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What incentives do contributors have?
I believe they earn no money. And usually, they earn no reputation either, because most of the contributions are anonymous.
I believe this is a public goods game. Have economists studied this "Wikipedia puzzle"? How might they explain it? To what extent would economists consider this a "puzzle"?
By "contributors", I mean those who edit Wikipedia pages, not those who contribute in other ways (e.g. donations).
Voluntarily contributing to a public good (such as Wikipedia) is a strong social norm. The tendency to follow such norms even if this is costly in the short run has developed over humans' evolutionary history, as in small to medium-sized hunter-gatherer communities this behavior was adaptive, e.g. due to reputation effects ("community enforcement").
This evolved behavioral tendency has become engrained in "social" preferences exhibiting a taste for strong reciprocity or for following "moral" imperatives. In modern societies it therefore also shows up in contexts where it is actually maladaptive, as under anonymity or in one-shot interactions without reputational benefits. The same arguments explain why experimental subjects cooperate in the prisoner's dilemma and reciprocate in the trust game, why many humans engage in costly activities to decrease their carbon footprint (even though this has a negligible effect on climate change), and several other non-selfish actions.
I wouldn't underestimate the role of learning by answering.
Drafting a significant text typically forces a person to put their thoughts in order, to engage in research, and then to structure the information for the purpose of recording and conveying it. It is not unusual that further insights or questions emerge during this process, the answerer certainly becomes more familiar with the subject, and good communication is itself a skill that requires significant attention and practice to develop.
Moreover, publicising one's thinking (even to a very small audience) typically invites challenge and puts it to the test of what others think of it, which again tends to flush out all kinds of faults and oversights - either faults in the thinking itself, or faults in the way it has been articulated and formulated into words.
Clearly, the assumption embedded in this question is that communication is done purely for the benefit of the listener, and that knowledge transfer is done in a "jug and mug" style, but there is more truth than you might think in that hoary old claim that academics have much to learn from their students.
So part of the answer to why people freely labour to communicate on sites like Wikipedia (not to mention here at StackExchange) is therefore bound up in the question of what stake they have, not just in developing the knowledge they appear to possess, but also in developing and rehearsing all the broadly intellectual skills associated with the development, retention, and communication of knowledge.
tl;dr: There could be multiple explanations depending on how you want to treat Wikipedia. If you want to treat Wikipedia as public good where everyone contributes a small part towards its creation and that everyone then enjoys equality you can explain it as people trying to still satisfy their own preferences through consuming the final Wikipedia page.
You could also treat it as an example of pure altruism people provide for others because they enjoy knowing that others are now better as a result. Furthermore, it could also be treated as completely self-interested action because one enjoys it as a hobby or because they derive some other personal benefit such as improving their own skill as mentioned in the answer provided by Steve. It is also possible it is a mixture of these possible explanations.
Voluntary Provision of Public Goods:
There are actually several models of voluntary public good provision, these are nowadays even included in textbooks (see Mueller Public Choice III for example). For example, we could model the Wikipedia situation as an adapted version of one of the voluntary public provision goods models presented by Mueller in his book:
For example, let's subdivide Wikipedia into sub-Wikipedias by for example its subjects and model contribution to single subject area at a time (as suggest by Michael in his +1 comment). The total contribution to that particular subject area on Wikipedia will be our public good $W$ that will consist as a collection of individual article contributions to the subject $W_i$ so $W=W_1+W_2+...+W_n$. Individual utility will be given as $U_i(x_i,W)$ where $x_i$ is some standard consumption and $W$ is the Wikipedia a public good which is consumed by everyone. An individual budget constraint of individual will be given by $M = P_xx_i + P_w W_i $ where $M_i$ is a budget $P_x$ is the price for consumption and $P_w$ 'price' for the individual's contribution to Wikipedia - this is an abstraction of course in real life one does not pay a price to 'purchase' and post Wikipedia contribution but it is just simple way how to avoid explicitly modeling everything in terms of labor supply vs leisure trade-off and will save me a lot of work and make this problem shorter without any substantial change in result. Hence under the above assumption an individual optimum choices would be given by solving the following Lagrangian:
$$L = U_i(x_i,W) - \lambda_i(M_i - P_x x_i - P_w W_i)$$
which gives us the following FOC's:
$$\frac{\partial U_i}{\partial W} - \lambda_i P_w =0 $$
and
$$\frac{\partial U_i}{\partial x_i} -\lambda_i P_x=0$$
hence the condition for utility maximization is given by:
$$\frac{\partial U_i/\partial W}{\partial U_i/ \partial x_i}=\frac{P_w}{P_x}$$
from this we can even calculate an individual contribution to Wikipedia to be by specifying some exact utility function. For example, suppose that utility is given by Cobb-Douglas as $U_i= x_i^a W^b$ which would imply that individual contribution to creating Wikipedia in equilibrium will be:
$$W_i = -\frac{a}{a+b} \sum_{j\neq i} W_j + \frac{b}{a+b} \frac{M_i}{P_W}$$.
The above result is extremely intuitive as it shows a free rider behavior, the first term shows that the more other people contribute to Wikipedia the more you will free ride and write less of your own. The second term just shows that the higher your income is or the lower the 'price' for writing is the more you write.
We can even calculate the total contribution the give Wikipedia subject by whole community. For example, assume everyone has the same income $M$ to simplify math as it will imply that everyone will choose exactly the same contribution, then the total contribution of whole community will be given by:
$$W = nW_i = n \left(-\frac{a}{a+b} (n-1) W_i + \frac{b}{a+b} \frac{M}{P_W} \right) = \frac{nb}{an+b} \frac{M}{P_w}$$
Its also worth noting that this contribution will also be lower than pareto-optimal contribution (except for special cases such as a case where marginal utility of $x$ is zero) due to the free riding issue but it wont zero save special cases such as if income would be zero or 'price' for contributing to Wikipedia would tend to infinity in the limit etc.
This model would provide valuable insight especially if we can argue that Wikipedia entries are not solely written for the benefit of readers but also the writers themselves as pointed by Giskard in his insightful comments or argued implicitly by Steve.
Moreover, as per Michael's valuable suggestion this model is more appropriate when applied to individual sub-Wikipedias. Hence these would be better way to model contributions to for example different subject-matters, but at the same time Wikipedia is ultimately a collection of all individual sub-Wikipedias.
Altruistic Explanation:
In case we would not want to assume that writer derives any benefit from writing Wikipedia articles then we can treat more as an charitable activity. In that case you could explain it by utility function that is dependent also on utility of others. For example, you could model that person's utility as being interdependent. For example, with utility $U_i=\Psi( u_i(x), u_j(x))$ where $\partial U_i/ \partial u_j >0$ (see for example Hori 2002 for an more complex example). In this case people would provide Wikipedia article just because they would enjoy knowing that some other people will derive some utility/benefit from reading the articles.
Other explanations:
Alternatively as mentioned by Steve you could treat it as a learning experience where individuals write these articles as investment in improving their human capital. In that case you can view them as cost of accruing more human capital which will bring benefits later in form of higher income thanks to having better communication or retention skills (see an overview of theory of human capital in Becker, Gary S. Human capital: A theoretical and empirical analysis, with special reference to education).
You could also view it as a 'hobby' so it would be work one is doing for themselves where utility is derived actually from performing the task and I bet that some other explanations might exist as well.
To what extent would economists consider this a "puzzle"?:
This is a good question but quite subjective one. There are some authors that refer to voluntary provision of public goods as a 'puzzle' (see Anderoni 1995), but I also don't think that this ever became puzzle in the same prominent way as let's say equity-premium puzzle. Also I don't think contemporary public economists still consider it to be an unsolved puzzle - there are some related puzzles where some experiments show that sometimes people tend to contribute more than expected - but there are also all sort of behavioral/evolutionary/repeated game explanations for that.
For starters, the obvious thing is to look at the data about the self-reported reasons for contributing to wikipedia (and I'm surprised that neither the question asker nor most of the answers have done so). For example, Wikipedia itself has a section on the motivation that refers to multiple studies - though many of them are behind a paywall if you're not accessing from an academic institution with a subscription.
The surveys show that non-economic reasons for contribution dominate:
There are some reported reasons based on an incentive ("Want to popularize topics that I care about" and "Demonstrate my knowledge"/"Gain reputation") but those are, at least in self-reporting, not the main reasons for contribution.
I believe that rationality is the wrong perspective to approach this question, and the answer is more about social psychology rather than economics and concepts like the public goods game.
First, it's worth noting that in general, people do not contribute to Wikipedia. The people who do are a very small minority of users, rare exceptions.
Second, it's well known that the 'rational choice assumption' in economics is a simplification that's not universally true. While it can explain lots of aggregate behavior, it's not at all surprising to have situations where a significant minority do not behave as theoretical rational actors.
Third, there's no reason to presume that the priorities and motivation of that small minority is representative of the wider population. Given the survey data and the fact that the vast majority of people choose not to contribute, it's reasonable to suppose that the contributors are a specific, 'abnormal' part of population who are more inclined to act on the basis of altruism, who (unlike most others) have core values that require them to contribute in this manner, or who (unlike most others) consider writing encyclopedia articles as entertainment.
So I believe that we can conclude that the rational, economic answer to "Why should people contribute to Wikipedia" is "There is no good reason, don't contribute", which is also the choice that most people have made; and the answer to "Why do people contribute to Wikipedia" is "Because sometimes some people act counter to rational economic considerations".
A competent economist has only one answer for this:
Not everything is about money.
Economics can't explain everything, and a good economist will recognize this. It's not a puzzle, any more than it is a puzzle why people have children, buy expensive cars, or go on vacation.
Any explanations lie outside the field of economics, and so are off topic here.
Wikipedia in a sense is informal domestic production, in the sense that it is the sum of valuable work you could be paying for but provide for free.
Usually, informal domestic production are directly consumed (such as cooking) and the economist summarize the incentive easily in the fact you'd be trading your time for something enjoyable or useful to you directly or to give someone you share the house with and have an implicit contract with.
What happens in Wikipedia is not so well understood and predictable (many people predicted Wikipedia model would fail in the early days), but I believe it's partly explained by the study of gift economies.
In a gift economy people give things to each other with no expectation of direct return. Gifts are extremely common and take various forms. Sometimes theys are institutionalized by a social norm (e.g. Christmas), sometimes they are meant to show power or impress (could be the case in diplomatic relationships)... in all the cases, when being offered a gift, one should be predisposed to positive feelings and is sometimes expected to return a favor, something which tend to help communities to build.
Perhaps the people that read Wikipedia feel a gift is made to them. It is made even more visible by the "branding" about non-profit model. This could explain some of them feel inclined to contribute, due to having a culture of returning favors.
We consider also that the ultility of time and knowledge are special. Time and knowledge are valuable to recieve but their cost can be very little to the person giving, as some people have time in excess and find teaching pleasurable.
The answer is different depending on which view you take. From an individual view, to some the act of contributing is comparable to any other hobby. I mean, people do not go fishing or do gardering or play the bassoon in order to gain economically from it.
I tend to define a hobby as something where you spend surplus time and surplus money. The only problem, compared to the definition, is that it does not cost money to add texts.
How do economists explain unpaid social activities? Sociologically.
In the USA males contribute 85% of editing, and females 15%, even though women have higher education accolades in the USA than men. In the USSR, female contribution is much higher, about 30%.
So, oddly, one of the motivations is masculine psychology.
The reason for that is mostly supposed to be with male ambition, self confidence, and sense of authority on topics, compared to women's trepidation and aversion to conflict.
That reveals interesting dynamics about wikipedia motivations for editing, some reasons for which have been suggested in this list which we can invert, i.e. people edit wiki because:
1/it's simple to edit, easy user interface 2/editors feel confident and want to put their knowledge forwards 3/editors disagree with a particular view of wiki and want to add coutner arguements 4/they think that their addition will be recorded and influential 5/editors like the overall atmosphere of learning and academia 6/it's better to write on wiki than on a social media site like facebook.
