Neyman A, Gossner O, Hernandez P. Optimal Use of Communication Resources. Econometrica. 2006 :1603 - 1636.Abstract

We study a repeated game with asymmetric information about a dynamic state of nature. In the course of the game, the better informed player can communicate some or all of his information with the other. Our model covers costly and/or bounded communication. We characterize the set of equilibrium payoffs, and contrast these with the communication equilibrium payffs, which by definition entail no communication costs.

Neyman A, Smordinsky R. Asymptotic Values of Vector Measure Games. Mathematics of Operations Research. 2004 :739 - 775.Abstract

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of u(S) where u is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games, where a two-house weighted majority game is a game in which a coalition is winning if and only if it is winning in two given weighted majority games. All weighted majority games have an asymptotic value. However, not all two-house weighted majority games have an asymptotic value. In this paper, we prove that the existence of infinitely many atoms with sufficient variety suffice for the existence of the asymptotic value in a general class of nonsmooth vector measure games that includes in particular two-house weighted majority games.

Neyman A, Olivier G, Hernandez P. Dynamiques de Communication. Dynamiques de Communication. 2004;55 :509 - 516.
Neyman A, Gossner O, Hernandez P. Online Information Transmission. 2003. slidesseerus103.pdf
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
Neyman A, Mertens JF. A value on `AN. International Journal of Game Theory. 2003 : 109-120.Abstract

We prove here the existence of a value (of norm 1) on the spaces 'NA and even 'AN, the closure in the variation distance of the linear space spanned by all games f°µ, where µ is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0,1] which satisfies a much weaker continuity at zero and one.

Neyman A, Bavly G. Online Concealed Correlation by Boundedly Rational Players. Center for the Study of Rationality, DP336. 2003 :DP-336.Abstract

In a repeated game with perfect monitoring, correlation among a group of players may evolve in the common course of play (online correlation). Such a correlation may be concealed from a boundedly rational player. The feasibility of such online concealed correlation'' is quantified by the individually rational payoff of the boundedly rational player. We show that ``strong'' players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate online correlation of the actions of ``weak'' players, in a manner that is concealed from an opponent of ``intermediate'' strength. The result is illustrated in two models, each captures another aspect of bounded rationality. In the first, players use bounded recall strategies. In the second, players use strategies that are implementable by finite automata.

Gossner O, Hernandez P, Neyman A. Online Matching Pennies. Center for the Study of Rationality, Discussion Paper 316 . 2003.Abstract

We study a repeated game in which one player, the prophet, acquires more information than another player, the follower, about the play that is going to be played. We characterize the optimal amount of information that can be transmitted online by the prophet to the follower, and provide applications to repeated games played by finite automata, and by players with bounded recall.

Stochastic Games and Applications
Neyman A, Sorin S. Stochastic Games and Applications. NATO ASI series. Kluwer Academic Publishers; 2003.
Neyman A. Values of Games with Infinitely Many Players. In: Aumann RJ, sergiu hart Handbook of Game Theory, with Economic Applications. Vol. 3. Amsterdam: North-Holland ; 2002. pp. 2121--2167. Paper
Neyman A. Values of Non-Atomic Vector Measure Games. Israel Journal of Mathematics. 2001;124 :1-27.Abstract

Much of economic theory is concerned with the existence of prices. In particular, economists are interested in whether various outcomes defined by diverse postulates turn out to be actually generated by prices. Whenever this is the case, a theory of endogenous price formation is derived. In the present analysis, a well-known game-theoretic solution concept is considered: value. Nonatomic games are considered that are defined by finitely many nonnegative measures. Nonatomic vector measure games arise, for example, from production models and from finite-type markets. It is shown that the value of such a game need not be a linear combination of the nonatomic nonnegative measures. This is in contrast to all the values known to date. Moreover, this happens even for certain differentiable market games. In the economic models, this means that the value allocations are not necessarily produced by prices. All the examples presented are special cases of a new class of values.

Neyman A, Okada D. Repeated games with bounded entropy. Games and Economic Behavior. 2000;30 :228--247.Abstract

We investigate the asymptotic behavior of the maxmin values of repeated two-person zero-sum games with a bound on the strategic entropy of the maximizer's strategies while the other player is unrestricted. We will show that if the bound (n), a function of the number of repetitions n, satisfies the condition (n)/n (n), then the maxmin value Wn ((n)) converges to (cavU)(), the concavification of the maxmin value of the stage game in which the maximizer's actions are restricted to those with entropy at most . A similar result is obtained for the infinitely repeated games.

Neyman A, Okada D. Two-person repeated games with finite automata. International Journal of Game Theory. 2000;29 :309--325.Abstract

We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An exogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player. We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels.

Kohlberg E, Neyman A. A strong law of large numbers for nonexpansive vector-valued stochastic processes. Israel Journal of Mathematics. 1999;111 :93-108. Paper
Neyman A. Cooperation in Repeated Games when the Number of Stages is not Commonly Known. Econometrica. 1999;67 :45--64.Abstract

It is shown that an exponentially small departure from the common knowledge assumption on the number T of repetitions of the prisoners’ dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one-shot game can be ap

Neyman A, Okada D. Strategic entropy and complexity in repeated games. Games and Economic Behavior. 1999;29 :191--223.Abstract

We introduce the entropy-based measure of uncertainty for mixed strategies of repeated games-strategic entropy. We investigate the asymptotic behavior of the maxmin values of repeated two-person zero-sum games with a bound on the strategic entropy of player 1's strategies while player 2 is unrestricted, as the bound grows to infinity. We apply the results thus obtained to study the asymptotic behavior of the value of the repeated games with finite automata and bounded recall.

Neyman A, Sorin S. Equilibria in Repeated Games with Incomplete Information: The General Symmetric Case. International Journal of Game Theory. 1998;27 : 201--210.Abstract

Every two person repeated game of symmetric incomplete information, in which the signals sent at each stage to both players are identical and generated by a state and moves dependent probability distribution on a given finite alphabet, has an equilibrium payoff.