215 research outputs found

### Phase diagram of a Schelling segregation model

The collective behavior in a variant of Schelling's segregation model is
characterized with methods borrowed from statistical physics, in a context
where their relevance was not conspicuous. A measure of segregation based on
cluster geometry is defined and several quantities analogous to those used to
describe physical lattice models at equilibrium are introduced. This physical
approach allows to distinguish quantitatively several regimes and to
characterize the transitions between them, leading to the building of a phase
diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We
also establish links with 'spin-1' models in physics. Our approach provides
generic tools to analyze the dynamics of other socio-economic systems

### A model of riots dynamics: shocks, diffusion and thresholds

We introduce and analyze several variants of a system of differential
equations which model the dynamics of social outbursts, such as riots. The
systems involve the coupling of an explicit variable representing the intensity
of rioting activity and an underlying (implicit) field of social tension. Our
models include the effects of exogenous and endogenous factors as well as
various propagation mechanisms. From numerical and mathematical analysis of
these models we show that the assumptions made on how different locations
influence one another and how the tension in the system disperses play a major
role on the qualitative behavior of bursts of social unrest. Furthermore, we
analyze here various properties of these systems, such as the existence of
traveling wave solutions, and formulate some new open mathematical problems
which arise from our work

### Between order and disorder: a 'weak law' on recent electoral behavior among urban voters?

A new viewpoint on electoral involvement is proposed from the study of the
statistics of the proportions of abstentionists, blank and null, and votes
according to list of choices, in a large number of national elections in
different countries. Considering 11 countries without compulsory voting
(Austria, Canada, Czech Republic, France, Germany, Italy, Mexico, Poland,
Romania, Spain and Switzerland), a stylized fact emerges for the most populated
cities when one computes the entropy associated to the three ratios, which we
call the entropy of civic involvement of the electorate. The distribution of
this entropy (over all elections and countries) appears to be sharply peaked
near a common value. This almost common value is typically shared since the
1970's by electorates of the most populated municipalities, and this despite
the wide disparities between voting systems and types of elections. Performing
different statistical analyses, we notably show that this stylized fact reveals
particular correlations between the blank/null votes and abstentionists ratios.
We suggest that the existence of this hidden regularity, which we propose to
coin as a `weak law on recent electoral behavior among urban voters', reveals
an emerging collective behavioral norm characteristic of urban citizen voting
behavior in modern democracies. Analyzing exceptions to the rule provide
insights into the conditions under which this normative behavior can be
expected to occur.Comment: Version 1: main text 19 pages, 13 figures, 2 tables; Supporting
Information: 19 pages. Version 2: minor correction

### Interacting Agents and Continuous Opinions Dynamics

We present a model of opinion dynamics in which agents adjust continuous
opinions as a result of random binary encounters whenever their difference in
opinion is below a given threshold. High thresholds yield convergence of
opinions towards an average opinion, whereas low thresholds result in several
opinion clusters. The model is further generalised to network interactions,
threshold heterogeneity, adaptive thresholds and binary strings of opinions.Comment: 21 pages, 13 figures.
http://www.lps.ens.fr/~weisbuch/contopidyn/contopidyn.htm

### Monopoly Market with Externality: an Analysis with Statistical Physics and ACE

In this paper, we explore the effects of localised externalities introduced through interaction structures upon the properties of the simplest market model: the discrete choice model with a single homogeneous product and a single seller (the monopoly case). The resulting market is viewed as a complex interactive system with a communication network. Our main goal is to understand how generic properties of complex adaptive systems can enlighten our understanding of the market mechanisms when individual decisions are inter-related. To do so we make use of an ACE (Agent based Computational Economics) approach, and we discuss analogies between simulated market mechanisms and classical collective phenomena studied in Statistical Physics. More precisely, we consider discrete choice models where the agents are subject to local positive externality. We compare two extreme special cases, the McFadden (McF) and the Thurstone (TP) models. In the McF model the individuals' willingness to pay are heterogeneous, but remain fixed. In the TP model, all the agents have the same homogeneous part of willingness to pay plus an additive random (logistic) idiosyncratic characteristic. We show that these models are formally equivalent to models studied in the Physics literature, the McF case corresponding to a `Random Field Ising model' (RFIM) at zero temperature, and the TP case to an Ising model at finite temperature in a uniform (non random) external field. From the physicist's point of view, the McF and the TP models are thus quite different: they belong to the classes of, respectively,`quenched' and `annealed' disorder, which are known to lead to very different aggregate behaviour. This paper explores some consequences for market behaviour. Considering the optimisation of profit by the monopolist, we exhibit a new `first order phase transition': if the social influence is strong enough, there is a regime where, if the mean willingness to pay increases, or if the production costs decreases, the optimal solution for the monopolist jumps from a solution with a high price and a small number of buyers, to a solution with a low price and a large number of buyers.Agent-Based Computational Economics, discret choices, consumers externality, complex adaptive system, phase transition, avalanches, interactions, hysteresis.

### Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary
choice in a context of positive additive endogenous externalities. It
encompasses as particular cases several models from the sociology and economics
literature. We extend previous results to the case of a general distribution of
idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay
(IWP). Positive additive externalities yield a family of inverse demand curves
that include the classical downward sloping ones but also new ones with non
constant convexity. When j, the ratio of the social influence strength to the
standard deviation of the IWP distribution, is small enough, the inverse demand
is a classical monotonic (decreasing) function of the adoption rate. Even if
the IWP distribution is mono-modal, there is a critical value of j above which
the inverse demand is non monotonic, decreasing for small and high adoption
rates, but increasing within some intermediate range. Depending on the price
there are thus either one or two equilibria. Beyond this first result, we
exhibit the generic properties of the boundaries limiting the regions where the
system presents different types of equilibria (unique or multiple). These
properties are shown to depend only on qualitative features of the IWP
distribution: modality (number of maxima), smoothness and type of support
(compact or infinite). The main results are summarized as phase diagrams in the
space of the model parameters, on which the regions of multiple equilibria are
precisely delimited.Comment: 42 pages, 15 figure

### Discrete Choices under Social Influence: Generic Properties

We consider a model of socially interacting individuals that make a binary choice in a context of positive additive endogenous externalities. It encompasses as particular cases several models from the sociology and economics literature. We extend previous results to the case of a general distribution of idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay (IWP).Positive additive externalities yield a family of inverse demand curves that include the classical downward sloping ones but also new ones with non constant convexity. When $j$, the ratio of the social influene strength to the standard deviation of the IWP distribution, is small enough, the inverse demand is a classical monotonic (decreasing) function of the adoption rate. Even if the IWP distribution is mono-modal, there is a critical value of $j$ above which the inverse demand is non monotonic, decreasing for small and high adoption rates, but increasing within some intermediate range. Depending on the price there are thus either one or two equilibria.Beyond this first result, we exhibit the {\em generic} properties of the boundaries limiting the regions where the system presents different types of equilibria (unique or multiple). These properties are shown to depend {\em only} on qualitative features of the IWP distribution: modality (number of maxima), smoothness and type of support (compact or infinite).The main results are summarized as {\em phase diagrams} in the space of the model parameters, on which the regions of multiple equilibria are precisely delimited.discrete choice; social influence; externalities; heterogeneous agents; socioeconomic behavior

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