Seminar

Existence of the Uniform value in some example of stochastic games with signals

Xavier Venel (Toulouse School of Economics - GREMAQ)

October 14, 2011, 13:45–15:00

Toulouse

Room MS 003

Decision Mathematics Seminar

Abstract

We consider some example of two-player zero-sum stochastic games with signals. First we are interested in stochastic games where both players monitor past actions but have no information on the state. Under a commutation assumption on the transition, we prove that the uniform value exists. The transition of the game commutes if the action profile a1 followed by the action profile a2 whatever is the state at stage 1 leads to the same distribution of state as playing first the action profile a2 and then a1. Secondly we consider stochastic games where player 1 controls the transition and has more information than player 2. Since player 2 does not influence the state, the problem shares some properties with the one-player case (Markov Decision Process). We adapt previous work of Renault [2011] in order to prove that these games have also a uniform value.