An Emerging Small World

This paper examines the small world hypothesis. The first part of the paper presents empirical evidence on the evolution of a particular world: the world of journal publishing economists during the period 1970-2000. We find that in the 1970’s the world of economics was a collection of islands, with the largest island having about 15% of the population. Two decades later, in the 1990’s the world of economics was much more integrated, with the largest island covering close to half the population. At the same time, the distance between individuals on the largest island had fallen significantly. Thus we believe that economics is an an emerging small world. What is it about the network structure that makes the world small? An exploration of the micro aspects of the network yields three findings: one, the average number of co-authors is very small but increasing; two, the distribution of co-authors is very unequal; and three, there exist a number of ‘stars’, individuals who have a large number of co-authors (25 times the average number) most of whom do not write with each other. Thus the economics world is a set of inter-connected stars. We take the view that individuals decide on whether to work alone or with others; this means that individual incentives should help us understand why the economics world has the structure it does. The second part of the paper develops a simple theoretical model of co-authorship. The main finding of the model is that in the presence of productivity differentials and a shortage of high productivity individuals, inter-connected stars will arise naturally in equilibrium. Falling costs of communication and increasing credit for joint research leads to greater co-authorship and this is consistent with the growth in the size of the giant component. ∗University of Essex and Tinbergen Institute. E-mail: sgoyal@essex.ac.uk †Tinbergen Institute Rotterdam. E-mail: mvanderleij@few.eur.nl ‡Erasmus University Rotterdam, Tinbergen Institute and CESifo. E-mail: moraga@few.eur.nl This paper has been presented at Amsterdam, Essex, Marseille, UCL, SAET 2003 and the VI Summer School of San Sebastian. We thank Venkataraman Bhaskar, Ken Burdett, Alberto Bisin, Francis Bloch, Alessandra Casella, Andrea Galeotti, Christian Ghiglino, Guillaume Haeringer, Alan Kirman, Otto Swank and participants at these presentations for useful comments.

[1]  Béla Bollobás,et al.  Random Graphs , 1985 .

[2]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[3]  E. Glaeser,et al.  Crime and Social Interactions , 1995 .

[4]  Sanjeev Goyal,et al.  A Noncooperative Model of Network Formation , 2000 .

[5]  John Hudson,et al.  Trends in Multi-authored Papers in Economics , 1996 .

[6]  S. Goyal.  Learning in Networks , 2002 .

[7]  Manfred Kochen,et al.  Small World , 2002 .

[8]  M. Jackson.  A Survey of Models of Network Formation: Stability and Efficiency , 2003 .

[9]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[10]  M. Kochen,et al.  Contacts and influence , 1978 .

[11]  A. Nouweland.  Group Formation in Economics: Models of Network Formation in Cooperative Games , 2005 .

[12]  R. Burt.  The Social Structure of Competition , 2004 .

[13]  Tools or Toys? the Impact of High Technology on Scholarly Productivity , 1998 .

[14]  A. Shaked,et al.  Altruists, Egoists and Hooligans in a Local Interaction Model , 1996 .

[15]  M. Mobius,et al.  Getting Closer or Drifting Apart , 2004 .

[16]  M. Jackson,et al.  A Strategic Model of Social and Economic Networks , 1996 .

[17]  Glenn Ellison,et al.  Rules of Thumb for Social Learning , 1993, Journal of Political Economy.

[18]  Frances Cairncross.  The death of distance : how the communications revolution will change our lives , 1997 .

[19]  M. Newman.  Coauthorship networks and patterns of scientific collaboration , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[21]  Jie Wu,et al.  Small Worlds: The Dynamics of Networks between Order and Randomness , 2003 .

[22]  M. Mcluhan.  Understanding Media: The Extensions of Man , 1964 .

[23]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[26]  S. Goyal,et al.  Learning from neighbours , 1998 .

[27]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[28]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[29]  J. McDowell,et al.  The Determinants of Co-Authorship: An Analysis of the Economics Literature , 1983 .

[30]  S. Goyal,et al.  Economics: An Emerging Small World , 2004, Journal of Political Economy.

[31]  Sanjeev Goyal,et al.  Learning in Networks: a survey , 2003 .

[32]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  S. Goyal,et al.  Conformism and diversity under social learning , 2001 .