edit per sentence) with a competitive orientation (i.e., peripheral community members). In essence, creators with a cooperative orientation lose ownership of the article. This result was corroborated through an empirical analysis of 219, 811 distinct contributors co-producing 864 representative articles over an eleven-year period, which used the proxies mentioned earlier. Employing a temporal bracketing approach, we analyzed the data for each yearly bracket independently, to find that already from the second year of an article’s life and onward the empirical pattern of results converges to our analytical predictions.
• Analytically, we show that excessive governance should be curtailed, by identifying and maintaining a permissible upper limit, beyond which it discourages contributors from making contributions to an article, bringing the co-production process to a halt. Furthermore, our empirical analysis suggests that a low level of governance i s optimal for ensuring neutrality while maintaining articles’ comprehensiveness.

We note that prior studies have discussed individual contributors’ attempts to influence articles’ contents [33, 56, 64, 65], but these studies did not consider peer production dynamics. Namely, in a large system such as Wikipedia, where participants’ contributions tend to be in reference to some existing content (contributed by others), knowing the effects of contributors’ actions on others is essential for understanding the system’s dynamics. We, thus, extend prior research by investigating the effects of collaborators’ behavior on others’ actions and studying the system’s dynamics.

The finding from the non-cooperative game that a competitive orientation yields content ownership suggests that the benefits associated with content ownership outweigh the effort that is associated with governance-enforcing tax (at least up to a certain limit; see below). This result is rather straightforward, whereas the findings regarding creators and curators is less intuitive, given that creators are major contributors of content to the article. One may argue that this could be explained by the temporal order of editing: creators add content early on, only to be overwriten by curators’ later contributions. However, our temporal bracketing analysis accounts for this possible effect, and we demonstrate that our results hold even when excluding the first year of articles’ lives (i.e. the results from Year 2 and onward). How, then, could this result be explained? One line of explanation points to community’s effort to ensure neutrality [25, 33]. The “creators” who make large contributions and take ownership of large portions of the article pose a potential threat to the article’s neutrality. In response, the community works collectively to fight such manipulations and restores neutrality. In the long run, the result is a more neutral content [30, 84]. Not withstanding the role of community efforts to ensure neutrality, our results may also be explained by paying attention to the profile of those making the large contributions. Prior studies have identified the “creators” [34–37, 85] or “content-oriented” contributors as those whose main interest is to demonstrate their knowledge of the topic, and are much less invested in Wikipedia’s internal processes. In contrast, the “curators” (also referred to as “community-oriented” contributors [8]), who engage in refining, shaping, and reorganizing content [86], act as “janitors of knowledge” [87] and end up owning larger portions of articles. That is, at the end of the day, it is the curators who play the leading role in shaping articles’ contents. We note that both these lines of explanation highlight the effectiveness of Wikipedia’s social processes.

A second powerful result of this study is in demonstrating that that the community’s efforts to govern content creation and ensure neutrality, although essential for maintaining a balanced position, should be carefully monitored and kept limited. The reason is that when the “tax” imposed on contributors in terms of complying with NPOV norms, policies and procedures is too high, it outweighs the benefits associated with content ownership, such that contributors stop competing for ownership (and in effect, co-production is stalled). Prior studies have documented the growing bureaucracy of Wikipedia [80], and have suggested that the increasing complexity of Wikipedia’s governance structure is deterring newcomers and may eventually lead to the decline of Wikipedia [1]. Our results provide analytical proof of the risk associated with increased governance cost and highlight the need to balance the cost and benefits associated with the governance of online production communities. Furthermore, our analysis indicates that a low level of governance is optimal for ensuring neutrality while maintaining articles’ comprehensiveness, suggesting that light-weight governance mechanisms may be optimal. Whereas prior research did suggest that governance levels should be curtailed, the current study adds to the literature by identifying the appropriate levels of governance.

In sum, our study makes important contributions to research on peer production, First we shed light on the dynamics underlying peer production. Second, we show how Wikipedia’s governance and in particular, the community’s efforts to maintain neutrality, affect contributors’ behavior and consequently, the quality of the co-produced articles. Although there have been studies using game theory and network ties to study collaboration in social networks in general [88] and applied to Wikipedia in particular [89], we are not aware of prior research in this area that linked governance to individuals’ actions.

Notwithstanding these contributions, our work could be extended in several directions, for example by employing alternative measures for our model’s constructs (alternative measures of articles’ objectivity through an analysis of Wikipedia’s discussion pages) or extending the model to include additional constructs related to contributors (for example: contributors’ intent and their psychological ownership, their compliance with Wikipedia’s policies, or the phase in an article’s life on which they concentrate their edits) or related to the articles (the extent to which articles are controversial or the importance of the knowledge-based product). Future research could also attempt to empirically validate our model’s prediction that excessive levels of governance impede peer production. Finally, a more complex convex cost model (e.g., a quadratic cost model) and its effect on co-production and governance can also be explored.

An additional important contribution of this study is in applying game theory to investigate peer production in Wikipedia. Prior studies have called for the development of new economic models [90] and in particular, the application of game theory to investigate emerging socio-technical systems such as Wikipedia [91]. A few studies have used game-theoretic models to compare the efficiency of closed- and open-source software development regimes [92], investigate the competitive dynamics of the process by which participants provide feedback on each other’s work (i.e. rating and reputation systems) [93], and to study co-production in user generated content [94], crowd sourcing [95] and Wikipedia [96]. Our study extends prior work in the area by using game theory to shed light on the role that governance mechanisms play in moderating the competition between contributors to peer production. Our game-theoretic model provides insights into the complexities of cooperation and competition in peer production, while making several simplifying assumptions.

Although our empirical analysis corroborated the game-theoretic model, we did observe small discrepancies between the model’s predictions and the empirical data. One possible explanation for these differences is that our model provided only an approximation of Wikipedia’s complexities. Future research could help make progress: such work could relax some of our model’s assumptions, for example, by distinguishing between different contributors’ knowledge and capabilities, modeling learning effects, capturing other important qualities of articles such as accuracy or completeness, and exploring multi-stage games to consider various classes of contributors that differ in their roles and goals. In particular, we foresee three avenues for extending our study. First, in our model a contributor owns his newly-added content thus impacting others’ relative ownership. A more sophisticated model could also account for overwriting (or deleting) another contributor’s content, thus directly impacting the ownership of a specific other. A challenge for such a model would be to handle the complexity associated with numerous pair-wise relationships. Second, our model could possibly be extended to capture a tighter linkage between the leader-follower game (community governance) and the non-cooperative game (cooperation and competition over content ownership), for example by linking the effectiveness of the community’s governance to the aggregate of contributors’ governance effort.

Beyond the theoretical contributions and directions for future work, our study’s findings also have important implications for custodians of online production communities. The most important insight pertains to the levels of governance that are required. Namely, we find that low levels of governance are sufficient for curbing much of the competition over content ownership, ensuring a relatively even distribution of ownership, while only resulting in a very minor reduction in activity levels, thus having a minimal impact on articles’ comprehensiveness. Another important contribution pertains to the importance of peripheral community members that have a less cooperative orientation. In fact, as a consequence of their pursuit of content ownership, their activity levels are increased, such that they add contents to the article, making the article more comprehensive and of higher quality. Hence, communities such as Wikipedia should encourage peripheral participation [97] in addition to their efforts to encourage cooperative participants to take on additional functions and roles.

In conclusion, we believe that game theory can reveal deep insights into the complex dynamics underlying peer production. While game theory, and in particular leader-follower game, has already been employed in the context of allocation of divisible resources [98], the application of such techniques to community-based peer production is novel. Future research directions for game theory in this area include the use of cooperative game theory [99] to study the stability of the production process; applying coalitional game models [100] to analyze how competing coalitions of contributors emerge, applying resilience and immunity models [101] to investigate how the peer production process performs in cases of deviations from expected behavior, and using evolutionary game theory [102] to study how unexpected behaviors emerge as a result of sequential actions by different contributors. Game theory can also be used to develop models that would account for the relationship between individual’s governance work and the community’s overall governance level while using algorithm and mechanism design [103] to determine the most effective community governance structures.

Supporting information

Acknowledgments

The authors thank the anonymous reviewers for their constructive criticism which greatly enabled us to enhance the results and presentation in the manuscript.