On the stability of equilibria in replicator dynamics modelling: an application in industrial dynamics considering resource constraints
Replicator dynamic modelling (rdm) is used to discuss industrial evolution problems with heterogeneous agents. However, some of the models tend to be very complex and, therefore, analytical solutions cannot be obtained. Hence, the paper proposes to start with a relatively simple model and check its stability of the equilibria before expanding the model. This strategy is more effective than relying on simulation based studies where instability cannot be ruled out ex ante. Thus, the aim of this paper is to introduce a stability check for rdm, especially, if one ore more real Eigenvalues with value zero occur. Besides the (Strogatz, 1994) and (Hilborn, 1994) local stability theorem, this method provides an alternative and more flexible procedure for stability analysis for rdm. To apply this approach, an industrial replicator dynamic model containing three differential equations is set up.
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- Dosi, Giovanni, 1993.
"Technological paradigms and technological trajectories : A suggested interpretation of the determinants and directions of technical change,"
Elsevier, vol. 22(2), pages 102-103, April.
- Dosi, Giovanni, 1982. "Technological paradigms and technological trajectories : A suggested interpretation of the determinants and directions of technical change," Research Policy, Elsevier, vol. 11(3), pages 147-162, June.
- Kamien, Morton I & Schwartz, Nancy L, 1975. "Market Structure and Innovation: A Survey," Journal of Economic Literature, American Economic Association, vol. 13(1), pages 1-37, March.
- Kraft, Kornelius, 1989. "Market Structure, Firm Characteristics and Innovative Activity," Journal of Industrial Economics, Wiley Blackwell, vol. 37(3), pages 329-336, March.
- Joïlle Noailly & Jeroen C.J.M. van den Bergh & Cees A. Withagen, 2003. "Evolution of harvesting strategies: replicator and resource dynamics," Journal of Evolutionary Economics, Springer, vol. 13(2), pages 183-200, 04.
- Joelle Noailly & Jeroen van den Bergh & Cees Withagen, 2001. "Evolution of Harvesting Strategies: Replicator and Resource Dynamics," Tinbergen Institute Discussion Papers 01-056/3, Tinbergen Institute.
- Joelle Noailly, Jeroen van den Bergh, Cees Withagen, 2001. "Evolution of Harvesting Strategies: Replicator and Resource Dynamics," Computing in Economics and Finance 2001 263, Society for Computational Economics.
- Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers 8904, University of Western Ontario, Department of Economics.
- Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
- Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers 90-12, DELTA (Ecole normale supérieure).
- Philippe Aghion & Peter Howitt, 1990. "A Model of Growth Through Creative Destruction," NBER Working Papers 3223, National Bureau of Economic Research, Inc.
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," Working papers 527, Massachusetts Institute of Technology (MIT), Department of Economics.
- Metcalfe, J S, 1994. "Competition, Fisher's Principle and Increasing Returns in the Selection Process," Journal of Evolutionary Economics, Springer, vol. 4(4), pages 327-346, November.
- Flaig, Gebhard & Stadler, Manfred, 1994. "Success Breeds Success. The Dynamics of the Innovation Process," Empirical Economics, Springer, vol. 19(1), pages 55-68.
- Flaig, Gebhard & Stadler, Manfred, 1994. "Success breeds success. The dynamics of the innovation process," Munich Reprints in Economics 20366, University of Munich, Department of Economics.
- Joëlle Noailly, 2008. "Coevolution of economic and ecological systems," Journal of Evolutionary Economics, Springer, vol. 18(1), pages 1-29, February.
- H. Scott Gordon, 1954. "The Economic Theory of a Common-Property Resource: The Fishery," Journal of Political Economy, University of Chicago Press, vol. 62, pages 124-124.
- Kenneth J. Arrow, 1962. "The Economic Implications of Learning by Doing," Review of Economic Studies, Oxford University Press, vol. 29(3), pages 155-173.
- Malerba, Franco & Orsenigo, Luigi & Peretto, Pietro, 1997. "Persistence of innovative activities, sectoral patterns of innovation and international technological specialization," International Journal of Industrial Organization, Elsevier, vol. 15(6), pages 801-826, October. Full references (including those not matched with items on IDEAS)
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