The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.
Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution
Open accessAbstract
The paper examines the behaviour of “evolutionary” models with ɛ-noise like those which have been used recently to discuss the evolution of social conventions. The paper is built around two main observations: that the “long run stochastic stability” of a convention is related to the speed with which evolution toward and away from the convention occurs, and that evolution is more rapid (and hence more powerful) when it may proceed via a series of small steps between intermediate steady states. The formal analysis uses two new measures, the radius and modified coradius, to characterize the long run stochastically stable set of an evolutionary model and to bound the speed with which evolutionary change occurs. Though not universally powerful, the result can be used to make many previous analyses more transparent and extends them by providing results on waiting times. A number of applications are also discussed. The selection of the risk dominant equilibrium in 2 × 2 games is generalized to the selection of ½-dominant equilibria in arbitrary games. Other applications involve two-dimensional local interaction and cycles as long run stochastically stable sets.
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Citations
Cites
Kemeny, J. G., & Snell, J. L. (1976) · Medical Entomology and Zoology · Cited by 2,813
Random perturbations of dynamical systems
(1997) · Translations of Mathematical Monographs · doi:10.1090/mmono/161/03 · Cited by 2,584
Young, H. P. (1993) · Econometrica · doi:10.2307/2951778 · Cited by 2,399
A General Theory of Equilibrium Selection in GamesPreprint
Harsanyi, J. C., & Selten, R. (1988) · RePEc: Research Papers in Economics · Cited by 2,104
Learning, Mutation, and Long Run Equilibria in Games
Kandori, M., Mailath, G. J., & Rob, R. (1993) · Econometrica · doi:10.2307/2951777 · Cited by 2,044
Bush, K. A., Kemeny, J. G., & Snell, J. L. (1960) · The American Mathematical Monthly · doi:10.2307/2309264 · Cited by 1,546
The Statistical Mechanics of Strategic Interaction
Blume, L. E. (1993) · Games and Economic Behavior · doi:10.1006/game.1993.1023 · Cited by 1,402
Learning, Local Interaction, and Coordination
Ellison, G. (1993) · Econometrica · doi:10.2307/2951493 · Cited by 1,106
Self-citationStochastic evolutionary game dynamics∗
Foster, D., & Young, P. (1990) · Theoretical Population Biology · doi:10.1016/0040-5809(90)90011-j · Cited by 948
An Evolutionary Model of Bargaining
Young, H. P. (1993) · Journal of Economic Theory · doi:10.1006/jeth.1993.1009 · Cited by 374
Cited by
The Stag Hunt and the Evolution of Social Structure
Skyrms, B. (2003) · Cambridge University Press eBooks · doi:10.1017/cbo9781139165228 · Cited by 1,524
Young, H. P. (2015) · Annual Review of Economics · doi:10.1146/annurev-economics-080614-115322 · Cited by 497
Imitation processes with small mutations
Fudenberg, D., & Imhof, L. A. (2006) · Journal of Economic Theory · doi:10.1016/j.jet.2005.04.006 · Cited by 335
The emergence of consensus: a primer
Baronchelli, A. (2018) · Royal Society Open Science · doi:10.1098/rsos.172189 · Cited by 161
Metadata
- Authors
- Ellison, G.
- Venue
- Review of Economic Studies
- Publisher
- Oxford University Press (OUP)
- Published
- 2000-01
- Volume
- 67
- Issue
- 1
- Pages
- 17-45
- ISSN
- 0034-6527 (ISSN-L)
- 1467-937X
- OpenAlex
- W2095803264
- Cited by
- 406
- References
- 23
- FWCI
- 29.86
- Type
- journal article
- Language
- en
- Open access
- green
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- Ellison, G. (2000). Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution. Review of Economic Studies. https://doi.org/10.1111/1467-937x.00119
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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