A note on institutional hierarchy and volatility in financial markets

Alfarano, Simone; Milaković, Mishael; Raddant, Matthias

doi:10.1080/1351847x.2011.601871

Cited by 13 publications

(13 citation statements)

References 31 publications

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“…33,37 While the effect of different network topologies on the behavior of the voter model has been well established, [38][39][40][41] the case of the noisy voter model has received much less attention, most of the corresponding literature focusing only on regular lattices 30,34 or on a fully-connected network. 33,37 Finally, the use of a mean-field approach in some recent studies considering more complex topologies [42][43][44] did not allow to find any effect of the network properties -apart from its size and mean degree-on the results of the model.…”

Section: Introductionmentioning

confidence: 93%

The noisy voter model on complex networks

Carro

Toral

Miguel

2016

Sci Rep

131

122

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We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity—variance of the underlying degree distribution—has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured.

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Section: Introductionmentioning

confidence: 93%

The noisy voter model on complex networks

Carro

Toral

Miguel

2016

Sci Rep

131

122

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“…Nevertheless, we note that the global approach, equivalent to the all-to-all approximation, completely disregards the details of the network connectivity and, as shown in the the next sections, is not capable of explaining the differences observed between different networks. The reason for the failure near the critical region of the stochastic PA combined with a vanKampen expansion lies in the ansatz stated in equations (63) and (64), which requires σ 2 [m] to scale as ∼N −1 and also to be small enough for the expansion to be accurate, which is only true in the limit a a c  (see equation (26)). This is strongly related to the associated deterministic dynamics and to the slow eigendirection v 1 having an infinite time scale as a 0  , which eventually leads to large fluctuations following this direction.…”

Section: [ ]mentioning

confidence: 99%

“…The finite-size character of the transition is due to the fact that the critical point tends to zero in the thermodynamic limit of large system sizes. Although most of the initial literature about the noisy voter model focused only on regular lattices [57,61] and a fully connected network [60,62], recent studies have addressed more complex topologies, both from an effective-field perspective [26,63,64] and using an annealed network approximation [42]. In particular, while the effective-field approach was only able to broadly capture the effect of the network size and mean degree on the results of the model for highly homogeneous and connected networks, the annealed approximation [42] was, in addition, able to reproduce the impact of the degree heterogeneity-variance of the underlying degree distribution-on the critical point of the transition and the temporal correlations with a high level of accuracy, as well as the main effects on the local order parameter, though with significantly less accuracy.…”

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confidence: 99%

Stochastic pair approximation treatment of the noisy voter model

et al. 2018

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We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and finite-size effects, as well as for the temporal evolution of all relevant variables. We test this scheme for a prototypical model of opinion dynamics known as the noisy voter model that has a finite-size critical point. Using a closure approach based on a system size expansion around a stochastic dynamical attractor we obtain very accurate results, as compared with numerical simulations, for stationary and time-dependent quantities whether below, within or above the critical region. We also show that finite-size effects in complex networks cannot be captured, as often suggested, by merely replacing the actual system size N by an effective network dependent size N eff . IntroductionFrom classical problems in statistical physics [1, 2] to questions in biology and ecology [3][4][5], and over to the spreading of opinions and diseases in social systems [6-10], stochastic binary-state models have been widely used to study the emergence of collective phenomena in systems of stochastically interacting components. In general, these components are modeled as binary-state variables -spin up or down-sitting at the nodes of a network whose links represent the possible interactions among them. While initial research focused on the limiting cases of a well-mixed population, where each of the components is allowed to interact with any other, and regular lattice structures, later works turned to more complex and heterogeneous topologies [11][12][13][14]. A most important insight derived from these more recent works is that the macroscopic dynamics of the system can be greatly affected by the particular topology of the underlying network. In the case of systems with critical behavior, different network characteristics have been shown to have a significant impact on the critical values of the model parameters [15][16][17], such as the critical temperature of the Ising model [18][19][20] and the epidemic threshold in models of infectious disease transmission [21][22][23][24][25]. Thus, the identification of the particular network characteristics that have an impact on the dynamics of these models, as well as the quantification of their effect, are of paramount importance.The first theoretical treatments introduced for the study of stochastic, binary-state dynamics on networks relied on a global-state approach [2, 26], i.e. they focused on a single variable-for example, the number of nodes in one of the two possible states-assumed to represent the whole state of the system. In order to write a master equation for this global-state variable, some approximation is required to move from the individual particle transition rates defining the model to some effective transition rates depending only on the chosen global variable. Within this global-state approach, the effective-field approximation assumes...

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“…The proposed model is built upon a two-state herding model originally proposed by Kirman in [41]. In the recent years the two-state herding model was quite frequently and rather successfully applied to reproduce the statistical patterns observed in the empirical data of the financial markets [42][43][44][45][46][47][48]. In this paper we extend the two-state herding model to allow the agents to switch between more than two states.…”

Section: Introductionmentioning

confidence: 99%

Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections

Kononovičius¹

2017

Complexity

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In this contribution we analyze a parties' vote share distribution across the polling stations during the Lithuanian parliamentary elections of 1992, 2008 and 2012. We find that the distribution is rather well fitted by the Beta distribution. To reproduce this empirical observation we propose a simple multi-state agent-based model of the voting behavior. In the proposed model agents change the party they vote for either idiosyncratically or due to a linear recruitment mechanism. We use the model to reproduce the vote share distribution observed during the election of 1992. We discuss model extensions needed to reproduce the vote share distribution observed during the other elections.

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A note on institutional hierarchy and volatility in financial markets

Cited by 13 publications

References 31 publications

The noisy voter model on complex networks

The noisy voter model on complex networks

Stochastic pair approximation treatment of the noisy voter model

Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections

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