4 Presentations

• 
  08:30 AM - 08:55 AM

  Markov Games with a Single Transition and Incomplete Information on One Side

  • Galit Ashkenazi-Golan, presenter, Tel-Aviv university

  We provide a nite-stage algorithm for calculating the value and optimal strategies of
  Markov games with incomplete information on one side with two states, where one state
  is absorbing.

• 
  08:55 AM - 09:20 AM

  Primal-dual methods for approximating saddle points of zero-sum games with random non-convex payoffs.

  • Kimon Antonakopoulos, presenter, INRIA
  • Panayotis Mertikopoulos, CNRS

  In this paper, we will focus on the convergence of stochastic mirror descent algorithms in zero-sum games with random payoffs. More precisely, the main idea of these algorithimic schemes is to take small steps along a random sample of the subdifferential of the payoffs and then "mirror" the outcome back to the action sets. In terms of feedback, we assume that players can only estimate these elements of payoff’s subdifferential up to a zero-mean error with bounded variance.
  For obtaining almost sure convergence of the algorithm towards a saddle point, we intro- duce the general class of zero-sum games, which we call variationally stable, and it is large enough for including convex and pseudoconvex games.
  Lastly, we provide some explicit estimates of the method’s speed of convergence and we fur- ther discuss some extensions of this method which go beyond the zero-sum case.

• 
  09:20 AM - 09:45 AM

  On some aspect of asymmetric information in Dynkin games

  • Krzysztof Szajowski, presenter, Faculty of Pure and Applied Mathematics, Wroclaw University of Technology

  Non-zero-sum stopping game models are applied in various circumstances. An important, not fully explored case is the competition between players with different knowledge or asymmetrical rights to use information. The considered non-zero-sum Dynkin game between two players admits the various accuracy of process observation which determines the pay-offs. It also means asymmetry in the strategies they have. We are investigating the existence of a game solution in the sense of the Nash equilibrium point. The natural conditions (situations) at which the game has value will be shown. With additional conditions, you can construct strategies in equilibrium. The discussion refers to the recently obtained results of Lempa & Matomäki (2013), Grün (2013) and Skarupski & Szajowski (2017).

• 
  09:45 AM - 10:10 AM

  symmetric stochastic games of resource extraction with weakly continuous transitions

  • Anna Jaśkiewicz, presenter, Politechnika Wrocławska
  • Andrzej Nowak, Uniwersytet Zielonogórski

  Stochastic games of resource extraction are studied. It is assumed that the players
  have identical preferences and the transition probability is either non-atomic or a convex
  combination of transition probabilities depending on the investment with coefficients
  also dependent on the investment. Our approach covers the unbounded utility case,
  which was not examined in this class of games beforehand. We prove the existence of
  a stationary Markov perfect equilibrium in a non-randomised class of strategies.