@article {11244,
title = {Continuous-Time Stochastic Games. Revised version},
journal = {Games and Economic Behavior},
year = {In Press},
author = {Abraham Neyman}
}
@article {13579,
title = {Cooperative Strategic Games},
journal = {The Federmann Center for the Study of Rationality, Hebrew University},
volume = {DP 706},
year = {2017},
abstract = {\ We examine a solution concept, called the {\textquoteleft}{\textquoteleft}value," for n-person strategic games.In applications, the value provides an a-priori assessment of the monetary worth of a player{\textquoteright}s position in a strategic game, comprising not only the player{\textquoteright}s contribution to the total payoff but also the player{\textquoteright}s ability to inflict losses on other players. \ A salient feature is that the value takes account of the costs that {\textquoteleft}{\textquoteleft}spoilers" impose on themselves.Our main result is an axiomatic characterization of the value.For every subset, S, consider the zero-sum game played between S and its complement, where the players in each of these sets collaborate as a single player, and where the payoff is the difference between the sum of the payoffs to the players in S and the sum of payoffs to the players not in S. \ We say that S has an effective threat if the minmax value of this game is positive. The first axiom is that if no subset of players has an effective threat then all players are allocated the same amount.The second axiom is that if the overall payoff to the players in a game is the sum of their payoffs in two unrelated games then the overall value is the sum of the values in these two games.The remaining axioms are the strategic-game analogs of the classical coalitional-games axioms for the Shapley value: \ efficiency, symmetry, and null player.\ },
author = {Abraham Neyman and Elon Kohlberg}
}
@article {2180,
title = {Online Concealed Correlation and Bounded Rationality},
journal = {Games and Economic Behavior},
year = {2014},
pages = { 71 - 89},
abstract = {Correlation of players{\textquoteright} actions may evolve in the common course of the play of a repeated game with perfect monitoring ({\textquotedblleft}online correlation{\textquotedblright}). In this paper we study the concealment of such correlation from a boundedly rational player. We show that {\textquotedblleft}strong{\textquotedblright} players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate the online correlation of the actions of {\textquotedblleft}weak{\textquotedblright} players, where this correlation is concealed from an opponent of {\textquotedblleft}intermediate{\textquotedblright} strength. The feasibility of such {\textquotedblleft}online concealed correlation{\textquotedblright} is reflected in the individually rational payoff of the opponent and in the equilibrium payoffs of the repeated game. This result enables the derivation of a folk theorem that characterizes the set of equilibrium payoffs in a class of repeated games with boundedly rational players and a mechanism designer who sends public signals. The result is illustrated in two models, bounded recall strategies and finite automata.},
author = {Abraham Neyman and Gilad Bavly}
}
@article {2310,
title = {Stochastic Games with Short-Stage Duration},
journal = {Dyn Games Appl},
volume = {3},
year = {2013},
pages = {236-278},
abstract = {We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage k, $k\geq 0$, of a stochastic game $\Gamma_\delta$ with stage duration $\delta$ is interpreted as the play in time $k\delta\leq t\<(k+1)\delta$, and therefore the average payoff of the $n$-stage play per unit of time is the sum of the payoffs in the first $n$ stages divided by $n\delta$, and the $\lambda$-discounted present value of a payoff $g$ in stage $k$ is $\lambda^{k\delta} g$. We define convergence, strong convergence, and exact convergence of the data of a family $(\Gamma_\delta)_{\delta\>0}$ as the stage duration $\delta$ goes to $0$, and study the asymptotic behavior of the value, optimal strategies, and equilibrium. The asymptotic analogs of the discounted, limiting-average, and uniform equilibrium payoffs are defined. Convergence implies the existence of an asymptotic discounted equilibrium payoff, strong convergence implies the existence of an asymptotic limiting-average equilibrium payoff, and exact convergence implies the existence of an asymptotic uniform equilibrium payoff.},
author = {Abraham Neyman}
}
@article {2311,
title = {The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information},
journal = {Journal of Theoretical Probability},
year = {2013},
pages = {557-567},
abstract = {The variation of a martingale m[k] of k+1 probabilities p(0),...,p(k) on a finite (or countable) set X is the expectation of the sum of ||p(t)-p(t-1)|| (the L one norm of the martingale differences p(t)-p(t-1)), and is denoted V(m[k]). It is shown that V(m[k]) is less than or equal to the square root of 2kH(p(0)), where H(p) is the entropy function (the some over x in X of p(x)log p(x) and log stands for the natural logarithm. Therefore, if d is the number of elements of X, then V(m[k]) is less than or equal to the square root of 2k(log d). It is shown that the order of magnitude of this bound is tight for d less than or equal to 2 to the power k: there is C\>0 such that for every k and d less than or equal to 2 to the power k there is a martingale m[k]=p(0),...,p(k) of probabilities on a set X with d elements, and with variation V(m[k]) that is greater or equal the square root of Ck(log d). It follows that the difference between the value of the k-stage repeated game with incomplete information on one side and with d states, denoted v(k), and the limit of v(k), as k goes to infinity, is bounded by the maximal absolute value of a stage payoff times the square root of 2(log d)/k, and it is shown that the order of magnitude of this bound is tight.},
author = {Abraham Neyman}
}
@article {2312,
title = {The Value of Two-Person Zero-Sum Repeated Games with Incomplete Information and Uncertain Duration},
journal = {International Journal of Game Theory},
volume = {41},
year = {2012},
pages = {195-207},
abstract = {It is known that the value of a zero-sum infinitely repeated game with incomplete information on both sides need not exist. It is proved that any number between the minmax and the maxmin of the zero-sum infinitely repeated game with incomplete information on both sides is the value of the long finitely repeated game where players{\textquoteright} information about the uncertain number of repetitions is asymmetric.},
author = {Abraham Neyman}
}
@article {2360,
title = {Singular Games in bv{\textquoteright}NA},
journal = {Journal of Mathematical Economics},
year = {2010},
pages = {384 - 387},
abstract = {Every simple game in bv{\textquoteright}NA is a weighted majority game, and every game in bv{\textquoteright}NA is a sume of a game in pNA and a convergent series of singular scalar measure games.},
author = {Abraham Neyman}
}
@article {2314,
title = {Complexity and Effective Prediction},
journal = {Games and Economic Behavior},
year = {2010},
pages = {165-168},
abstract = {Let G = be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which players 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per-stage payoff when the two automata face off. We are interested in the cases in which player 1 is {\textquotedblleft}smart{\textquotedblright} in the sense that k is large but player 2 is {\textquotedblleft}much smarter{\textquotedblright} in the sense that m\>\>k. Let S(g) be the value of G where the second player is clairvoyant, i.e., would know the player 1{\textquoteright}s move in advance. The threshold for clairvoyance is shown to occur for m near min(|I|, | J |) to the power k. For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).},
author = {Abraham Neyman and Joel Spencer}
}
@article {2313,
title = {Repeated Games with Public Uncertain Duration Process},
journal = {International Journal of Game Theory},
year = {2010},
pages = {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_{\"e} and their equality to lim v_U. This analysis applies in particular to stochastic games and repeated games of incomplete information.},
author = {Abraham Neyman and Sylvain Sorin}
}
@article {2357,
title = {Absorbing Games with Compact Action Spaces},
journal = {Mathematics of Operations Research},
volume = {34},
year = {2009},
pages = {257-262},
abstract = {We prove that games with absorbing states with compact action sets have a value.},
author = {Abraham Neyman and J. F. Mertens and D. Rosenberg}
}
@article {2358,
title = {Growth of Strategy Sets, Entropy, and Nonstationary Bounded Recall},
journal = {Games and Economic Behavior},
year = {2009},
pages = {404-425},
abstract = {The paper initiates the study of long term interactions where players{\textquoteright} bounded rationality varies over time. Time dependent bounded rationality, for player i, is reflected in part in the number ψi(t) of distinct strategies available to him in the first t-stages. We examine how the growth rate of ψi(t) affects equilibrium outcomes of repeated games. An upper bound on the individually rational payoff is derived for a class of two-player repeated games, and the derived bound is shown to be tight. As a special case we study the repeated games with nonstationary bounded recall and show that, a player can guarantee the minimax payoff of the stage game, even against a player with full recall, by remembering a vanishing fraction of the past. A version of the folk theorem is provided for this class of games},
author = {Abraham Neyman and Daijiro Okada}
}
@article {2359,
title = {Existence of Optimal Strategies in Markov Games with Incomplete Information},
journal = {International Journal of Game Theory},
year = {2008},
pages = {581 - 596},
abstract = {The existence of a value and optimal strategies is proved for the class of two-person repeated games where the state follows a Markov chain independently of players{\textquoteright} actions and at the beginning of each stage only player one is informed about the state. The results apply to the case of standard signaling where players{\textquoteright} stage actions are observable, as well as to the model with general signals provided that player one has a nonrevealing repeated game strategy. The proofs reduce the analysis of these repeated games to that of classical repeated games with incomplete information on one side.},
author = {Abraham Neyman}
}
@article {2367,
title = {Aumann Awarded Nobel Prize},
journal = {Notices of the AMS},
volume = {53},
year = {2006},
pages = {44 - 46},
author = {Abraham Neyman}
}
@article {2362,
title = {Optimal Use of Communication Resources},
journal = {Econometrica},
year = {2006},
pages = {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.},
author = {Abraham Neyman and Olivier Gossner and Penelope Hernandez}
}
@article {2369,
title = {Asymptotic Values of Vector Measure Games},
journal = {Mathematics of Operations Research},
year = {2004},
pages = {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.},
author = {Abraham Neyman and Rann Smordinsky}
}
@article {2368,
title = {Dynamiques de Communication},
journal = {Dynamiques de Communication},
volume = {55},
year = {2004},
pages = {509 - 516},
author = {Abraham Neyman and Gossner Olivier and Penelope Hernandez}
}
@article {2735,
title = {A value on {\textquoteleft}AN},
journal = {International Journal of Game Theory},
year = {2003},
pages = { 109-120},
abstract = {We prove here the existence of a value (of norm 1) on the spaces {\textquoteright}NA and even {\textquoteright}AN, the closure in the variation distance of the linear space spanned by all games f{\textdegree}{\textmu}, where {\textmu} 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.},
author = {Abraham Neyman and J. F. Mertens}
}
@article {2743,
title = {Values of Non-Atomic Vector Measure Games},
journal = {Israel Journal of Mathematics},
volume = {124},
year = {2001},
pages = {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.},
author = {Abraham Neyman}
}
@article {2751,
title = {Repeated games with bounded entropy},
journal = {Games and Economic Behavior},
volume = {30},
year = {2000},
pages = {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{\textquoteright}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{\textquoteright}s actions are restricted to those with entropy at most . A similar result is obtained for the infinitely repeated games.},
author = {Abraham Neyman and Daijiro Okada}
}
@article {2744,
title = {Two-person repeated games with finite automata},
journal = {International Journal of Game Theory},
volume = {29},
year = {2000},
pages = {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.},
author = {Abraham Neyman and Daijiro Okada}
}
@article {2752,
title = {A strong law of large numbers for nonexpansive vector-valued stochastic processes},
journal = {Israel Journal of Mathematics},
volume = {111},
year = {1999},
pages = {93-108},
author = {Elon Kohlberg and Abraham Neyman}
}
@article {2754,
title = {Cooperation in Repeated Games when the Number of Stages is not Commonly Known},
journal = {Econometrica},
volume = {67},
year = {1999},
pages = {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{\textquoteright} dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one-shot game can be ap},
author = {Abraham Neyman}
}
@article {2753,
title = {Strategic entropy and complexity in repeated games},
journal = {Games and Economic Behavior},
volume = {29},
year = {1999},
pages = {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{\textquoteright}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.},
author = {Abraham Neyman and Daijiro Okada}
}
@article {2756,
title = {Equilibria in Repeated Games with Incomplete Information: The General Symmetric Case},
journal = {International Journal of Game Theory},
volume = {27},
year = {1998},
pages = { 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.},
author = {Abraham Neyman and Sylvain Sorin}
}
@article {2755,
title = {Finitely Repeated Games with Finite Automata},
journal = {Mathematics of Operations Research},
volume = {23},
year = {1998},
pages = {513--552},
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.},
author = {Abraham Neyman}
}
@article {2820,
title = {Correlated Equilibrium and Potential Games},
journal = {International Journal of Game Theory},
volume = {26},
year = {1997},
pages = { 223--227.},
abstract = {Any correlated equilibrium of a strategic game with bounded payoffs and convex strategy sets which has a smooth concave potential, is a mixture of pure strategy profiles which maximize the potential. If moreover, the strategy sets are compact and the potential is strictly concave, then the game has a unique correlated equilibrium.},
author = {Abraham Neyman}
}
@article {2757,
title = {Equilibria in Repeated Games with Incomplete Information: The Deterministic Symmetric Case},
journal = {Kluwer Academic Publishers },
year = {1997},
pages = {129--131.},
author = {Abraham Neyman and Sylvain Sorin}
}
@article {2823,
title = {Value of Games with a Continuum of Players},
journal = {Game-Theoretic Methods in General Equilibrium Analysis},
volume = {77},
year = {1994},
pages = {67--79}
}
@article {2821,
title = {An Equivalence Principle for Perfectly Competitive Economies},
journal = {Journal of Economic Theory},
volume = {75},
year = {1994},
pages = {314-344},
abstract = {Four axioms are placed on a correspondence from smooth, non-atomic economies to their allocations. We show that the axioms categorically determine the (coincident) competitive-core-value correspondence. Thus any solution is equivalent to the above three if, and only if, it satisfies the axioms. In this sense our result is tantamount to an "equivalence principle." At the same time, our result implies that the three solutions themselves are determined by the axioms and so serves as an axiomatic characterization of the well-known competitive (or core, or value) correspondence.},
author = {Abraham Neyman and Pradeep Dubey}
}
@article {2824,
title = {The Positive Value of Information},
journal = {Games and Economic Behavior},
volume = {3},
year = {1991},
pages = {350-355},
abstract = {It has been remarked that in rational interactions more information to one player, while all others{\textquoteright} information remains the same, may reduce his payoff in equilibrium. This classical observation relies on comparing equilibria of two different games. It is argued that this analysis is not tenably performed by comparing equilibria of two different games. Rather, one is compelled to perform the analysis in an interaction without complete information, and to compare equilibria of two interactions that are embedded in some compounded game. It is then shown that the player whose information is unilaterally refined cannot be worse off at equilibrium.\ },
author = {Abraham Neyman}
}
@article {2825,
title = {On Non-Atomic Weighted Majority Games},
journal = {Journal of Mathematical Economics},
volume = {19},
year = {1990},
pages = {391-403},
author = {Abraham Neyman and Ezra.Einy}
}
@article {2827,
title = {Large Symmetric Games are Characterized by Completeness of the Desirability Relation},
journal = {Journal of Economic Theory},
volume = {148},
year = {1989},
pages = {369-385},
author = {E.Einy and Abraham Neyman}
}
@article {2826,
title = {Uniqueness of the Shapley Value},
journal = {Games and Economic Behavior},
volume = {1},
year = {1989},
pages = {116-118},
abstract = {It is shown that the Shapley value of any given game v is characterized by applying the value axioms -- efficiency, symmetry, the null player axiom, and either additivity or strong positivity -- to the additive group generated by the subgames of v.},
author = {Abraham Neyman}
}
@article {2865,
title = {Values of Vector Measure Games: Are They Linear Combinations of the Measures?},
journal = {Journal of Mathematical Economics},
volume = {17},
year = {1988},
pages = {31-40},
author = {Abraham Neyman and sergiu hart}
}
@article {2828,
title = {Weighted Majority Games have an Asymptotic Value},
journal = {Mathematics of Operations Research},
volume = {13},
year = {1988},
pages = {556-580},
author = {Abraham Neyman}
}
@article {2829,
title = {Payoffs in Non-Atomic Games: An Axiomatic Approach},
journal = {The Shapley Value, A. Roth (ed.), Cambridge Univ. Press},
year = {1988},
pages = {207-216.},
author = {Abraham Neyman and Pradeep Dubey}
}
@article {2830,
title = {Values of Smooth Non-Atomic Games: The Method of Multilinear Approximation},
journal = {The Shapley Value, A. Roth (ed.), Cambridge Univ. Press},
year = {1988},
pages = {217-234},
author = {Abraham Neyman and Dov Monderer}
}
@article {2831,
title = {Power and Public Goods},
journal = {Journal of Economic Theory},
volume = {42},
year = {1987},
pages = {108-127},
author = {Robert J. Aumann and M. Kurtz and Abraham Neyman}
}
@article {2832,
title = {A Counter-Example to the Folk Theorem with Discounting},
journal = {Economic Letters},
volume = {19},
year = {1986},
pages = {227-229},
author = {F. Forges and J. F. Mertens and Abraham Neyman}
}
@article {2840,
title = {Bounded Complexity Justifies Cooperation in the Finitely Repeated Prisoner{\textquoteright}s Dilemma},
journal = {Economic Letters},
volume = {19},
year = {1985},
pages = {227-229},
author = {Abraham Neyman}
}
@article {2844,
title = {Diagonality of Cost Allocation Prices},
journal = {Mathematics of Operations Research},
volume = {9},
year = {1984},
pages = {66-74},
author = {Leonard J. Mirman and Abraham Neyman}
}
@article {2843,
title = {Payoffs of Non-Atomic Markets: An Axiomatic Approach},
journal = {Econometrica},
volume = {52},
year = {1984},
pages = {1129-1150},
author = {Pradeep Dubey and Abraham Neyman}
}
@article {2842,
title = {Representation of Lp-Norms and Isometric Embedding in Lp-Spaces},
journal = {Israel Journal of Mathematics},
volume = {48},
year = {1984},
pages = {129-138.},
author = {Abraham Neyman}
}
@article {2841,
title = {Semi-Values of Political Economic Games},
journal = {Mathematics of Operations Research},
volume = {10},
year = {1984},
pages = {390-402},
abstract = {The class of continuous semivalues is completely characterized for various spaces of nonatomic games.},
author = {Abraham Neyman}
}
@article {2847,
title = {Convergence in Hilbert{\textquoteright}s Metric and Convergence in Directions},
journal = {Journal of Mathematical Analysis and Applications},
volume = {93},
year = {1983},
pages = {104-108},
author = {E. Kohlberg and Abraham Neyman}
}
@article {2845,
title = {Prices for Homogeneous Cost Functions},
journal = {Journal of Mathematical Economics},
volume = {12},
year = {1983},
pages = {257-273},
abstract = {The problem of allocating the production cost of a finite bundle of infinitely divisible consumption goods by means of prices is a basic problem in economics. This paper extends the recent axiomatic approach in which one considers a class of cost problems and studies the maps from the class of cost problems to prices by means of the properties these prices satisfy. The class of continuously differentiable costs functions used in previous studies is narrowed to the subclass containing non-decreasing, homogeneous of degree one and convex functions. On this subclass it is shown that there exists a unique continuous price mechanism satisfying axioms similar to those assumed in previous studies.},
author = {Leonard J. Mirman and Abraham Neyman}
}
@article {2846,
title = {Voting for Public Goods},
journal = {Review of Economic Studies},
volume = {50},
year = {1983},
pages = {677-693},
abstract = {It is shown that when resources are privately owned, the institution of voting is irrelevant to the choice of non-exclusive public goods: the total bundle of such goods produced by Society is the same whether or not minority coalitions are permitted to produce them. This is in sharp contrast to the cases of redistribution and of exclusive public goods, where public decisions depend strongly on the vote. The analytic tool used is the Harsanyi-Shapley non-transferable utility value.},
author = {Robert J. Aumann and M. Kurtz and Abraham Neyman}
}
@article {2849,
title = {Nim-Type Games},
journal = {International Journal of Game Theory},
volume = {11},
year = {1982},
pages = {17-20},
author = {D. Gale and Abraham Neyman}
}
@article {2850,
title = {Integrals of Production Sets with Restricted Substitution},
journal = {Journal of Mathematical Economics},
volume = {9},
year = {1982},
pages = {71-82},
abstract = {It is well known that the set of all zonoids (integrals of line segments) in R" (n\>2) is a closed\ and nowhere defise subset in the space of all compact, convex and centrally symmetric subsets of\ R". We generalize this result to sets which are the integral of k-dimensional convex sets, k \<n.},
author = {Abraham Neyman and Werner Hildenbrand}
}
@article {2851,
title = {Renewal Theory for Sampling without Replacement},
journal = {Annals of Probability},
volume = {10},
year = {1982},
pages = {464-481},
author = {Abraham Neyman}
}
@article {2848,
title = {Stochastic Games have a Value},
journal = {Proceedings of the National Academy of Sciences},
volume = {79},
year = {1982},
pages = {2145-2146},
abstract = {Undiscounted nontenninating stochastic games in which the state and action spaces are finite have a value.},
author = {J. F. Mertens and Abraham Neyman}
}
@article {2853,
title = {Minimax Theorems for Undiscounted Stochastic Games},
journal = {Game Theory and Mathematical Economics},
year = {1981},
pages = {83-87},
author = {J.-F. Mertens and Abraham Neyman}
}
@article {2852,
title = {Decomposition of Ranges of Vector Measures},
journal = {Israel Journal of Mathematics},
volume = {40},
year = {1981},
pages = {54-64},
author = {Abraham Neyman}
}
@article {2856,
title = {Asymptotic Behavior of Nonexpansive Mappings in Normed Linear Spaces},
journal = {Israel Journal of Mathematics},
volume = {38},
year = {1981},
pages = {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.},
author = {Elon Kohlberg and Abraham Neyman}
}
@article {2854,
title = {Asymptotic Behavior of Nonexpansive Mappings in Uniformly Convex Banach Spaces},
journal = {American Mathematical Monthly},
volume = {88},
year = {1981},
pages = {698-700},
author = {Elon Kohlberg and Abraham Neyman}
}
@article {2857,
title = {Singular Games have Asymptotic Values},
journal = {Mathematics of Operations Research},
volume = {6},
year = {1981},
pages = {205-212},
abstract = {The asymptotic value of a game v with a continuum of players is defined whenever all the sequences of Shapley values of finite games that "approximate" v have the same limit. In this paper we prove that if v is defined by v(S) = f( p(S)), where p is a nonatomic probability measure and f is a function of bounded variation on [0, I] that is continuous at 0 and at I, then v has an asymptotic value. This had previously been known only when v is absolutely continuous. Thus, for example, our result implies that the nonatomic majority voting game, defined by v(S) = 0 or I according as p(S) \ less than or equal to 1/2 or p(S) \> 1/2, has an asymptotic value. We also apply our result to show that other games of interest in economics and political science have asymptotic values, and adduce an example to show that the result cannot be extended to functions f that are not of bounded variation.},
author = {Abraham Neyman}
}
@article {2855,
title = {Stochastic Games},
journal = {International Journal of Game Theory},
volume = {10},
year = {1981},
pages = {53-66},
abstract = {Stochastic Games have a value.},
author = {J. F. Mertens and Abraham Neyman}
}
@article {2858,
title = {Value Theory without Efficiency},
journal = {Mathematics of Operations Research},
volume = {6},
year = {1981},
pages = {122--128},
abstract = {A semivalue is a symmetric positive linear operator on a space of games, which leaves the additive games fixed. Such an operator satisfies all of the axioms defining the Shapley value, with the possible exception of the efficiency axiom. The class of semivalues is completely characterized for the space of finite-player games, and for the space pNA of nonatomic games.},
author = {Abraham Neyman and Pradeep Dubey and Roberth J. Weber}
}
@article {2860,
title = {The Partition Value},
journal = {Mathematics of Operations Research},
volume = {2},
year = {1979},
pages = {236-267},
author = {Abraham Neyman and Yair Tauman}
}
@article {2861,
title = {Continuous Values are Diagonal},
journal = {Mathematics of Operations Research},
volume = {2},
year = {1977},
pages = {338-342.},
abstract = {It is. proved that every continuous value is. diagonal, which in particular implies that every value on a closed reproducing space is diagonaL We deduce als.o that there are noncontinuous values.},
author = {Abraham Neyman}
}
@article {2862,
title = {The Existence of Non-Diagonal Axiomatic Values},
journal = {Mathematics of Operations Research},
volume = {1},
year = {1976},
pages = {246--250},
author = {Abraham Neyman and Yair Tauman}
}