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About

About

My name is Filipe Martins. I am a Phd student of Applied Mathematics at the Department of Mathematics of the Faculty of Sciences of the University of Porto and at LIAAD-INESC. My supervisor is Professor Alberto Adrego Pinto.

My research interests are Mathematics and Applications to Biology, Economics and Social Sciences. With the goal of studying these applications I am interested in Dynamical Systems, bifurcation theory and Game theory. I also have an interest in Mathematical Finance and stochastic optimal control.

Interest
Topics
Details

Details

  • Name

    Luís Filipe Martins
  • Cluster

    Computer Science
  • Role

    Researcher
  • Since

    01st August 2013
Publications

2017

NASH AND SOCIAL WELFARE IMPACT IN AN INTERNATIONAL TRADE MODEL

Authors
Zubelli, JP; Pinto, AA; Martins, F;

Publication
JOURNAL OF DYNAMICS AND GAMES

Abstract
We study a classic international trade model consisting of a strategic game in the tariffs of the governments. The model is a two-stage game where, at the first stage, governments of each country use their welfare functions to choose their tariffs either (i) competitively (Nash equilibrium) or (ii) cooperatively (social optimum). In the second stage, firms choose competitively (Nash) their home and export quantities. We compare the competitive (Nash) tariffs with the cooperative (social) tariffs and we classify the game type according to the coincidence or not of these equilibria as a social equilibrium, a prisoner's dilemma or a lose-win dilemma.

2017

Who controls the controller? A dynamical model of corruption

Authors
Accinelli, E; Martins, F; Oviedo, J; Pinto, A; Quintas, L;

Publication
JOURNAL OF MATHEMATICAL SOCIOLOGY

Abstract
The aim of this article is to give at least a partial answer to the question made in the title. Several works analyze the evolution of the corruption in different societies. Most of such papers show the necessity of several controls displayed by a central authority to deter the expansion of the corruption. However there is not much literature that addresses the issue of who controls the controller. This article aims to approach an answer to this question. Indeed, as it is well known, in democratic societies an important role should be played by citizens. We show that politically active citizens can prevent the spread of corruption. More precisely, we introduce a game between government and officials where both can choose between a corrupt or honest behavior. Citizens have a political influence that results in the prospects of a corrupt and a non-corrupt government be re-elected or not. This results in an index of intolerance to corruption. We build an evolutionary version of the game by means of the replicator dynamics and we analyze and fully characterize the possible trajectories of the system according to the index of intolerance to corruption and other relevant quantities of the model.

2017

A bifurcation theorem for evolutionary matrix models with multiple traits

Authors
Cushing, JM; Martins, F; Pinto, AA; Veprauskas, A;

Publication
JOURNAL OF MATHEMATICAL BIOLOGY

Abstract
One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1. In this paper we consider an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. We extend the fundamental bifurcation theorem to this evolutionary model. We apply the results to an evolutionary version of a Ricker model with an added Allee component. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena, such as backward bifurcation induced strong Allee effects.