We examine a solution concept, called the ``value," for n-person strategic games.

In applications, the value provides an a-priori assessment of the monetary worth of a player's position in a strategic game, comprising not only the player's contribution to the total payoff but also the player's ability to inflict losses on other players. A salient feature is that the value takes account of the costs that ``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.

VL - DP 706 ER - TY - Generic T1 -

The Cooperative Solution of Stochastic Games

Y1 - 2015 A1 - Abraham Neyman A1 - Elon Kohlberg AB -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.

ER - TY - Generic T1 -Should I Remember more than you?? – on the best response to factored based strategies

Y1 - 2014 A1 - Abraham Neyman A1 - Rene Levinsky A1 - MIROSLAV ZELENY AB -In this paper we offer a new approach to modeling strategies of bounded complexity, the so-called factor-based strategies. In our model, the strategy of a player in the multi-stage game does not directly map the set of histories H to the set of her actions. Instead, the player’s perception of H is represented by a factor ϕ : H → X, where X reflects the “cognitive complexity” of the player. Formally, mapping ϕ sends each history to an element of a factor space X that represents its equivalence class. The play of the player can then be conditioned just on the elements of the set X. From the perspective of the original multi-stage game we say that a function ϕ from H to X is a factor of a strategy σ if there exists a function ω from X to the set of actions of the player such that σ = ω ◦ ϕ. In this case we say that the strategy σ is ϕ-factorbased. Stationary strategies and strategies played by finite automata and strategies with bounded recall are the most prominent examples of factor-based strategies. In the discounted infinitely repeated game with perfect monitoring, a best reply to a profile of ϕ-factor-based strategies need not be a ϕ-factor-based strategy. However, if the factor ϕ is recursive, namely, its value ϕ(a(1), . . . , a(t)) on a finite string of action profiles (a(1), . . . , a(t)) is a function of ϕ(a(1), . . . , a(t−1)) and at, then for every profile of factor-based strategies there is a best reply that is a pure factor-based strategy. We also study factor-based strategies in the more general case of stochastic games.

ER - TY - JOUR T1 -Online Concealed Correlation and Bounded Rationality

JF - Games and Economic Behavior Y1 - 2014 A1 - Abraham Neyman A1 - Gilad Bavly AB -Correlation of players’ actions may evolve in the common course of the play of a repeated game with perfect monitoring (“online correlation”). In this paper we study the concealment of such correlation from a boundedly rational player. We show that “strong” players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate the online correlation of the actions of “weak” players, where this correlation is concealed from an opponent of “intermediate” strength. The feasibility of such “online concealed correlation” 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.

ER - TY - JOUR T1 -Stochastic Games with Short-Stage Duration

JF - Dyn Games Appl Y1 - 2013 A1 - Abraham Neyman AB -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.

VL - 3 ER - TY - JOUR T1 -The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information

JF - Journal of Theoretical Probability Y1 - 2013 A1 - Abraham Neyman AB -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.

ER - TY - Generic T1 -Continuous-Time Stochastic Games

Y1 - 2012 A1 - Abraham Neyman AB -Every continuous-time stochastic game with finitely many states and actions has a uniform and limiting-average equilibrium payoff.

ER - TY - JOUR T1 -The Value of Two-Person Zero-Sum Repeated Games with Incomplete Information and Uncertain Duration

JF - International Journal of Game Theory Y1 - 2012 A1 - Abraham Neyman AB -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' information about the uncertain number of repetitions is asymmetric.

VL - 41 ER - TY - JOUR T1 -Singular Games in bv'NA

JF - Journal of Mathematical Economics Y1 - 2010 A1 - Abraham Neyman AB -Every simple game in bv'NA is a weighted majority game, and every game in bv'NA is a sume of a game in pNA and a convergent series of singular scalar measure games.

ER - TY - JOUR T1 -Complexity and Effective Prediction

JF - Games and Economic Behavior Y1 - 2010 A1 - Abraham Neyman A1 - Joel Spencer AB -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 “smart” in the sense that k is large but player 2 is “much smarter” 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’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).

ER - TY - JOUR T1 -Repeated Games with Public Uncertain Duration Process

JF - International Journal of Game Theory Y1 - 2010 A1 - Abraham Neyman A1 - Sylvain Sorin AB -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.

ER - TY - JOUR T1 -Absorbing Games with Compact Action Spaces

JF - Mathematics of Operations Research Y1 - 2009 A1 - Abraham Neyman A1 - J. F. Mertens A1 - D. Rosenberg AB -We prove that games with absorbing states with compact action sets have a value.

VL - 34 ER - TY - JOUR T1 -Growth of Strategy Sets, Entropy, and Nonstationary Bounded Recall

JF - Games and Economic Behavior Y1 - 2009 A1 - Abraham Neyman A1 - Daijiro Okada AB -The paper initiates the study of long term interactions where players’ 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

ER - TY - JOUR T1 -Existence of Optimal Strategies in Markov Games with Incomplete Information

JF - International Journal of Game Theory Y1 - 2008 A1 - Abraham Neyman AB -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' 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' 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.

ER - TY - Generic T1 -Learning Effectiveness and Memory Size

Y1 - 2008 A1 - Abraham Neyman JF - Center for the Study of Rationality, Hebrew University. VL - DP 476 ER - TY - Generic T1 -Public Goods and Budget Deficit

Y1 - 2006 A1 - Abraham Neyman A1 - Tim Russo AB -We examine incentive-compatible mechanisms for fair financing and efficient selection of a public budget (or public good). A mechanism selects the level of the public budget and imposes taxes on individuals. Individuals' preferences are quasilinear. Fairness is expressed as weak monotonicity (called scale monotonicity) of the tax imposed on an individual as a function of his benefit from an increased level of the public budget. Efficiency is expressed as selection of a Pareto-optimal level of the public budget. The budget deficit is the difference between the public budget and the total amount of taxes collected from the individuals. We show that any efficient scale-monotonic and incentive-compatible mechanism may generate a budget deficit. Moreover, it is impossible to collect taxes that always cover a fixed small fraction of the total cost.

JF - Center for the Study of Rationality, Hebrew University. ER - TY - JOUR T1 -Aumann Awarded Nobel Prize

JF - Notices of the AMS Y1 - 2006 A1 - Abraham Neyman VL - 53 ER - TY - JOUR T1 -Optimal Use of Communication Resources

JF - Econometrica Y1 - 2006 A1 - Abraham Neyman A1 - Olivier Gossner A1 - Penelope Hernandez AB -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.

ER - TY - JOUR T1 -Asymptotic Values of Vector Measure Games

JF - Mathematics of Operations Research Y1 - 2004 A1 - Abraham Neyman A1 - Rann Smordinsky AB -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.

ER - TY - JOUR T1 -Dynamiques de Communication

JF - Dynamiques de Communication Y1 - 2004 A1 - Abraham Neyman A1 - Gossner Olivier A1 - Penelope Hernandez VL - 55 ER - TY - Generic T1 -Online Information Transmission

Y1 - 2003 A1 - Abraham Neyman A1 - Olivier Gossner A1 - Penelope Hernandez ER - TY - CHAP T1 -From Markov chains to stochastic games

T2 - Kluwer Academic Publishers Y1 - 2003 A1 - Abraham Neyman ED - Abraham Neyman ED - Sylvain Sorin JF - Kluwer Academic Publishers PB - Kluwer Academic Publishers CY - Dordrecht / Boston / London ER - TY - CHAP T1 -Stochastic games: Existence of the minmax

T2 - Kluwer Academic Publishers Y1 - 2003 A1 - Abraham Neyman ED - Abraham Neyman ED - Sylvain Sorin JF - Kluwer Academic Publishers PB - Kluwer Academic Publishers ER - TY - CHAP T1 -Real algebraic tools in stochastic games

T2 - Kluwer Academic Publishers Y1 - 2003 A1 - Abraham Neyman ED - Abraham Neyman ED - Sylvain Sorin JF - Kluwer Academic Publishers PB - Kluwer Academic Publishers ER - TY - CHAP T1 -Stochastic games and nonexpansive maps

T2 - Stochastic Games Y1 - 2003 A1 - Abraham Neyman ED - Abraham Neyman ED - Sylvain Sorin JF - Stochastic Games PB - Kluwer Academic Publishers ER - TY - JOUR T1 -A value on `AN

JF - International Journal of Game Theory Y1 - 2003 A1 - Abraham Neyman A1 - J. F. Mertens AB -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.

ER - TY - Generic T1 -Online Concealed Correlation by Boundedly Rational Players

Y1 - 2003 A1 - Abraham Neyman A1 - Gilad Bavly AB -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.

JF - Center for the Study of Rationality, DP336 ER - TY - Generic T1 -Online Matching Pennies

Y1 - 2003 A1 - Olivier Gossner A1 - Penelope Hernandez A1 - Abraham Neyman AB -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.

JF - Center for the Study of Rationality, Discussion Paper 316 ER - TY - BOOK T1 -Stochastic Games and Applications

Y1 - 2003 A1 - Abraham Neyman A1 - Sylvain Sorin PB - Kluwer Academic Publishers ER - TY - CHAP T1 -Values of Games with Infinitely Many Players

T2 - Handbook of Game Theory, with Economic Applications Y1 - 2002 A1 - Abraham Neyman ED - Roberth J. Aumann ED - sergiu hart JF - Handbook of Game Theory, with Economic Applications PB - North-Holland CY - Amsterdam VL - 3 ER - TY - JOUR T1 -Values of Non-Atomic Vector Measure Games

JF - Israel Journal of Mathematics Y1 - 2001 A1 - Abraham Neyman AB -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.

VL - 124 ER - TY - JOUR T1 -Repeated games with bounded entropy

JF - Games and Economic Behavior Y1 - 2000 A1 - Abraham Neyman A1 - Daijiro Okada AB -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.

VL - 30 ER - TY - JOUR T1 -Two-person repeated games with finite automata

JF - International Journal of Game Theory Y1 - 2000 A1 - Abraham Neyman A1 - Daijiro Okada AB -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.

VL - 29 ER - TY - JOUR T1 -A strong law of large numbers for nonexpansive vector-valued stochastic processes

JF - Israel Journal of Mathematics Y1 - 1999 A1 - Elon Kohlberg A1 - Abraham Neyman VL - 111 ER - TY - JOUR T1 -Cooperation in Repeated Games when the Number of Stages is not Commonly Known

JF - Econometrica Y1 - 1999 A1 - Abraham Neyman AB -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

VL - 67 ER - TY - JOUR T1 -Strategic entropy and complexity in repeated games

JF - Games and Economic Behavior Y1 - 1999 A1 - Abraham Neyman A1 - Daijiro Okada AB -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.

VL - 29 ER - TY - JOUR T1 -Equilibria in Repeated Games with Incomplete Information: The General Symmetric Case

JF - International Journal of Game Theory Y1 - 1998 A1 - Abraham Neyman A1 - Sylvain Sorin AB -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.

VL - 27 ER - TY - JOUR T1 -Finitely Repeated Games with Finite Automata

JF - Mathematics of Operations Research Y1 - 1998 A1 - Abraham Neyman AB -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.

VL - 23 ER - TY - JOUR T1 -Correlated Equilibrium and Potential Games

JF - International Journal of Game Theory Y1 - 1997 A1 - Abraham Neyman AB -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.

VL - 26 ER - TY - CHAP T1 -Cooperation, Repetition and Automata

T2 - Cooperation: Game-Theoretic Approaches, NATO ASI Series Y1 - 1997 A1 - Abraham Neyman ED - sergiu hart ED - Andreu Mas-Colell JF - Cooperation: Game-Theoretic Approaches, NATO ASI Series VL - 155 ER - TY - JOUR T1 -Equilibria in Repeated Games with Incomplete Information: The Deterministic Symmetric Case

JF - Kluwer Academic Publishers Y1 - 1997 A1 - Abraham Neyman A1 - Sylvain Sorin ER - TY - BOOK T1 -Games and Economic Theory: Selected Contributions in Honor of Robert J. Aumann

Y1 - 1995 A1 - Abraham Neyman A1 - sergiu hart PB - The University of Michigan Press CY - Michigan ER - TY - CHAP T1 -Values of Games with a Continuum of Players

T2 - Game-Theoretic Methods in General Equilibrium Analysis Y1 - 1994 A1 - Abraham Neyman ED - Jean-Francois Mertens ED - Sylvain Sorin JF - Game-Theoretic Methods in General Equilibrium Analysis PB - Kluwer Academic Publishers CY - Amsterdam ER - TY - JOUR T1 -Value of Games with a Continuum of Players

JF - Game-Theoretic Methods in General Equilibrium Analysis Y1 - 1994 VL - 77 ER - TY - CHAP T1 -An Axiomatic Approach to the Equivalence Phenomenon

T2 - Game-Theoretic Methods in General Equilibrium Analysis Y1 - 1994 A1 - Pradeep Dubey A1 - Abraham Neyman ED - Jean-Francois Mertens ED - Sylvain Sorin JF - Game-Theoretic Methods in General Equilibrium Analysis PB - Kluwer Academic Publishers CY - Dordrecht / Boston / London VL - 77 ER - TY - JOUR T1 -An Equivalence Principle for Perfectly Competitive Economies

JF - Journal of Economic Theory Y1 - 1994 A1 - Abraham Neyman A1 - Pradeep Dubey AB -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.

VL - 75 ER - TY - JOUR T1 -The Positive Value of Information

JF - Games and Economic Behavior Y1 - 1991 A1 - Abraham Neyman AB -It has been remarked that in rational interactions more information to one player, while all others' 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.

VL - 3 ER - TY - JOUR T1 -On Non-Atomic Weighted Majority Games

JF - Journal of Mathematical Economics Y1 - 1990 A1 - Abraham Neyman A1 - Ezra.Einy VL - 19 ER - TY - BOOK T1 -Game Theory and Applications

Y1 - 1990 A1 - Abraham Neyman A1 - T. Ichiishi A1 - Y. Tauman PB - Harcourt Brace Jovanovich, ER - TY - JOUR T1 -Large Symmetric Games are Characterized by Completeness of the Desirability Relation

JF - Journal of Economic Theory Y1 - 1989 A1 - E.Einy A1 - Abraham Neyman VL - 148 ER - TY - JOUR T1 -Uniqueness of the Shapley Value

JF - Games and Economic Behavior Y1 - 1989 A1 - Abraham Neyman AB -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.

VL - 1 ER - TY - JOUR T1 -Values of Vector Measure Games: Are They Linear Combinations of the Measures?

JF - Journal of Mathematical Economics Y1 - 1988 A1 - Abraham Neyman A1 - sergiu hart VL - 17 ER - TY - JOUR T1 -Weighted Majority Games have an Asymptotic Value

JF - Mathematics of Operations Research Y1 - 1988 A1 - Abraham Neyman VL - 13 ER - TY - JOUR T1 -Payoffs in Non-Atomic Games: An Axiomatic Approach

JF - The Shapley Value, A. Roth (ed.), Cambridge Univ. Press Y1 - 1988 A1 - Abraham Neyman A1 - Pradeep Dubey ER - TY - JOUR T1 -Values of Smooth Non-Atomic Games: The Method of Multilinear Approximation

JF - The Shapley Value, A. Roth (ed.), Cambridge Univ. Press Y1 - 1988 A1 - Abraham Neyman A1 - Dov Monderer ER - TY - JOUR T1 -Power and Public Goods

JF - Journal of Economic Theory Y1 - 1987 A1 - Robert J. Aumann A1 - M. Kurtz A1 - Abraham Neyman VL - 42 ER - TY - JOUR T1 -A Counter-Example to the Folk Theorem with Discounting

JF - Economic Letters Y1 - 1986 A1 - F. Forges A1 - J. F. Mertens A1 - Abraham Neyman VL - 19 ER - TY - JOUR T1 -Bounded Complexity Justifies Cooperation in the Finitely Repeated Prisoner's Dilemma

JF - Economic Letters Y1 - 1985 A1 - Abraham Neyman VL - 19 ER - TY - JOUR T1 -Diagonality of Cost Allocation Prices

JF - Mathematics of Operations Research Y1 - 1984 A1 - Leonard J. Mirman A1 - Abraham Neyman VL - 9 ER - TY - JOUR T1 -Payoffs of Non-Atomic Markets: An Axiomatic Approach

JF - Econometrica Y1 - 1984 A1 - Pradeep Dubey A1 - Abraham Neyman VL - 52 ER - TY - JOUR T1 -Representation of Lp-Norms and Isometric Embedding in Lp-Spaces

JF - Israel Journal of Mathematics Y1 - 1984 A1 - Abraham Neyman VL - 48 ER - TY - JOUR T1 -Semi-Values of Political Economic Games

JF - Mathematics of Operations Research Y1 - 1984 A1 - Abraham Neyman AB -The class of continuous semivalues is completely characterized for various spaces of nonatomic games.

VL - 10 ER - TY - JOUR T1 -Convergence in Hilbert's Metric and Convergence in Directions

JF - Journal of Mathematical Analysis and Applications Y1 - 1983 A1 - E. Kohlberg A1 - Abraham Neyman VL - 93 ER - TY - JOUR T1 -Prices for Homogeneous Cost Functions

JF - Journal of Mathematical Economics Y1 - 1983 A1 - Leonard J. Mirman A1 - Abraham Neyman AB -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.

VL - 12 ER - TY - JOUR T1 -Voting for Public Goods

JF - Review of Economic Studies Y1 - 1983 A1 - Robert J. Aumann A1 - M. Kurtz A1 - Abraham Neyman AB -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.

VL - 50 ER - TY - JOUR T1 -Nim-Type Games

JF - International Journal of Game Theory Y1 - 1982 A1 - D. Gale A1 - Abraham Neyman VL - 11 ER - TY - JOUR T1 -Integrals of Production Sets with Restricted Substitution

JF - Journal of Mathematical Economics Y1 - 1982 A1 - Abraham Neyman A1 - Werner Hildenbrand AB -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.

VL - 9 ER - TY - JOUR T1 -Renewal Theory for Sampling without Replacement

JF - Annals of Probability Y1 - 1982 A1 - Abraham Neyman VL - 10 ER - TY - JOUR T1 -Stochastic Games have a Value

JF - Proceedings of the National Academy of Sciences Y1 - 1982 A1 - J. F. Mertens A1 - Abraham Neyman AB -Undiscounted nontenninating stochastic games in which the state and action spaces are finite have a value.

VL - 79 ER - TY - JOUR T1 -Minimax Theorems for Undiscounted Stochastic Games

JF - Game Theory and Mathematical Economics Y1 - 1981 A1 - J.-F. Mertens A1 - Abraham Neyman ER - TY - JOUR T1 -Decomposition of Ranges of Vector Measures

JF - Israel Journal of Mathematics Y1 - 1981 A1 - Abraham Neyman VL - 40 ER - TY - JOUR T1 -Asymptotic Behavior of Nonexpansive Mappings in Normed Linear Spaces

JF - Israel Journal of Mathematics Y1 - 1981 A1 - Elon Kohlberg A1 - Abraham Neyman AB -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.

VL - 38 ER - TY - JOUR T1 -Asymptotic Behavior of Nonexpansive Mappings in Uniformly Convex Banach Spaces

JF - American Mathematical Monthly Y1 - 1981 A1 - Elon Kohlberg A1 - Abraham Neyman VL - 88 ER - TY - JOUR T1 -Singular Games have Asymptotic Values

JF - Mathematics of Operations Research Y1 - 1981 A1 - Abraham Neyman AB -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.

VL - 6 ER - TY - JOUR T1 -Stochastic Games

JF - International Journal of Game Theory Y1 - 1981 A1 - J. F. Mertens A1 - Abraham Neyman AB -Stochastic Games have a value.

VL - 10 ER - TY - JOUR T1 -Value Theory without Efficiency

JF - Mathematics of Operations Research Y1 - 1981 A1 - Abraham Neyman A1 - Pradeep Dubey A1 - Roberth J. Weber AB -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.

VL - 6 ER - TY - Generic T1 -Asymptotic Values of Mixed Games

T2 - Game Theory and Related Topics Y1 - 1979 A1 - Abraham Neyman JF - Game Theory and Related Topics ER - TY - JOUR T1 -The Partition Value

JF - Mathematics of Operations Research Y1 - 1979 A1 - Abraham Neyman A1 - Yair Tauman VL - 2 ER - TY - JOUR T1 -Continuous Values are Diagonal

JF - Mathematics of Operations Research Y1 - 1977 A1 - Abraham Neyman AB -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.

VL - 2 ER - TY - CONF T1 -The Limiting Behavior of the Shapley Value in a Class of Games with Many Players

T2 - Cahiers du Centre d'Etudes de Recherche Operationelle Y1 - 1976 A1 - Abraham Neyman JF - Cahiers du Centre d'Etudes de Recherche Operationelle VL - 18 ER - TY - JOUR T1 -The Existence of Non-Diagonal Axiomatic Values

JF - Mathematics of Operations Research Y1 - 1976 A1 - Abraham Neyman A1 - Yair Tauman VL - 1 ER -