Dinah Rosenberg

AN OPERATOR APPROACH TO ZERO-SUM REPEATED GAMES

We consider two person zero-sum stochastic games. The recursive formula for the valuesvλ (resp.vn) of the discounted (resp. finitely repeated) version can be written in terms of a single basic operator Φ(α,f) where α is the weight on the present payoff andf the future payoff. We give sufficient conditions in terms of Φ(α,f) and its derivative at 0 for limvn and limvλ to exist and to be equal.We apply these results to obtain such convergence properties for absorbing games with compact action spaces and incomplete information games.

Informational externalities and emergence of consensus

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. These results imply extensions of many known results in the literature of social learning and getting to agreement.

Stochastic Games with a Single Controller and Incomplete Information

We study stochastic games with incomplete information on one side, in which the transition is controlled by one of the players. We prove that if the informed player also controls the transitions, the game has a value, whereas if the uninformed player controls the transitions, the max-min value as well as the min-max value exist, but they may differ. We discuss the structure of the optimal strategies, and provide extensions to the case of incomplete information on both sides.

The MaxMin value of stochastic games with imperfect monitoring

Abstract.We study finite zero-sum stochastic games in which players do not observe the actions of their opponent. Rather, at each stage, each player observes a stochastic signal that may depend on the current state and on the pair of actions chosen by the players. We assume that each player observes the state and his/her own action. We prove that the uniform max-min value always exists. Moreover, the uniform max-min value is independent of the information structure of player 2. Symmetric results hold for the uniform min-max value.

Zero Sum Absorbing Games with Incomplete Information on One Side: Asymptotic Analysis

We prove the existence of the limit of the values of finitely repeated (resp., discounted) absorbing games with incomplete information on one side, as the number of repetitions goes to infinity (resp., the discount factor goes to zero). The main tool is the study of the Shapley operator, for which the value of the

Absorbing Games with Compact Action Spaces

\lambda

Cav U and the Dual Game

-discounted game is a fixed point, and of its derivative with respect to

Stochastic Games with Imperfect Monitoring

\lambda

On a Markov Game with One-Sided Information

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Duality and markovian strategies

We prove that games with absorbing states with compact action sets have a value.(This abstract was borrowed from another version of this item.)