Telmo Peixe

Research Fellow

CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica
REM - Research in Economics and Mathematics
ISEG - Lisbon School of Economics & Management
Universidade de Lisboa

Rua do Quelhas 6, 1200-781 Lisboa, Portugal
Email: telmop at iseg.ulisboa.pt
Phone: (+351) 213 925 831
Office: 505, Quelhas 6 Building

I am also a Visiting Assistant Professor at Department of Mathematics, ISEG-Lisbon School of Economics & Management, Universidade de Lisboa, and member of the LxDS-Lisbon Dynamical Systems Group.

Research:

Dynamics of a dissipative polymatrix replicator.

Basins of attraction of the discrete time best-response dynamics of the rock-paper-scissors game.

Chaotic behavior in a polymatrix replicator.

Flows on Polytopes - Mathematica code

We provide here the Mathematica code we had developed to explore the dynamics of polymatrix replicators for lower dimensional polytopes.

Education:

BSc in Psychology, Universidade de Lisboa, 1999.
BSc in Mathematics, Universidade de Lisboa, 2008.
MSc in Mathematics (supervisor: Pedro Miguel Duarte), Universidade de Lisboa, 2010.
PhD in Mathematics (supervisor: Pedro Miguel Duarte), Universidade de Lisboa, 2015.

Publications:

1. Recorrências, Progressões Aritméticas e Teoria Ergódica: Teoremas de van der Warden e de Green-Tao
   (with J. Buescu)
   Revista Matemática Universitária, 48/49, 39-51, 2010.
2. Rank of stably dissipative graphs
   (with P. Duarte)
   Linear Algebra and Its Applications, 437, 2537-2586, 2012.
3. Conservative and Dissipative Polymatrix Replicators
   (with H. N. Alishah, P. Duarte)
   Journal of Dynamics and Games, 2, 157-185, 2015.
4. Asymptotic Poincaré Maps along the edges of Polytopes
   (with H. N. Alishah, P. Duarte)
   Nonlinearity, 33, 469-510, 2020.
5. Permanence in Polymatrix Replicators
   Submitted, 2019.
6. Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game
   (with J. P. Gaivão)
   Submitted, 2020.

Monographs and other works:

1. Sistemas Lotka-Volterra dissipativos (in portuguese)
   MSc thesis, University of Lisboa, 2010.
2. Lotka-Volterra systems and Polymatrix Replicators
   PhD thesis, University of Lisboa, 2015.
3. Observar Golfinhos... Com Trigonometria
   (with P. Duarte, T. Caissotti)
   Gazeta de Matemática, 169, 16-22, 2013.
4. Evaluating the effect of measurement error in pairs of 3D bearings in point transect sampling estimates of density
   (with T. A. Marques, P. Duarte, D. Moretti, L. Thomas)
   CREEM Technical Report, no.1, University of St Andrews, 2018.
5. 2017/2018 Lecture notes of Matemática I (in portuguese) for the undergraduates in Economics, in Management, and in Finance.

Communications in Conferences:

• Estabilidade e Inércia de Matrizes, national meeting of the Novos Talentos em Matemática program by Fundação Calouste Gulbenkian, Lisboa, 2007.
• The Rank of Stably Dissipative Graphs (poster), Dynamical Models in Life Sciences, University of Évora, 2011.
• Polymatrix Games and Replicators, Seventh Workshop Dynamical Systems Applied to Biology and Natural Sciences, University of Évora, 2016.
• Jogos e replicadores polimatriciais, National Meeting of the SPM - Sociedade Portuguesa de Matemática, Escola Superior de Tecnologia do Barreiro do Instituto Politécnico de Setúbal, 2016.
• From Lotka-Volterra systems to Polymatrix Replicators, 12th International ISAAC Congress, University of Aveiro, 2019.
• Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game, The Lisbon Meetings in Game Theory and Applications #11, ISEG, Universidade de Lisboa, 2019.

Seminars:

• Stable Dissipativity in the Replicator Equation, Differential Equations and Numerical Analysis Seminar, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2012.
• Polymatrix Replicators and Lotka-Volterra Systems, CMUP Seminar, Faculdade de Ciências, Universidade do Porto, 2015.
• Polymatrix Replicators and Lotka-Volterra Systems, LxDS Seminar, Faculdade de Ciências, Universidade de Lisboa, 2015.
• From Lotka-Volterra systems to Polymatrix Replicators, PhD program in Matemática Aplicada à Economia e à Gestão of ISEG, University of Lisboa, 2018.
• Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game, Dia das Equações, Center of Mathematics, Universidade do Minho, 2019.
• Open problems in fictitious play dynamics for bimatrix games, Dynamical Systems Seminar, Faculdade de Ciências, University of Lisboa, 2019.

Events organization:

• LxDS Spring School 2018, May 28-30, 2018, ISEG, University of Lisboa, Portugal.
• LxDS Spring School 2019, May 29-31, 2019, FCUL, University of Lisboa, Portugal.
• Evolutionary Game Theory session in the conference The Lisbon Meetings in Game Theory and Applications #11, November 7-9, 2019, ISEG, University of Lisboa, Portugal.
• LxDS Spring School 2020, May 27-29, 2020, ISEG, University of Lisboa, Portugal.
• New Trens in Lyapunov Exponents, July 6-10, 2020, ISEG & FCUL, University of Lisboa, Portugal.

Management:

• 2017 - 2019, Managing board of CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica, and its representative at CIM - Centro Internacional de Matemática and at CNM - Comissão Nacional de Matemática.
• 2019 - now , Managing board of CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica, and its representative at CIM - Centro Internacional de Matemática and at CNM - Comissão Nacional de Matemática.

Scholarships:

• 2006 – 2007 Novos Talentos em Matemática program by Fundação Calouste Gulbenkian.
• 2008 Scholarship by the Portugal|UT-Austin Colab to attend the “Summer School on Multiscale Modeling and Analysis” at the University of Austin-Texas.
• 2008 – 2009 Scientific initiation scholarship in Dynamical Systems by CMAF - Centro de Matemática e Aplicações Fundamentais and FCT - Fundação para a Ciência e a Tecnologia.
• 2011 – 2015 PhD scholarship SFRH/BD/72755/2010 by FCT - Fundação para a Ciência e a Tecnologia.