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Dynamic Games and Applications
Erschienen in: Dynamic Games and Applications 3/2021

19.10.2020 | Original Article

Stochastic Value Formation

verfasst von: Jiabin Wu

Erschienen in: Dynamic Games and Applications | Ausgabe 3/2021

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Abstract

We propose a simple model of value formation in two societies (communities). When forming values, individuals face conformity pressure within their own society and they are intolerant toward the other society. When such a value formation process is noisy, the interaction between conformity, intolerance and noise can give rise to interesting dynamic outcomes including two polarized societies and polarization across the two societies.
Vorheriger Artikel Dynamic Coordination Games with Activation Costs
Nächster Artikel Structural Heterogeneity and Evolutionary Dynamics on Complex Networks

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Fußnoten
1
We assume that the value space is a closed interval on the real line, which is a common assumption made in the economics literature to study preferences, values, beliefs over a single-dimensional issue. See, for example, Michaeli and Spiro [45, 46] and Cheung and Wu [27].
 
2
We use quadratic function because it is commonly adopted in the studies of social norms for tractability. See, for example, Manski and Mayshar [44] and Kuran and Sandholm [40]. Nevertheless, it is the convexity of the intolerance function that leads to our main results.
 
3
When we check if a certain state is steady or stable, we drop the time subscript and use \(E_i, E_j\).
 
4
The derivation is provided in Anderson et al. [2].
 
5
The Fokker–Planck equation is not yet widely used in the economic analysis. See Binmore et al. [10], Friedman and Yellin [30] and Anderson et al. [2, 3] for applications of the Fokker–Planck equation in game theory; and Benhabib et al. [7] for an application of the Fokker–Planck equation to the study of income distributions.
 
6
An alternative choice is the strong topology induced by the variation norm. See Bomze [18, 19] and Oechssler and Riedel [47, 48]. The strong topology is more restrictive than the weak topology in the sense that it only allows perturbations from a small fraction of individuals changing their values.
 
7
We discretize both the set of values [0,1] (with grid size being 0.0001) and time to make the simulation work. By discretizing time, we use a normal distribution with mean 0 to approximate the noise. In addition, to ensure the dynamic stays in [0, 1], we impose boundary conditions to revert the dynamic back in range every time it escapes. Hence, in the plot we show, a very small portion of the graph is situated outside of [0,1]. The program is available upon request.
 
8
The results remain the same if we instead run 100,000 periods.
 
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Metadaten
Titel
Stochastic Value Formation
verfasst von
Jiabin Wu
Publikationsdatum
19.10.2020
Verlag
Springer US
Erschienen in
Dynamic Games and Applications / Ausgabe 3/2021
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-020-00370-z

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