4 Presentations

• 
  09:00 AM - 09:25 AM

  Evolutionary Dynamics in Time-Varying Environments

  • Mathias Staudigl, presenter, Maastricht University

  Population games are a very useful mathematical framework to model various strategic settings in biology, economics and engineering. However, the standard model of a population games assumes that the environment in which the agents act is time-invariant. Over long-time horizons this assumption is rather strict. In this paper we discuss a general class of evolutionary game dynamics in population games where the strategic environment is randomly changing according to a finite-state Markov chain. The resulting dynamics are seen to belong to the rich class of piecewise-deterministic Markov processes, which is the most general class of Markovian dynamics without diffusive component. We study existence and uniqueness of solutions and investigate asymptotic properties of the dynamics.

• 
  09:25 AM - 09:50 AM

  On the Douglas–Rachford splitting for generalized Nash equilibrium seeking in aggregative games

  • Giuseppe Belgioioso, presenter, Eindhoven Univesity of Technology
  • Sergio Grammatico, Eindhoven University of Technology

  We address the generalized Nash equilibrium problem for monotone aggregative games with affine coupling

  constraints. We use operator theory to characterize the generalized Nash equilibria of the game as the zeros

  of a monotone set-valued operator and we apply the Douglas–Rachford operator splitting to solve the monotone

  inclusion problem. Consequently, a semi-decentralized algorithm with convergence guarantee is derived. Our

  numerical experience shows that the Douglas–Rachford algorithm usually has faster convergence than projected-

  pseudo-gradient algorithms.

• 
  09:50 AM - 10:15 AM

  Multiplicative Weights Update algorithm in congestion games and emergence of chaos

  • Fryderyk Falniowski, presenter, Cracow University of Economics

  The Multiplicative Weights Update method is a ubiquitous meta-algorithm used e.g. in machine learning, optimization, theoretical computer science and game theory.
  We will analyze convergence of MWU for congestion games to exact Nash equilibria. We will show how aggressive behavior (fast learning) of players may result in lack of convergence - appearance of limit cycles and chaotic behavior.

• 
  10:15 AM - 10:40 AM

  Distributed Optimisation of Routing Decisions

  • Bruno Gaujal, presenter, Inria
  • Amelie Heliou, Univ. Grenoble Alpes
  • Panayotis Mertikopoulos, cnrs

  In this talk I will present a new distributed algorithm, run in each node
  of a communication network, to optimize routing decision in the multi-flot case,
  when link delays depend on the load of the link.
  When the delays are strictly convex function of the load, the algorithm converges to the unique
  optimal total sum of delays for all flows.