Adaptive growth processes modeled by URN schemes

Artur, V. B.; Ermol’ev, Yu. M.; Kaniovskii, Yu. M.

doi:10.1007/bf01070240

Cited by 7 publications

(3 citation statements)

References 2 publications

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“…We have hinted earlier that considering all notional combinations of new technologies as a sort of "higher level" new technologies, although formally possible, does not look too attractive. An alternative method for handling inter-technological compatibilities has been introduced by Arthur et al (1987a). For the case of two (A and B) competing technologies it looks like the following.…”

Section: Urn Schemes With Multiple Additions -A Tool For Analysis Of ...mentioning

confidence: 99%

“…where (x, y)E [O, l]. Since, in general, we do not assume continuity of the functions Ji(-,•), the solutions should be defined in the appropriate sense (see Arthur et al 1987a). So far, one has been totally agnostic in the form of the functions Ji(•,•), i = I, 2,: 26 in our earlier example they depend on how buyers and sellers adjust their behaviors in the course of their interactions and, thus, on the fitness functions of the populations, qi(•,•), i = I, 2, but several other processes come easily to mind.…”

Section: T + T + Smentioning

confidence: 99%

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On "Badly Behaved" Dynamics: Some Applications of Generalized urn Schemes to Technological and Economic Change

Dosi,

Kaniovski

2000

Innovation, Organization and Economic Dynamics

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Section: Urn Schemes With Multiple Additions -A Tool For Analysis Of ...mentioning

confidence: 99%

Section: T + T + Smentioning

confidence: 99%

On "Badly Behaved" Dynamics: Some Applications of Generalized urn Schemes to Technological and Economic Change

Dosi,

Kaniovski

2000

Innovation, Organization and Economic Dynamics

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“…In particular, agents never change their action, but the distribution of actions can change because the action of each new agent is the outcome of a random variable. This is an example of a generalized urn model (Arthur, Ermoliev, and Kaniovski, 1987;).…”

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confidence: 99%

Stochastic Adaptive Dynamics

Young¹

2008

The New Palgrave Dictionary of Economics

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Stochastic adaptive dynamics require analytical methods and solution concepts that differ in important ways from those used to study deterministic processes. Consider, for example, the notion of asymptotic stability: in a deterministic dynamical system, a state is locally asymptotically stable if all sufficiently small deviations from the original state are self-correcting. We can think of this as a first step toward analyzing the effect of stochastic shocks, namely, a state is locally asymptotically stable if, after the impact of a onetime, small stochastic shock, the process evolves back to its original state. This idea is not very satisfactory, however, because it treats shocks as if they were isolated events. Economic systems are typically composed of large numbers of interacting agents who are constantly being jostled about by perturbations from a variety of sources. Persistent shocks have substantially different effects than do one-time shocks; in particular, persistent shocks can accumulate and tip the process out of the basin of attraction of an asymptotically stable state. Thus, in a stochastic setting, conventional notions of dynamic stability-including evolutionarily stable strategiesare often inadequate to characterize the long-run behavior of the process. Here we shall outline an alternative approach that is based on the theory of large deviations in Markov processes (Freidlin and Wentzell, 1984; Foster and Young, 1990; Young, 1993a).

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