Stochastic games

2017
Neyman A. Continuous-Time Stochastic Games. Games and Economic Behavior [Internet]. 2017;104 :92-130. Publisher's Version Paper
2015
Neyman A, Kohlberg E. The Cooperative Solution of Stochastic Games. 2015.Abstract

Building on the work of Nash, Harsanyi, and Shapley, we define a cooperative solution for strategic games that takes account of both the competitive and the cooperative aspects of such games. We prove existence in the general (NTU) case and uniqueness in the TU case. Our main result is an extension of the definition and the existence and uniqueness theorems to stochastic games - discounted or undiscounted.

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2010
Neyman A, Sorin S. Repeated Games with Public Uncertain Duration Process. International Journal of Game Theory. 2010 :29-52.Abstract

We consider repeated games where the number of repetitions u is unknown. The information about the uncertain duration can change during the play of the game. This is described by an uncertain duration process U that defines the probability law of the signals that players receive at each stage about the duration. To each repeated game G and uncertain duration process U is associated the U-repeated game G(U). A public uncertain duration process is one where the uncertainty about the duration is the same for all players. We establish a recursive formula for the value V_U of a repeated two-person zero-sum game G(U) with a public uncertain duration process U. We study asymptotic properties of the normalized value v_U = V_U/E(u) as the expected duration E(u) goes to infinity. We extend and unify several asymptotic results on the existence of lim v_n and lim v_ë and their equality to lim v_U. This analysis applies in particular to stochastic games and repeated games of incomplete information.

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2003
Neyman A. From Markov chains to stochastic games . In: Neyman A, Sorin S Kluwer Academic Publishers . 2003rd ed. Dordrecht / Boston / London: Kluwer Academic Publishers ; 2003. pp. 9--25. 02.pdf
Neyman A. Stochastic games: Existence of the minmax . In: Neyman A, Sorin S Kluwer Academic Publishers. Kluwer Academic Publishers ; 2003. pp. 173--193. 11.pdf
Neyman A. Real algebraic tools in stochastic games . In: Neyman A, Sorin S Kluwer Academic Publishers. Kluwer Academic Publishers ; 2003. pp. 58--75. 06.pdf
Neyman A. Stochastic games and nonexpansive maps . In: Neyman A, Sorin S Stochastic Games. Kluwer Academic Publishers ; 2003. pp. 397--415. 26.pdf
1982
Mertens JF, Neyman A. Stochastic Games have a Value. Proceedings of the National Academy of Sciences. 1982;79 :2145-2146.Abstract

Undiscounted nontenninating stochastic games in which the state and action spaces are finite have a value.

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1981
Mertens J-F, Neyman A. Minimax Theorems for Undiscounted Stochastic Games. Game Theory and Mathematical Economics. 1981 :83-87.
Kohlberg E, Neyman A. Asymptotic Behavior of Nonexpansive Mappings in Normed Linear Spaces. Israel Journal of Mathematics. 1981;38 :269-275.Abstract

Let T be a non expansive mapping on a normed linear space X. We show that there exists a linear functional f, with ||f|| = 1, such that, for all x in X, the Iimit, as n goes to infinity, of  f(T"x/n) equals the limit of IIT"x/nll=a, where a=inf_{y}IITy-yli. This means, if X is reflexive, that there is a face F of the ball of radius a to which T"x/n converges weakly to F for all x  if X is strictly convex as well as reflexive, the convergence is to a point; and if X satisfies the stronger condition that its dual has Frechet differentiable norm then the convergence is strong. Furthermore, we show that each of the foregoing conditions on X is satisfied if and only if the associated convergence property holds for all nonexpansive T.

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Mertens JF, Neyman A. Stochastic Games. International Journal of Game Theory. 1981;10 :53-66.Abstract

Stochastic Games have a value.

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