8 research outputs found
A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic games
We prove a Tauberian theorem for nonexpansive operators, and apply it to the
model of zero-sum stochastic game. Under mild assumptions, we prove that the
value of the lambda-discounted game v_{lambda} converges uniformly when lambda
goes to 0 if and only if the value of the n-stage game v_n converges uniformly
when n goes to infinity. This generalizes the Tauberian theorem of Lehrer and
Sorin (1992) to the two-player zero-sum case. We also provide the first example
of a stochastic game with public signals on the state and perfect observation
of actions, with finite state space, signal sets and action sets, in which for
some initial state k_1 known by both players, (v_{lambda}(k_1)) and (v_n(k_1))
converge to distinct limits
Markov games with frequent actions and incomplete information
We study a two-player, zero-sum, stochastic game with incomplete information
on one side in which the players are allowed to play more and more frequently.
The informed player observes the realization of a Markov chain on which the
payoffs depend, while the non-informed player only observes his opponent's
actions. We show the existence of a limit value as the time span between two
consecutive stages vanishes; this value is characterized through an auxiliary
optimization problem and as the solution of an Hamilton-Jacobi equation