4 Presentations

• 
  10:40 AM - 11:05 AM

  Operator approach to values of stochastic games with varying stage duration

  • Guillaume Vigeral, presenter, CEREMADE, U. Paris-Dauphine
  • Sylvain Sorin, Université Pierre et Marie Curie

  We study the links between the values of stochastic games with varying stage dura-
  tion, the corresponding Shapley operators, and the solution of an
  evolution equation in continuous time. Considering general non expansive maps we establish two
  kinds of results, under both the discounted or the finite length framework, that apply to the class
  of “exact” stochastic games. First, for a fixed length or discount factor, the value converges as
  the stage duration go to 0. Second, the asymptotic behavior of the value as the length goes to
  infinity, or as the discount factor goes to 0, does not depend on the stage duration. In addition,
  these properties imply the existence of the value of the finite length or discounted continuous
  time game (associated to a continuous time jointly controlled Markov process), as the limit of
  the value of any discretization with vanishing mesh.

• 
  11:05 AM - 11:30 AM

  Markov perfect equilibria in OLG models with risk sensitive agents

  • Łukasz Balbus, presenter, University of Zielona Góra

  In this paper, we present an overlapping generation model (OLG for short) of resource extraction with a random production function, and an altruism having both paternalistic and non-paternalistic features. All generations are risk sensitive with a constant coefficient of absolute risk aversion. The preferences are represented by a possibly dynamic inconsistent dynamic recursive utility function with non-cooperating generations. Under general conditions on the aggregator and transition probability, we examine the existence and the uniqueness of a recursive utility function and the existence of a stationary mixed Markov Perfect Nash Equilibria.

• 
  11:30 AM - 11:55 AM

  On Tauberian theorem for Nash equilibria

  • Dmitrii Khlopin, presenter, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

  The report is devoted to $n$-player nonzero-sum dynamic games, which is not limited to e.g. differential games and could accommodate both discrete and continuous time. Assuming common dynamics, we study two game families with total payoffs that are defined either as the Cesaro average (long run average game family) or Abel average (discounting game family) of the running costs. We analyze asymptotic Nash equilibria---strategy profiles that are approximately optimal if the planning horizon tends to infinity in long run average games and if the discount tends to zero in discounting games. Moreover, we also assume that this strategy profile is stationary. Under a mild assumption on players' strategy sets, we prove a uniform Tauberian theorem for stationary asymptotic Nash equilibrium.
  This study was supported by the Russian Science Foundation (project no.~17-11-01093).

• 
  11:55 AM - 12:20 PM

  Discrete-Time Ergodic Mean Field Games with Average Reward on Compact Spaces

  • Piotr Wiecek, presenter, Wroclaw University of Technology

  We present a model of discrete-time mean-field game with compact state and action spaces and average reward. Under some strong ergodicity assumption we show it possesses a stationary mean-field equilibrium. We show that in general the equilibrium strategy for this game is not always a good approximation of Nash equilibria of the n-person stochastic game counterparts of the mean-field game for large n. Finally, we identify some cases when the approximation is good.