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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

    Assistant Researcher
  • Since

    01st August 2013
002
Publications

2019

Evolutionary Game Theory: A Generalization of the ESS Definition

Authors
Accinelli, E; Martins, F; Oviedo, J;

Publication
International Game Theory Review

Abstract
In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with n = 3 players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with n = 3 players. We show that unlike the case of n = 2, when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment. © 2019 World Scientific Publishing Company.

2019

A fit of CD4+ T cell immune response to an infection by lymphocytic choriomeningitis virus

Authors
Afsar, A; 1 Departamento de Matemática, Faculdade de Ciências da Universidade do Porto and LIAAD-INESC. Rua do Campo Alegre, 687, 4169-007 Porto, Portugal,; Martins, F; M. P. M. Oliveira, B; A. Pinto, A; 2 Faculdade de Ciências da Nutrição e Alimentação da Universidade do Porto, and LIAAD-INESC. Rua Dr. Roberto Frias, 4200-465 Porto, Portugal,;

Publication
Mathematical Biosciences and Engineering

Abstract
We fit an immune response model to data reporting the CD4+ T cell numbers from the 28 days following the infection of mice with lymphocytic choriomeningitis virus LCMV.We used an ODE model that was previously used to describe qualitatively the behaviour of CD4+ T cells, regulatory T cells (Tregs) and interleukine-2 (IL-2) density. The model considered two clonotypes of T cells in order to fit simultaneously the two time series for the gp61 and NP309 epitopes. We observed the proliferation of T cells and, to a lower extent, Tregs during the immune activation phase following infection and subsequently, during the contraction phase, a smooth transition from faster to slower death rates. The six parameters that were optimized were: the beginning and ending times of the immune response, the growth rate of T cells, their capacity, and the two related with the homeostatic numbers of T cells that respond to each epitope. We showed that the ODE model was able to be calibrated thus providing a quantitative description of the data. © 2019 the Author(s).

2019

Evolutionary dynamics for the generalized Baliga–Maskin public good model

Authors
Accinelli, E; Martins, F; Pinto, AA;

Publication
Chaos, Solitons and Fractals

Abstract
The problem of the consumption or provision of common and public goods is a well known and well studied problem in economic sciences. The nature of the problem is the existence of non-excludable externalities which gives rise to incentives to free-riding behaviour. There are several economical frameworks trying to deal with the problem such as coalition theory or mechanism design and implementation theory to ensure a Pareto efficient consumption or provision of such good. Baliga and Maskin considered an environmental game where several communities face a problem of pollution reduction. They show that all communities except one of them have incentives to act as a free-rider, i.e. only one community is willing to face the costs that air cleaning implies, namely the one with greatest preference for the good. In this work we introduce an adaptive evolutionary dynamics for the generalization of the Baliga–Maskin model to quasi-linear utility functions. We show that the Baliga–Maskin equilibrium is the only asymptotically stable dynamical equilibrium, all others being unstable. This result reasserts the problem of free-riding and externalities for the case of a common good in a dynamically/evolutionary setting, and reiterates the relevance of mechanism design and coalition formation in the context of dynamical models. © 2019

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.