The economics of scientific collaboration

What economics can tell us about scientific collaboration

In this and several future posts I’m going to discuss what economics can tell us about scientific collaboration.

This may sound like a strange topic. Why should economics tell us anything interesting about scientific collaboration? Most discussions of economics are couched in terms of money, interest rates, prices, and so on. While these are relevant to science in a shallow, who’s-paying-for-this-lab-space kind of way, it’s not obvious we can learn anything deep about scientific collaboration by thinking in economic terms.

At a deeper level, though, economics is about understanding how human beings behave when one or more resources are scarce. How are those resources allocated? Are there more efficient ways they might be allocated? What tradeoffs are incurred?

There is a fundamental scarce resource in science, one whose allocation largely determines how science progresses. That scarce resource is expert attention. Who pays attention to what problems? How long do they spend on those problems? What institutional structures determine the answers to those questions? In short, what determines the architecture of scientific attention?

We can learn interesting things by thinking about these questions using ideas from economics. In this post I pull apart the way scientific collaboration works, and put it back together again within the conceptual framework economists use to understand free trade, using concepts like comparative advantage, opportunity cost, and markets. The reason I’m doing this is because the way we structure scientific attention is currently changing rapidly (by historical standards), as networked tools like wikis, blogs, twitter, email, online databases and friendfeed change the architecture of scientific attention. To understand these changes is in part an economic problem, and the point of this post is to begin developing an economic perspective.

Comparative advantage, opportunity cost, and the benefits of free trade

Scientific collaboration can be viewed as a type of trade in expert attention. I can, for example, trade some of my skill as a theoretical physicist for someone else’s skills as a computational physicist, enabling us to jointly write a paper neither of us could have written alone.

To understand this collaboration-as-trade perspective, let’s review some ideas about trade in the context where trade is most often discussed, namely, free trade of goods. We’ll start with a beautiful simplifed model of free trade, a model that goes back to a famous 1817 book “On the Principles of Political Economy and Taxation”, by the economist David Ricardo. Like many useful models, it leaves out a lot that’s relevant to the real world, but it does capture an essential element of the world, and we can learn a great deal by thinking about the model. In particular, the model demonstrates vividly why all parties involved in free trade can benefit, and is one of the main reasons most economists strongly support free trade.

(A small digression: there’s a family connection in this post, since David Ricardo was my Great-Great-Great-Great-Great-Uncle.)

Here’s the model. Imagine there are just two people in the world, Alice the farmer, and Bob the car technician. Alice is good at producing potatoes, but not much good at assembling cars, while Bob is good at assembling cars, but not so good at producing potatoes. Pretty obviously, both Alice and Bob can benefit if Alice concentrates on producing potatoes, Bob concentrates on assembling cars, and they then trade potatoes for cars. While this is intuitively clear, it’s worth making precise with more concrete details. Let’s suppose the effort required for Alice to assemble a car is equal to the effort she requires to produce 20 tonnes of potatoes. Put another way, each car she assembles has an opportunity cost of 20 tonnes of potatoes, since that’s how much assembling a car will cost her in lost production of potatoes. Similarly, suppose the effort for Bob to assemble a car is equal to the effort he requires to produce 2 tonnes of potatoes. That is, each car has an opportunity cost for Bob of just 2 tonnes of potatoes.

In this situation, Bob has a comparative advantage over Alice in the production of cars, because Bob’s opportunity cost for producing cars is less than Alice’s. Equivalently, Alice has a comparative advantage over Bob in the production of potatoes, for her opportunity cost to produce a tonne of potatoes is 1/20th of a car, which is less than Bob’s opportunity cost of half a car.

Suppose Alice and Bob each concentrate in the areas where they have a comparative advantage, i.e., Alice concentrates on producing potatoes, and Bob concentrates on building cars. They then trade potatoes for cars. Both Alice and Bob benefit if the rate at which they trade is greater than 2 and less than 20 tonnes of potatoes per car, because they both will end up with more cars and potatoes than either could have produced on their own. Furthermore, the greater the comparative advantage, the more both parties benefit. Put another way, the more people specialize, the more possible benefit there is in free trade.

It’s worth stressing that the key factor determing the benefits of trade is comparative advantage, not Alice and Bob’s absolute abilities. It might be, for example, that Bob is a layabout who’s lousy both at assembling cars and producing potatoes. Perhaps he’s only capable of assembling one car (or producing 2 tonnes of potatoes) for every ten days of labour. Alice, despite being a farmer, might actually be better than layabout-Bob at assembling cars, producing one car (or twenty tonnes of potatoes) for every 5 days of labour. Even though Alice has an absolute advantage in producing both cars and potatoes, she and Bob are both better off if they concentrate on the areas where they have a comparative advantage, and then trade. Although this example is contrived, it has many implications in the real world. For example, differences in education and infrastructure mean that people in different countries often have enormous differences in their absolute ability to produce goods. Despite this, people in both countries may still benefit from trade if they all concentrate on areas where they have a comparative advantage.

This is all pretty simple, but it’s not universally understood. Much anti-business rhetoric assumes a zero-sum world in which evil captains of industry exploit the defenseless poor, i.e., if one person benefits from a transaction, the other person must lose. Very often, that’s a bad assumption. Good businesspeople look for transactions where both parties benefit; wouldn’t you prefer doing business with enthusiastic trading partners, rather than people who feel coerced or exploited? Of course, sometimes unethical businesspeople do coerce their trading partners, and sometimes trade between two parties can damage a third – environmental issues like pollution often have this nature. But Ricardo’s model is a good starting point to understand how free trade can work to the benefit of all parties.

Markets as a mechanism for aggregating information about comparative advantage

One question not answered in Ricardo’s model is how the trading rate is set. At what rate between 2 and 20 tonnes of potatoes per car should Alice and Bob trade? There are many possible ways to set the rate. In our society, the standard way is to use money as a medium of exchange, with markets determining the price of the relevant goods.

Let’s suppose Alice and Bob participate in such a market, and that the market price is 10,000 dollars per car, and 1,000 dollars per tonne of potatoes. The market thus provides a mechanism by which Alice and Bob can effectively trade cars for potatoes at a rate of one car for ten tonnes of potatoes. This is within the range where it is beneficial for both of them to trade, and so both may enter the market.

What if, instead, the market price was 5,000 dollars for a car, and 5,000 dollars for a tonne of potatoes? Then the effective trading rate is one car for one tonne of potatoes. Bob will be worse off if he enters the market: he’s better off both making cars and growing potatoes. The result is that Bob will withdraw from the car market, reducing the supply of cars. This will drive the market price of cars up a little, but this probably won’t be enough to change the price enough for Bob to re-enter the market. But if enough people withdraw, then the price of cars will go up a lot, and it will make sense for Bob to re-enter.

Money and markets thus serve several purposes. First, the market determines the price of different goods, and thus effectively sets exchange rates between different goods.

Second, the market price automatically aggregates information about comparative advantage, because the people who enter the market are those with a comparative advantage large enough that they can benefit from being in the market. People with a smaller comparative advantage have no reason to do so.

Third, while it’s possible to set up a barter market without the use of money, it’s obviously a great deal more efficient to use money as an intermediary, since for each type of good in the market, we need only keep track of a single price, rather than exchange rates with all the other types of good.

In fact, digressing briefly, it’s possible to prove that in an efficient barter market, an effective currency does emerge. By efficient, I mean that it’s not possible to increase your holdings by conducting a series of trades in immediate succession, e.g., by trading one ox for two cows, the two cows for one horse, and then the horse for two oxen. If this kind of trade is impossible, then it’s possible to just fix on one type of good – say, cows – as the effective unit of commerce, like the dollar, and peg all trades to that unit. From there it’s a small step to forgo the cows, introducing an abstract entity (i.e., money) to replace them. Furthermore, it’s reasonable to argue that you’d expect efficiency in this kind of market; if the market was inefficient in the way described above, then you’d expect one of the intermediaries in the transaction to realize it, and raise their prices, and so smooth away the inefficiency.

It’s remarkable how effective the market is at aggregating information about comparative advantage in this way. It lets us all take advantage of the combined efforts of millions of individuals, most doing tasks for which they have a considerable comparative advantage. Think about the number of people involved in producing a laptop computer. Tens or hundreds of thousands of people participated directly in designing and producing the components in that laptop; most of those people had considerable (in some cases, enormous) comparative advantage in the skills they contributed. When you buy a laptop, your few hundred dollars buys you the accumulated wisdom from a design history of billions of hours, stretching all the way back to the earliest computers. Beyond that, hundreds of millions of people contribute capital (e.g., via retirement funds) used to build infrastructure like chip foundries. Chances are that anywhere between a few dollars and a few hundred dollars from your retirement fund was invested in the chip foundry that produced the processor for the computer that I’m typing these words on. We’re both benefiting right now from differences in comparative advantage.

By providing a way of identifying and taking advantage of comparative advantage, markets encourage people to specialize, creating even greater disparaties in comparative advantage, and thus producing more mutual benefit. The better the market operates, the stronger this feedback effect becomes. Although it’s currently fashionable to bash markets (and economists), in fact many technologies we take for granted – cars, airliners, computers, telecommunications – would be near impossible without the modern market infrastructure.

Comparative advantage and scientific collaboration

Let’s construct a simple model of scientific collaboration inspired by Ricardo’s model of free trade. The model is, of course, a great oversimplification of how collaboration works; the point isn’t to capture the reality of collaboration exactly, but rather to illuminate some elements.

We’ll imagine two people, Alice and Bob, a physicist and a chemist, respectively. Alice is working on a problem in physics, but as she works an unanticipated problem arises, let’s say in chemistry. Let’s suppose for the sake of argument that the problem requires 100 hours of straightforward physics to solve, and 10 hours of straightforward chemistry. (The real numbers in most significant scientific problems are probably larger, but these numbers make the discussion below a little easier to read.) Unfortunately, Alice isn’t much of a chemist, and it would take her 200 hours to do the chemistry part of the problem, mostly spent bumbling around learning the required material. Alternately, if Bob got involved in the project, he could solve the chemistry problem in just ten hours.

There are two scenarios here. In the first, Alice does all the work, it takes 300 hours, and Alice gets all the credit for the paper published as a result. In the second, Alice does 100 hours of work, Bob does 10 hours of work, and they split the credit. Let’s say Alice ends up as first author on a paper describing the work, and Bob ends up as second author, and let’s further say that Alice gets two thirds of the credit as a result, and Bob gets one third of the credit.

Per hour worked, Alice is much better off in the collaborative scenario, getting two thirds of the reward for only one third of the effort. Bob is probably also better off, although the reason is more subtle: if Bob entered the collaboration freely, then it was presumably because Bob felt this was the best use of his time. This is not always the case – if Bob works for Alice he may have to do the work (or find another job), even though he’d do better science if he concentrated on other projects. This is a case where the trade is not completely free, but rather there is coercion. We’ll assume, though, that no coercion is involved, and that both parties benefit.

Let’s fill the model out a little more. Imagine that Bob’s alternative to collaboration is to go off and write straight-up chemistry papers, on his own, taking 110 hours to write each paper, and getting full credit for the paper. He is still better off working with Alice, for he gets one third of the credit for only 10 hours worth of work. Both Alice and Bob benefit, just as in Ricardo’s model.

Another similarity to Ricardo’s model is that it is comparative, not absolute, advantage which is critical. Let’s imagine Bob is actually a beginning chemistry student, and takes 100 hours to complete the work Alice needs done. He’s still better off working with Alice than working on his own, for on his own it would take 1100 hours to write a chemistry paper. Furthermore, Alice is still better off working with Bob than on her own, for the time she saves on doing chemistry is time she can put to work doing physics.

As an illustration of these ideas in a different context, consider the way many supervisors work with students and postodcs. The supervisors suggest problems, reading materials, likely angles of attack, and so on – all areas in which their experience gives them an enormous absolute advantage, and a sizable comparative advantage. The students do the detailed work in the lab. Many supervisors will have an absolute advantage in such lab work, but it is likely to be much smaller, and so the student likely has a comparative advantage in doing such work. Any time the supervisor spends doing such detailed lab work has an opportunity cost in lost time to be suggesting problems, reading materials and the like for another student.

An important difference between this model and Ricardo’s lies in the way we define the benefit to the parties involved. In the case of Ricardo’s model, the benefit is entirely intrinsic: Alice and Bob both want cars and potatoes. In the scientific case, there’s no intrinsic desire the parties have for “expert attention”. Rather, the benefit lies in the reputational credit derived from publications. This difference complicates the analysis of when it is worth it to collaborate. Instead of a simple trading rate, one must consider the way in which reputational credit is split. It is the ratio of this split to the opportunity cost that determines when it makes sense to collaborate. If Alice got 95 percent of the credit, and Bob only 5 percent of the credit, obviously it would not be in Bob’s interest to collaborate. In a future post, I’ll address this more fully, as well as many other aspects of this model.

For now, let me simply point out the relative lack of mechanisms science has for aggregating information about comparative advantage. Mostly, we do it by word of mouth and personal connection, the same way our ancestors traded goods, and so we don’t get the advantages that come from modern markets.

There are good reasons it’s difficult to set up efficient collaboration markets in expert attention. Creative problems are often highly specialized one-off problems, quite unlike the commodites traded in most markets. Until very recently, markets in such specialized goods were relatively uncommon and rather limited even in the realm of physical goods. This has recently changed, with online markets such as eBay showing that it is possible to set up markets which are highly specialized, provided suitable search and reputational tools are in place.

To the extent such collaboration markets do exist in science, they still operate very inefficiently compared with markets for trade in goods. There are considerable trust barriers that inhibit trading relationship being set up. There is no medium of exchange (c.f. the posts by Shirley Wu and Cameron Neylon’s on this topic). The end result is that mechanisms for identifying and aggregating comparative advantage are downright primitive compared with markets for physical goods.

Perhaps the best existing examples of collaboration markets occur in the open source programming community. No single model is used throughout that community, but for many open source projects the basic model is to set up one or more online fora (email discussion lists, wikis, bug-tracking software, etcetera) which is used to co-ordinate activity. The fora are used to advertise problems people are having, such as bugs they’d like fixed, or features they’d like added. People then volunteer to solve those problems, with self-selection ensuring that work is most often done by people with a considerable comparative advantage. The forum thus acts as a simple mechanism for aggregating information about comparative advantage. While this mechanism is primitive compared with modern markets, the success of open source is impressive, and the mechanisms for aggregating information about comparative advantage in expert attention will no doubt improve.

Let me conclude with a question that’s still puzzling me. As I mentioned before, markets have creative power: without them, it’s unlikely that sophisticated goods like laptops and aeroplanes could exist. I’d like to better understand whether more efficient collaboration markets can cause a similar shift in what scientific problems can be solved. Might scientific problems now regarded as out of reach become accessible with more effective ways of structuring scientific attention?


  1. Fascinating post! I am very intrigued by the whole notion, but I have only a fleeting understanding of the basic alice and bob economic scenario. In fact, I’m one of those making it “not universally understood.” Actually, I didn’t start to get comparative, versus absolute, advantage until you got to the alice / bob physics / chemistry story, which for some reason was much more evident, event though I suppose the numbers are the same. I have completely never thought of this before, and thus I think my intuition would have been towards absolute advantage.

    I started to think of “economic value added” (EVA) in “Quest for Value” by G. Bennett Stewart (which I read about 1/4 of and enjoyed about 8 years ago). I felt like I understood economic value added, but I don’t understand comparative advantage nearly enough to see how they fit together. One thing I was reminded of is that a company just needs to borrow money in order to invest in something with will add economic value. What do scientists do when they have many many more ideas than they have time to implement? There is a lot of EVA left unproduced. I definitely have felt like this for 10 years or more (not enough “capital” to produce what I think will be valuable scientific things). A company with lots of positive EVA ideas needs to grow bigger and bigger to create the value. I don’t want to do that as a science lab. How do I do it? More and bigger collaborations? More efficient science? Another interesting thing this made me think of is that EVA is a very convenient number for business decisions. I have no idea what we have in science, because it seems like we are always choosing between options that have a positive profit. Maybe that’s because I’m not factoring in the costs very well at all.

    In regards to your last question. I view “The Making of the Atomic Bomb” (Richard Rhodes) as having rescued my scientific career…is the Manhattan project a good clue as to what we can achieve? Maybe not, since the electronic communication and collaboration resources we have to day are so much more powerful?

  2. Hi Steve – Yeah, my intuition tilts toward absolute advantage as well. That’s why I like Ricardo’s model so much – it really shows that is the wrong way to think.

    As regards your comment about “many more ideas than there is time”: my guess is that there are more scientific ideas in scientists’ heads than there is problem-solving capacity in the system, no matter how efficiently we solve problems. Part of the reason being that every problem we solve produces more ideas! At least, every established scientist I’ve ever met seems rather rueful about all the ideas they don’t have time to pursue. I guess the only thing to do is to prioritize, and that’s not necessarily a bad thing.

    I’m also a big fan of Rhodes’ book. How did it rescue your career, if you don’t mind my asking? Coincidentally, I read the book on the recommendation of your colleague (and my supervisor) Carl Caves. Amazing story, and wonderfully told.

  3. I was mentally beaten down and warn out from the restrictive, paranoid lab I was in in grad school. I had sworn off ever going back to academia and was really hoping to get into the world of finance or business (which I still think would have been a fun career). After starting my postdoc at Sandia, I think I started to recover with a time constant of several months. I picked up Rhodes’ book and everything in it just made me love science again and I was so wishing AI could have been an early 20th century scientist discovering what the hell the atom is made of. Also much of the philosophy of science parts of it (particularly at the beginning talking about Polanyi) really clicked with me. At the time I didn’t think it “rescued” my career, and I may be over-stating it. But in retrospect, it really went a long way towards re-convincing me that science can be awesome and I can love it and it doesn’t have to be “1.0.” I also recommend this book to my students. Seems like both you and I made it past an undergraduate degree in physics without having read that book…it should be required reading for physics majors!

  4. Gee, I’m a huge fan of Rhodes book too!

    An account that wonderfully complements Rhodes’ science-focused account is an article by Charles Thorpe Against Time: Scheduling, Momentum, and
    Moral Order at Wartime Los Alamos
    . Thorpe’s account focuses on the interplay between morality and system engineering, as contrasted with Rhodes’ focus on morality and science.

    Thorpe’s article pointed me toward Al Christman’s [i]Target Hiroshima: Deak Parsons and the Creation of the Atomic Bomb[/i], and in particular, to a remarkable 1945 memorandum from Parsons to Oppenheimer, titled “Homestretch Measures”, concerning the system-level challenges of ensuring that the necessary technological elements of the atomic bomb “dovetailed in time and space.”

    Nowadays, this dovetailing in time and space is a nearly universal challenge for scientists and engineers—the Genome Project, LIGO and AdvLIGO, the LHC, and the LSST are among many contemporary examples—but back in 1945, these system-level challenges were novel, and they demanded new modes of thinking.

    Reading Rhodes’, Thorpe’s, and Christman’s separate accounts of the Manhattan Project is like watching Kurosawa’s Rashomon … which is why, arguably, all three should be required reading for physics majors.

    And Steve, best wishes for speedy progress + great fun with your teaching and research!

  5. Thank you, Steve. Thorpe also has a book Oppenheimer: the Tragic Intellect.

    I don’t have much sympathy with Thorpe’s overall view of technological history, but his work does highlight (better than Rhodes’ IMHO) a vast body of source material relating to the system engineering challenges of the Manhattan Project.

    It seems to me that seminal WWII-era mathematicians and scientists like von Neumann, Oppenheimer, Fermi, etc. ended up expending a great deal of their time and intellectual energy doing system engineering.

    This was partly forced by circumstance, but equally (IMHO) these leaders were strongly attracted to the intellectual challenge of system engineering, which in its broadest sense comprises “The design of the whole, as contrasted with the design of the parts” (Ramo).

    Nowadays the synoptic tools of system engineering are increasingly central to fields like biology, astronomy, mathematics, and quantum information science. In all of these disciplines, we are increasingly seeking to “describe the whole, as contrasted with describing the parts.”

    This is not (only) because hardware needs to be built and practical problems need to be solved, but (equally) because synoptic narratives and ethically well-grounded community norms need to be created. Modern system engineering does not shy away from regarding these challenges as a unitary whole.

  6. Michael Nielsen asks: “Might scientific problems now regarded as out of reach become accessible with more effective ways of structuring scientific attention?”

    Just to provide one answer to the above question: as simulation methods (both classical and quantum) become more efficient, and as computer power becomes cheaper, faster, and more decentralized, and as system engineering becomes more widely appreciated as a means for simultaneously creating technologies and binding together global communities, the net result is that science and engineering challenges formerly out-of-reach are becoming accessible.

    And there is no need to look far into the future for examples. Near-term global-scale scientific projects like Advanced LIGO, the Large Hadron Collider, the Large Synoptic Survey Telescope (LSST), and on a smaller scale, the increasing effectiveness of (for example) ab initio calculations of hadron masses and molecular crystal structures, all are good examples.

    The devil is in the Michael’s word “effective”. Very roughly speaking, it appears that global-scale science and engineering can potentially surpass traditional small-science and engineering in productivity as greatly as corporate farms surpass family farms.

    Yet undeniably, family farms possess virtues that corporate farms lack … virtues that “pure” markets do not respect. After all, suppose that science *could* be done more speedily by robots … or by people behaving by robots. Would we be better off?

    Michael, I don’t see how these issues can be considered without tackling issues of human morality head-on. After all, no previous generation of scientists, mathematicians, and engineers has been able to do so.

  7. Thanks Michael for this fascinating post. I’ve been thinking about this topic – especially how openness of research facilitates collaboration. I love the idea of a quantified model of scientific collaboration and perhaps i can start to add to it. In my experience the gains from collaboration are not so clear at the outset: the order of authors is usually not discussed at the outset since amount of input may be more or less than expected. So I think adding probability to this model will end up with a better representation of the choices scientists face. When collaborating we gamble that it won’t be an excessive amount of work (but even if turns out to be we are pretty much locked in), and we gamble we’ll end up with a prominent position in the list of authors ie. the amount of increase in reputation.

    It seems a straightforward extension of your model to introduce these probabilities and have Alice and Bob make decisions based on expected value, since collaboration isn’t as clear as the Ricardian model suggests (although I wish it was!).

  8. Existing academic institutions (conferences, journals, universities, funding agencies, etc.) could said to be scientific collaboration market mechanisms. Together they do play some coordinating role in bringing scientists together to solve problems like P vs NP, building a quantum computer, etc. But in asking whether we should set up new markets, I think an important question is to ask in which ways the existing structures are inefficient; i.e. which trades we do too little of, and which we do too much of.

    Not being a very efficient scientist myself, I’m not sure how to answer this question.

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