<figure><img src="image_1.png" /></figure>

HAL
open science

# Un dialogue interdisciplinaire, de Porquerolles au 54 bd Raspail.

## Annick Vignes

<figure><img src="image_2.png" /></figure>

### ► To cite this version:

Annick Vignes. Un dialogue interdisciplinaire, de Porquerolles au 54 bd Raspail. From Physics to neuroscience and social sciences: a conference in honour of Jean-Pierre Nadal, Annick Vignes (INRAE) et Vincent Hakim (ENS ULM), Mar 2024, Paris (Ecole normale supérieure), France. hal-05310538

HAL Id: hal-05310538

https://hal.inrae.fr/hal-05310538v1

Submitted on 12 Oct 2025

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_3.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Un dialogue interdisciplinaire, de Porquerolles au 54 bd Raspail.

Annick Vignes

Economiste, Directrice de recherche INRAE

Professeure Ecole des Ponts

<figure><img src="image_4.png" /></figure>
2001: Ecole d'économie cognitive.

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

* Econophysics (G. Weisbuch, M. Gordon, JP Nadal...)

* Power law

* Dynamic systems theory

* Multi-scale analysis

* Applications of statistical physics to economy

* Collective intelligence to animal societies

> « L'économie cognitive est née de la jonction de deux programmes de recherches, un programme épistémique, issu d'une critique de la rationalité substantive de l'acteur, et un programme évolutionniste, issu d'une critique de la notion statique d'équilibre. » (B. Walliser)
<figure><img src="image_8.png" /></figure>
# ANR Dyxi(2008): hétérogénéités spatiales et individuelles.

* Nuit blanche, interdisciplinarité et chocolat.

* Des physiciens, des sociologues, des économistes...

* Rupture avec le paradigme économique fondé sur individu représentatif, rationnel et maximisateur.

* Construction d'un langage commun à plusieurs disciplines
  « *au commencement était le verbe* »?

<figure><img src="image_9.png" /></figure>
Des logements, des riches et des pauvres...

* Gauvin, L., Vignes, A., & Nadal, J. P. (2013). Modeling urban housing market dynamics: can the socio-spatial segregation preserve some social diversity? *Journal of Economic Dynamics and Control*

* Pangallo, M., Nadal, J. P., & Vignes, A. (2019). Residential income segregation: A behavioral model of the housing market. *Journal of Economic Behavior & Organization*

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>
# What interdisciplinarity has made possible (1)

* Integrating economic agents et approche à la Schelling

* Analysing price formation of housing and not square meters (heterogeneity)

* Considering the distribution of prices in a city as a proxy of wealth.

* Modelling agents behaviour through three different states

* Integrating a dynamic social attractivity to individual preferences (going further the the classic amenities effect in urban economics)
What interdisciplinarity has made possible (2)

Showing that, with imperfect information, even when parameters vary, there always persists a zone of social diversity.

With perfect information (auction mechanism), we can get total segregation, when the income distribution is unequal enough.

Public policies implications: taxes or subsidies?
# What is a result? What is an important result?

## A.1. Proof of the Proposition, Section 4.2.3

We give here the proof by recurrence on $k$.

**Proof: case** $k \ge \bar{k}$.

At equilibrium, $u_k^*(X) = \frac{v_k^*(X)}{\alpha} = \frac{\nu_k^*(X)}{\alpha}$ which gives:

$$u_k^*(X) = \frac{\gamma}{K\alpha} \frac{A_k^*(X)}{(1/L^2) Z_k} \quad (A-1)$$

with

$$Z_k = \sum_{X \in \Omega} A_k^*(X) \quad (A-2)$$

From the fixed point equations, we get, for any $k \in \{0, ..., K-1\}$,

$$Z_k = Z^0 + \frac{\epsilon}{\omega} \sum_{X \in \Omega} \sum_{k' \ge k} v_{k'}(X) = Z^0 + L^2 \frac{\epsilon \gamma}{\omega K} (K-k) \quad (A-3)$$

In particular, for the housed ($K-1$)-agents (highest WTP):

$$u_{K-1}^*(X) = \frac{\gamma}{K\alpha} \frac{A^0(X) + \frac{\alpha}{\omega} u_{K-1}^*(X)}{(1/L^2)Z^0 + \frac{\epsilon}{\omega K}} \quad (A-4)$$

Solving this equation leads to:

$$u_{K-1}^*(X) = \frac{\gamma}{K\alpha} \frac{A^0(X)}{(1/L^2)Z^0} \quad (A-5)$$

Now assume that (30) is true for $k+1 \le k' \le K-1$ with $k \ge k$. Then we

> "Finally, we prove that segregation is due to the emergence of income thresholds which divide the space between richer and poorer people. This endogenous threshold varies following the dynamic attractiveness of the rich location. This result could have important economic implications for the regulation of the housing market. For example, a policy aiming to boost demand (by subsidizing the poorer potential buyers) without constraining the supply side would lead to an increase in the distribution of sellers' prices and thus exacerbate the segregation."

What physicists like.
<figure><img src="image_13.png" /></figure>

Several pioneers in the room (P. Bourgine, JP Nadal, G. Weisbuch....)

Prix de thèse systèmes complexes (José Moran)

Emergence of an interdisciplinary network of researchers working on complex systems

........

<figure><img src="image_14.png" /></figure>
* Au comité d'organisation

* Au laboratoire de physique de l'ENS (Vincent Hakim)

* Au CAMS-EHESS (Camille Roth, Laurent Bonnasse-Gahot, Nathalie Brusseaux, Sandrine Nadal)

* A l'ISC-PIF (David Chavalarias, Francesca Barbieri, Anne-Laure Thomas-Derepas)

<figure><img src="image_15.png" /></figure>

A Jean-Pierre!