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December 2021
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November 29, 2021 November 30, 2021 December 1, 2021 December 2, 2021

Category: SeminarsPolaris-tt: Chen Yan

Polaris-tt: Chen Yan
December 3, 2021 December 4, 2021 December 5, 2021
December 6, 2021 December 7, 2021 December 8, 2021 December 9, 2021

Category: SeminarsPolaris-tt: Till Kletti (Introducing the expohedron for fair and useful rankings)

Polaris-tt: Till Kletti (Introducing the expohedron for fair and useful rankings)
December 10, 2021 December 11, 2021 December 12, 2021
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  • November 25, 2021 @ -- Seminar Fryderyk Falniowski: Chaotic behavior in congestion games

    Abstract:
    Recently long-term behavior of the discrete counterpart of replicator dynamics - Multiplicative Weights Update (MWU) and its natural generalization - Follow the Regularized Leader (FTRL) were thoroughly studied. It turned out that in many game theoretic contexts the dynamics introduced by these algorithms can become very complex and hard to predict.
    In this talk I will describe how chaotic behavior of agents may emerge in a simple congestion game where agents use one of these algorithms. To test the robustness of chaos I will introduce discounting of the past by agents. This results in a dynamics closely related to penalty-regulated dynamics [1] and EWA dynamics [2,3]. I will discuss how interplay between discounting the past and characteristics of the game (costs of different paths) affects chaotic behavior.

    [1] P. Coucheney, B. Gaujal, P. Mertikopoulos. "Penalty-regulated dynamics and robust learning procedures in games." Mathematics of Operations Research 40.3 (2015): 611-633.
    [2] T. Galla, J. D. Farmer. "Complex dynamics in learning complicated games." Proceedings of the National Academy of Sciences 110.4 (2013): 1232-1236.
    [3] M. Pangallo, T. Heinrich, J. D. Farmer. "Best reply structure and equilibrium convergence in generic games." Science Advances 5.2 (2019): eaat1328.

  • November 25, 2021 @ Bâtiment IMAG (206) -- Seminar "Positive solutions for large random linear systems - application to theoretical ecology" by Jamal Najim
    Large Lotka-Volterra (LV) systems of coupled differential equations is a popular model to describe the dynamics and equilibrium of the abundances of large populations in interaction such as foodwebs for instance. For such large LV systems, calibrating the interaction coefficients between the coupled equations is a highly difficult task that people often circumvent by considering instead random coefficients. 
    In this talk, we will describe feasible equilibria for such systems. By feasible equilibrium, we mean an equilibrium with no vanishing species. The study of such an equilibrium amounts to finding a positive solution to a simple large linear equation involving a large random matrix. We will describe solutions for various models: fully random (i.i.d.), sparse, correlated. 
     
    Key words are: Theoretical ecology, random Matrix Theory, concentration of measure, extreme values. Reference: arXiv:1904.04559
     
    Joint work with I. Akjouj, P. Bizeul, M. Clénet, H. El Ferchichi. 
  • December 2, 2021 @ -- Polaris-tt: Chen Yan
  • December 9, 2021 @ -- Polaris-tt: Till Kletti (Introducing the expohedron for fair and useful rankings)

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