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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

    External Research Collaborator
  • Since

    01st August 2013
002
Publications

2022

The power of voting and corruption cycles

Authors
Accinelli, E; Martins, F; Pinto, AA; Afsar, A; Oliveira, BMPM;

Publication
JOURNAL OF MATHEMATICAL SOCIOLOGY

Abstract

2022

The basins of attraction in the generalized Baliga-Maskin public good model

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

Publication
JOURNAL OF EVOLUTIONARY ECONOMICS

Abstract
We study an evolutionary dynamics for the contributions by agents to a common/public good in a generalized version of Baliga and Maskin's environmental protection model. The dynamical equilibria consist of three scenarios: a single agent contributing to preserve the good with its optimal contribution level, and all the other agents being free-riders: a group of agents with the same optimal contribution level contributing to preserve the good, and all the other agents being free-riders; one where no agents contribute. The dynamics of the contributions can be complex but we prove that each trajectory converges to the equilibrium associated to the single agent (or group of agents) with the highest preference for the good that are contributing since the beginning. We note that while the aggregate contribution is below the optimal contribution level of the agent with the smallest preference for the good, then the aggregate contribution is increasing and there is no free-riding. Hence, if the optimal contribution level of the agent with the smallest preference is enough to not exhaust the good too quickly and the optimal contribution level of the agent with the greatest preference is enough to preserve the good, then, in spite of the appearance of free-riding in the contributions, the good might not be exhausted.

2021

Firms, technology, training and government fiscal policies: An evolutionary approach

Authors
Accinelli, E; Martins, F; Muniz, H; Oliveira, BMPM; Pinto, AA;

Publication
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Abstract
<p style='text-indent:20px;'>In this paper we propose and analyze a game theoretical model regarding the dynamical interaction between government fiscal policy choices toward innovation and training (I&amp;T), firm's innovation, and worker's levels of training and education. We discuss four economic scenarios corresponding to strict pure Nash equilibria: the government and I&amp;T poverty trap, the I&amp;T poverty trap, the I&amp;T high premium niche, and the I&amp;T ideal growth. The main novelty of this model is to consider the government as one of the three interacting players in the game that also allow us to analyse the I&amp;T mixed economic scenarios with a unique strictly mixed Nash equilibrium and with I&amp;T evolutionary dynamical cycles.</p>

2021

Immune Response Model Fitting to CD4$$^+$$ T Cell Data in Lymphocytic Choriomeningitis Virus LCMV infection

Authors
Afsar, A; Martins, F; Oliveira, BMPM; Pinto, AA;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract

2020

Evolutionary dynamics for the generalized Baliga–Maskin public good model

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

Publication
CHAOS SOLITONS & 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