Telmo Peixe

Assistant Professor

ISEG - Lisbon School of Economics & Management
CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica
REM - Research in Economics and Mathematics
ULisboa - 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 member of Cemapre, REM, and 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
   i (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(2), 157-185, 2015.
4. Asymptotic Poincaré Maps along the edges of Polytopes
   (with H. N. Alishah, P. Duarte)
   Nonlinearity, 33(1), 469-510, 2020.
5. Permanence in Polymatrix Replicators
   Journal of Dynamics and Games, 8(1), 21-34, 2021.
6. Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game
   (with J. P. Gaivão)
   Dynamic Games and Applications, 11(3), 491-511, 2021.
7. Persistent strange attractors in 3D Polymatrix Replicators
   (with A. A. Rodrigues)
   Physica D: Nonlinear Phenomena, 438, 2022.
8. Asymptotic Dynamics of Hamiltonian Polymatrix Replicators
   (with H. Alishah and P. Duarte)
   submitted, February, 2021.
9. On the Roots of Underdevelopment: "Wrong Equilibrium" or "Miscoordination"?
   (with J. P. Pontes)
   submitted, July, 2021.
10. Stability of heteroclinic cycles: a new approach
    (with A. A. Rodrigues)
    submitted, April, 2022.

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.
• Games and Polymatrix Replicators, National Meeting of the SPM - Sociedade Portuguesa de Matemática, Escola Superior de Tecnologia do Barreiro 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.
• Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game, GAMES 2020, The 6th World Congress of the Game Theory Society, Budapeste, 2020.
• Can Strange Attractors Occur in 3D Polymatrix Replicators?, SIAM Conference on Applications of Dynamical Systems (DS21), 2021, Virtual Conference | Originally scheduled in Portland, Oregon, U.S.
• Permanence in Polymatrix Replicators, 13th International ISAAC Congress, Ghent University, Belgium, @Zoom, 2021.

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.
• The maximum principle of Pontryagin, Dynamical Systems Seminar, ISEG, University of Lisboa, 2016.
• 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.
• Persistent strange attractors in 3D Polymatrix Replicators, Dynamical Systems Seminar, Faculdade de Ciências, University of Lisboa, 2021.

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 Trends in Lyapunov Exponents, July 6-10, 2020, ISEG & FCUL, University of Lisboa, Portugal.
• 9th One Day Meeting on Dynamical Systems, dedicated to New Trends in Lyapunov Exponents, 7th July, @Zoom, 2020.
• Heteroclinic dynamics and beyond session in the conference Encontro Nacional SPM2021, @Zoom, July 12-16, 2021 (with A. A. Rodrigues).
• LxDS mini-course on Determinantal Point Processes, FCUL, University of Lisboa, 18th-22nd October, 2021.
• LxDS workshop on New Trends in Lyapunov Exponents, February 7-11, 2022, ISEG, University of Lisboa, Portugal.
• From elliptic islands to hyperbolic waves - Celebrating Pedro Duarte's 60th birthday, August 29-30 (PUC-Rio) and September 2 (UFRJ), 2022, Rio de Janeiro, Brasil.
• LxDS Spring School 2023, May 24-26, 2023, ISEG, 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
  CNM - Comissão Nacional de Matemática.
• 2019 - 2021, Managing board of CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica, and its representative at
  CIM - Centro Internacional de Matemática and
  CNM - Comissão Nacional de Matemática.

Scholarships and awards:

• 2006/2007 - Novos Talentos em Matemática program by Fundação Calouste Gulbenkian.
• 2007/2008 - BES-FCUL award for the best ranked graduate student.
• 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.