Information, The invisible Hand and Google Michael Rothschild Princeton University In 1900 (David Hilbert, 1902) addressed the International Congress of Mathematicians on Mathematical Problems. He discussed the importance of problems for the development of mathematics and described 23 unsolved problems from all branches of mathematics. The search for solutions of these problems inspired much of 20 th century mathematics. In summer 2003 the 24 panelists for this conference received an e-mail asking them to describe problems whose solution would motivate the economists of the 21 st century. I suspect few mathematicians will subscribe to the equation (1) 24 economists = 1 Hilbert or even (2) Joe Stiglitz + 24 other economists = 1 Hilbert -- but it is a nice thought. Before getting down to the serious work of setting problems Hilbert observed: In dealing with mathematical problems, specialization plays, as I believe, a still more important part than generalization. Perhaps in most cases where we seek in vain the answer to a question, the cause of the failure lies in the fact that problems simpler and easier than the one in hand have been either not at all or incompletely solved. All depends, then, on finding out these easier problems, and on solving them by means of devices as perfect as possible and of concepts capable of generalization. This rule is one of the most important levers for overcoming mathematical difficulties and it seems to me that it is used almost always, though perhaps unconsciously This is an excellent statement of the MIT approach to economic theory which runs through Joe s best work. 1 12/09/03
Since Hilbert set forth 23 problems, the implication of equations (1) or (2) is that my brief is to set at most one problem. Does the decline in costs of finding and processing information lead to the occasional reappearance of the invisible hand? I searched Google for Stiglitz on Sept 3rd and found roughly 211,000 references. The first is appropriately to Joe s home page. Curious about the last, I began scrolling through the references. Mindful of (Robert M. Solow, 1970) s advice about difficult and unglamorous work 1, I considered getting a research assistant. However, Google soon informed me that: In order to show you the most relevant results, we have omitted some entries very similar to the 828 already displayed. Most of the references were to Joe s work but the 828th reference was to CNdb: Hugo Stiglitz... Nude Male Celebs. When I googled economics imperfect information I found about 206,000 references, (817 without duplicates). While not a perfect guide, (Stiglitz is not explicitly mentioned until page 2) it is pretty good; most references are to an excellent book, The Economics Of Imperfect Information (Louis Phlips, 1988); references abound to key papers, including several by Joe, that show that markets in which information is not freely available to all do not work very well. One could consider this a paradox. Google is a very efficient way for the uninformed to find out about how the world doesn t work very well for the uninformed. The paradox is overstated although it does remind me that when we worked together Joe or I would often proclaim that an example we had just worked out was a stake 1 But it may be what God made graduate students for. Presumably he had something in mind. 2 12/09/03
through the heart of capitalism, a demonstration that socialism cannot work or, very rarely, an illustration of the beauty of the market 2. The paradox is overstated because Google is far from perfect for the unsophisticated. A search for economics information produces a grab bag of results, the most prominent of which are about data or the new information economy. Google requires a fast internet connection not available to all in a world where close to a quarter of all people live on less than $1 a day.. Google is still a wonder. Google and the internet are prime examples of decreasing costs (close to zero marginal cost) and network externalities that are textbook causes of market failure and the need for centralization. In this environment Google does what economists have claimed prices do; it aggregates information in a decentralized manner; grist for its (cheap) mill is the data provided by people going about their business with no interest in producing the information that Google spits out. Let s consider first what Google does and how it works and then ask what the implications are for the economics of imperfect information. The Google algorithm (Sergey Brin and Lawrence Page, 1999, Lawrence Page and Sergey Brin, 1998) will be familiar to all economists. Suppose we have a set of web pages. Let (3) W ij=the number of times page i links to (cites) page j and let (4) w ij W ij = W j ij Then w= w is a Markov matrix which for simplicity we assume is irreducible (every ij page eventually cites every other page.) w has a unique positive eigen vector p. When 2 Sometime recalculation changed a sign and the nature of the universe. 3 12/09/03
normalized so that p i = 1, then p i is just the ergodic probability that page i will be linked or cited. When you search Google for Stiglitz you get the web pages that contain the text Stiglitz ordered by the size of their p i coefficient. The first is, appropriately, Joe s home page. (Ignacio Palacios-Huertay and Oscar Volijz, 2003) have observed that the Google algorithm is, the unique index of intellectual influence satisfying a set of apparently reasonable axioms. Google is much more than the ergodic theorem (M. Golubitsky et al., 1975) 3. Since the number of web pages is large (the source of Google s name), storing the text of all web pages is not trivial; nor is constantly calculating the appropriate eigen value of w. The most important problem is defeating those who wish to cheat Google by artificially inflating their probability of being linked. (Some years ago five graduates students in economics sent out an e-mail to five other graduate student; the email consisted of their own names and a request that that recipients cite the papers of these students in their next paper, remove the name at the top of the list, append their own name to the list of names and forward the changed email to four other graduate students.) Colleagues in computer science tell me that a secret and escalating war continues in which web pages try to inflate their Google ranking and Google tries to prevent them from doing so. The invisible hand argument is that it may be in people s self interest to create web pages whose links are informative; this makes the web page more useful and more likely to be read and cited/linked. Google performs the aggregation. It is of course true that Google has competitors and that Google must make money. Still decreases in costs of acquiring and processing information make Google cheap to operate and Google 3 A tribute to Joe would be incomplete with out a citation to one of the authors (unjustly) obscure papers. 4 12/09/03
does for Web pages what (Friedrich A. von Hayek, 1932) rather vaguely claimed markets and prices did for commodities 4. A question for economic theory is whether or not this is rare and anomalous or whether changes in information technology can lead to a new economic paradigm of the economics of information. Much of the argument to date has centered on two questions: 1. The viability of open software. Economists, in particular, (J. Lerner and J. Tirole, 2002) argue that standard economic arguments about incentives and rewards can explain phenomena like Linux. Others (see in particular(y. Benkler, 2002)) argue that open software is akin to the scientific enterprise in which many scientists continually add to our understanding of the way in which the world works. In physics, say, knowledge advances at an uneven pace. Some people make large contributions, some small. Science advances without, or despite, a formal hierarchy. Those who contribute to science are human beings with interests and motives but they are more complex than, at least the caricature of, homo economicus. 2. What resources are or should be free? In the debate about Napster this takes the form of arguing about whether anyone should pay fixed costs for a good whose marginal cost is zero. This is an old argument to economists. In this sense one way of framing this question may be in part whether or not changes in information technology makes more of commerce like physics or more like the bourse. 4 An apocryphal story is that one of the motivations for developing Google was to help computer scientists convince academic administrators that those who had not published in journals or books had had an extraordinary impact on the profession. The first description of the Google algorithm that I could find was a submission to a 1998 conference Page and Brin (1998) 5 12/09/03
3. My fellow panelist and colleague, Avinash Dixit, pointed out to me that decreasing the cost of information processing will not eliminate the information asymmetries that Joe has studied with such skill and originality. Those concerned with privacy rights note with some foreboding that decreases in costs of finding information may drastically change who is likely to know more about whom. References Benkler, Y. "Coase's Penguin, or, Linux and the Nature of the Firm." Yale Law Journal, 2002, 112(3), pp. 369-+. Brin, Sergey and Page, Lawrence. "The Anatomy of a Large-Scale Hypertextual Web Search Engine," 1999. Golubitsky, M.; Keeler, E. B. and Rothschild, M. "Convergence of Age Structure - Applications of Projective Metric." Theoretical Population Biology, 1975, 7(1), pp. 84-93. Hayek, Friedrich A. von. Prices and Production. New York,: Macmillan, 1932. Hilbert, David. "Mathematical Problems Lecture Delivered before the International Congress of Mathematicians at Paris in 1900." Bulletin of the American Mathematical Society, 1902, 8, pp. 437-79. Lerner, J. and Tirole, J. "Some Simple Economics of Open Source." Journal of Industrial Economics, 2002, 50(2), pp. 197-234. Page, Lawrence and Brin, Sergey. "Pagerank, an Eigenvector Based Ranking Approach for Hypertext.," 21st Annual ACM/SIGIR International Conference on Research and Development in Information Retrieval. Melbourne, 1998. Palacios-Huertay, Ignacio and Volijz, Oscar. "The Measurement of Intellectual Influence," 2003. Phlips, Louis. The Economics of Imperfect Information. Cambridge Cambridgeshire ; New York: Cambridge University Press, 1988. Solow, Robert M. Growth Theory: An Exposition. Oxford,: Clarendon, 1970. 6 12/09/03