FIXED POINTS IN MULTIPLE EQUILIBRIA PROBABILITY-MIGRATION MODELS

Manuel Philippe Emile Garcon (1) , Josselin Garnier (2) , Abdennebi Omrane (3)

1 CRREF - Centre de recherches et de ressources en éducation et formation [UR6_3]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 UMR 228 Espace-Dev, Espace pour le développement

We analyze a probability-migration model in which the probability of migration depends on human capital (education essentially). In this model, the human capital can converge to two possible values (fixed points), a low or high value. The aim of this paper is to analyze how belief mechanisms can lead to the selection of a particular fixed point. In particular, we prove that for any belief mechanism, there exists a critical value H such that the result can always be expressed by an assertion of the form: if initially, the human capital is smaller than the critical value H, then the human capital will converge to the low fixed point, while if the initial human capital is larger than H, then the human capital will converge to the high fixed point value. The fixed points do not depend on the belief mechanism, while the critical value strongly depends on it.

Domaines: Mathématiques [math]; Education; Méthodes et statistiques

Manuel Philippe Emile Garcon, Josselin Garnier, Abdennebi Omrane. FIXED POINTS IN MULTIPLE EQUILIBRIA PROBABILITY-MIGRATION MODELS. Serdica Mathematical Journal, 2015, 41, pp.263 - 276. ⟨hal-02504289⟩