October 8 (Thursday) 10:00-11:00, room E.118.2 (main building, 1st floor)
Sylvain Sorin (Sorbonne University, Paris, France)
Long term properties of stochastic games
We will first describe the model of stochastic games introduced by Shapley (1953) and present the two main constructions to study long term properties in repeated games: the asymptotic and the uniform approaches. We will recall the principal results, in the finite framework, for the zero-sum case and their counterpart in the non zero-sum case.
We will then describe more recent advances on the non-existence of asymptotic value for 0-sum stochastic games with vanishing stage weight (general framework). Next we will present an alternative formulation introducing vanishing stage duration. This allows to prove convergence results for the values by establishing a connexion with differential games and linking discrete time/stochastic models to continuous time/deterministic ones.