The general idea of the proof is to define a class of sets, the solvable sets, which can safely be thought of as absorbing states.

We study zero-sum stochastic games in which players do not observe the actions of the opponent. Rather, they observe a stochastic signal that may depend on the state, and on the pair of actions chosen by the players. We assume each player observes the state and his own action. <p> We propose a...</p>

We obtain results on the sensitivity of the invariant measure and other statistical quantities of a Markov chain with respect to perturbations of the transition matrix. We use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

Given a sequence (s0; s1,..., sN) of observations from a finite set S, we construct a process (sn)n_N that satisfies the following properties: (i) (Sn)n_ ·N is a piecewise Markov chain, (ii) the conditional distribution of sn given S0,...,Sn-1 is close to the empirical transition given by the...

Presentation of somme recent results of stochastic games

We survey recent results on the existence of the value in zero-sum stopping games with discrete and continuous time, and on the existence of e-equilibria in non zero-sum games with discrete time.

We prove that every two-player non zero-sum deterministic stopping game with uniformly bounded payoffs admits an e-equilibrium, for every e0. The proof uses Ramsey Theorem that states that for every coloring of a complete infinite graph by finitely many colors there is a complete infinite...

We study a general model of dynamic games with purely informational externalities. We prove that eventually all motives for experimentation disappear, and provide the exact rate at which experimentation decays. We also provide tight conditions under which players eventually reach a consensus....

Dynamic decision-making without commitment is usually modelled as a game between the current and future selves of the decision maker. It has been observed that if the time-horizon is infinite, then such games may have multiple subgame-perfect equilibrium solutions. We provide a sufficient...