Spillover effects and the evolution of firm clusters

Abstract In this paper we consider the impact of spillovers occurring within each of two groups of firms on the long run agglomeration patterns in a market. In each period every single firm can either produce for this market or choose some outside option (e.g. a risky asset). Firms switch between the two options based on information about the relative profitability of the market and the outside option. In the market, due to spillovers, the production costs are influenced by the number of firms from the same population which are in the market. The resulting model describes the evolution of the size of the two firm clusters and their market shares over time. We provide a global analysis of the existence and basins of attraction of equilibria to address the question what impact different constellations of spillover effects have on the growth of dominant respectively incoming clusters. We demonstrate that the basins of attraction of coexisting long run equilibria do not depend continuously on the size of the spillover effects. Furthermore, an increase in the initial cluster size is not necessarily beneficial if the switching behavior of firms is fast.

[1]  Herbert Dawid,et al.  On the convergence of genetic learning in a double auction market , 1999 .

[2]  Glenn Ellison,et al.  Word-of-Mouth Communication and Social Learning , 1995 .

[3]  R. McAfee,et al.  The Evolutionary Stability of Auctions over Bargaining , 1996 .

[4]  Charles Stuart,et al.  Are Cournot and Bertrand equilibria evolutionary stable strategies? , 1997 .

[5]  Yih‐chyi Chuang,et al.  Foreign direct investment, R&D and spillover efficiency: Evidence from Taiwan's manufacturing firms , 1999 .

[6]  Edward L. Glaeser,et al.  Geographic Concentration in U.S. Manufacturing Industries: A Dartboard Approach , 1994, Journal of Political Economy.

[7]  E. Carlisle.  Spillover Asymmetries and a Comparative Technological Advantage , 1992 .

[8]  Herbert Dawid.  On the dynamics of word of mouth learningwith and without anticipations , 1999, Ann. Oper. Res..

[9]  M. Spence,et al.  Learning Curve Spillovers and Market Performance , 1985 .

[10]  D. Friedman.  EVOLUTIONARY GAMES IN ECONOMICS , 1991 .

[11]  E. Mansfield.  The speed and cost of industrial innovation in Japan and the United States: external vs. internal technology , 1988 .

[12]  H. Peyton Young,et al.  Individual Strategy and Social Structure , 2020 .

[13]  H. Lorenz.  Nonlinear Dynamical Economics and Chaotic Motion , 1989 .

[14]  Tore Ellingsen,et al.  The Evolution of Bargaining Behavior , 1997 .

[15]  Laura Gardini,et al.  Analysis of global bifurcations in a market share attraction model , 2000 .

[16]  D. Friedman.  On economic applications of evolutionary game theory , 1998 .

[17]  E. Muller,et al.  Research Joint Ventures and R&D Cartels , 1992 .

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

[19]  M. Feldman,et al.  R&D spillovers and the ge-ography of innovation and production , 1996 .

[20]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[21]  Fernando Vega Redondo,et al.  The evolution of walrasian behavior , 1996 .

[22]  D. Friedman,et al.  International trade and the internal organization of firms: An evolutionary approach , 1996 .

[23]  Gian Italo Bischi,et al.  Equilibrium selection in a nonlinear duopoly game with adaptive expectations , 2001 .

[24]  Glenn Ellison.  Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution , 2000 .

[25]  H. Young.  An Evolutionary Model of Bargaining , 1993 .

[26]  Christian Mira,et al.  Chaotic Dynamics in Two-Dimensional Noninvertible Maps , 1996 .

[27]  J. Enns,et al.  What competition? , 2002, Trends in Cognitive Sciences.

[28]  R. Bénabou.  Workings of a City: Location, Education, and Production , 1991 .