We provide an elementary mathematical description of the spread of the coronavirus. We explain two fundamental relationships: How the rate of growth in new infections is determined by the “effective reproductive number”; and how the effective reproductive number is affected by social distancing. By making a key approximation, we are able to formulate these relationships very simply and thereby avoid complicated mathematics. The same approximation leads to an elementary method for estimating the effective eproductive

number.

The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage.

The undiscounted Big Match has been much-studied. Blackwell and Ferguson (1968) give an epsilon-optimal

strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends on just the clock or just a finite memory is worthless (i.e., cannot guarantee strictly more than the least reward). The long-standing natural open problem has been whether every strategy that depends on just the clock and a nite memory is worthless.

The present paper proves that there is such a strategy that is epsilon-optimal. In fact, we show that just two states of memory are sfficient.

This paper characterizes the preferences over bounded infinite utility streams that satisfy the time value of money principle and an additivity property, and preferences that in addition are impatient. Based on this characterization, the paper introduces a concept of optimization that is robust to a small imprecision in the specification of the preference, and proves that the set of feasible streams of payoffs of a finite Markov decision process admits such a robust optimization.

%G eng %0 Journal Article %J Games and Economic Behavior %D Forthcoming %T Absorbing games with a clock and two bits of memory %A K. A. Hansen %A R. Ibsen-Jensen %A A. Neyman %X An absorbing game is a two-person zero-sum repeated game. Some of the entries are ``absorbing'' in the sense that, following the play of an absorbing entry, with positive probability all future payoffs are equal to that entry's payoff. The outcome of the game is the long-run average payoff.

We prove that a two-person zero-sum absorbing game, with either finite or compact action sets, has, for each e>0, e-optimal strategies with finite memory. In fact, we show that there is an e-optimal strategy that depends on the clock and three states of memory.

The value is a solution concept for n-person strategic games, developed by Nash,

Shapley, and Harsanyi. The value of a game is an a priori evaluation of the economic

worth of the position of each player, reflecting the players’ strategic possibilities,

including their ability to make threats against one another. Applications of the value in economics have been rare, at least in part because the existing definition (for games with more than two players) consists of an ad hoc scheme that does not easily lend itself to computation. This paper makes three contributions: We provide an axiomatic foundation for the value; exhibit a simple formula for its computation; and extend the value—its definition, axiomatic characterization, and computational formula—to Bayesian games. We then apply the value in simple models of corruption, oligopolistic competition, and information sharing.

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.

%B International Journal of Game Theory %V 49 %P 1105--1124 %8 2020 %G eng %U https://www.researchgate.net/publication/50252346_Should_I_remember_more_than_you_On_the_best_response_to_factor-based_strategies %N 6 %0 Journal Article %J Games and Economic Behavior %D 2018 %T Games of Threats. %A Elon Kohlberg %A Abraham Neyman %XA game of threats on a finite set of players, *N*, is a function *d* that assigns a real number to any coalition, S⊆N, such that d(S)=−d(N∖S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(∅)=0. We show that analogs of the classic Shapley axioms for coalitional games determine a unique value for games of threats. This value assigns to each player an average of d(S) across all the coalitions that include the player. Games of threats arise naturally in value theory for strategic games, and may have applications in other branches of game theory.

The value is a solution concept for n-person strategic games, developed by Nash, Shapley, and Harsanyi. The value of a game is an a priori evaluation of the economic worth of the position of each player, reflecting the players' strategic possibilities, including their ability to make threats against one another. Applications of the value in economics have been rare, at least in part because the existing definition (for games with more than two players)

consists of an ad hoc scheme that does not easily lend itself to computation.

This paper makes three contributions: We provide an axiomatic foundation for the value; exhibit a simple formula for its computation; and extend the value -- its definition, axiomatic characterization, and computational formula -- to Bayesian games. We then apply the value in simple models of corruption, oligopolistic competition, and information sharing.

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.

%B The Federmann Center for the Study of Rationality, Hebrew University %V DP 706 %G eng %0 Journal Article %J Games and Economic Behavior %D 2017 %T Continuous-Time Stochastic Games. %A Abraham Neyman %B Games and Economic Behavior %V 104 %P 92-130 %G eng %U https://ac.els-cdn.com/S0899825617300301/1-s2.0-S0899825617300301-main.pdf?_tid=5d1db742-c398-11e7-85bc-00000aacb360&acdnat=1510044662_36ce4b7b16597a71095aa66463f3e977 %0 Manuscript %D 2015 %T

The Cooperative Solution of Stochastic Games

%A Abraham Neyman %A Elon Kohlberg %XBuilding 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.

%G eng %0 Journal Article %J Games and Economic Behavior %D 2014 %TOnline Concealed Correlation and Bounded Rationality

%A Abraham Neyman %A Gilad Bavly %XCorrelation 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.

%B Games and Economic Behavior %P 71 - 89 %G eng %0 Journal Article %J Dyn Games Appl %D 2013 %TStochastic Games with Short-Stage Duration

%A Abraham Neyman %XWe 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.

%B Dyn Games Appl %V 3 %P 236-278 %G eng %0 Journal Article %J Journal of Theoretical Probability %D 2013 %TThe Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information

%A Abraham Neyman %XThe 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.

%B Journal of Theoretical Probability %P 557-567 %G eng %0 Manuscript %D 2012 %TContinuous-Time Stochastic Games

%A Abraham Neyman %XEvery continuous-time stochastic game with finitely many states and actions has a uniform and limiting-average equilibrium payoff.

%G eng %0 Journal Article %J International Journal of Game Theory %D 2012 %T The Value of Two-Person Zero-Sum Repeated Games with Incomplete Information and Uncertain Duration %A Abraham Neyman %XIt 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.

%B International Journal of Game Theory %V 41 %P 195-207 %G eng %0 Journal Article %J Journal of Mathematical Economics %D 2010 %TSingular Games in bv'NA

%A Abraham Neyman %XEvery 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.

%B Journal of Mathematical Economics %P 384 - 387 %G eng %0 Journal Article %J Games and Economic Behavior %D 2010 %TComplexity and Effective Prediction

%A Abraham Neyman %A Joel Spencer %XLet 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).

%B Games and Economic Behavior %P 165-168 %G eng %0 Journal Article %J International Journal of Game Theory %D 2010 %TRepeated Games with Public Uncertain Duration Process

%A Abraham Neyman %A Sylvain Sorin %XWe 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.

%B International Journal of Game Theory %P 29-52 %G eng %0 Journal Article %J Mathematics of Operations Research %D 2009 %TAbsorbing Games with Compact Action Spaces

%A Abraham Neyman %A J. F. Mertens %A D. Rosenberg %XWe prove that games with absorbing states with compact action sets have a value.

%B Mathematics of Operations Research %V 34 %P 257-262 %G eng %0 Journal Article %J Games and Economic Behavior %D 2009 %TGrowth of Strategy Sets, Entropy, and Nonstationary Bounded Recall

%A Abraham Neyman %A Daijiro Okada %XThe 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

%B Games and Economic Behavior %P 404-425 %G eng %0 Journal Article %J International Journal of Game Theory %D 2008 %TExistence of Optimal Strategies in Markov Games with Incomplete Information

%A Abraham Neyman %XThe 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.

%B International Journal of Game Theory %P 581 - 596 %G eng %0 Manuscript %D 2008 %TLearning Effectiveness and Memory Size

%A Abraham Neyman %B Center for the Study of Rationality, Hebrew University. %V DP 476 %G eng %0 Manuscript %D 2006 %TPublic Goods and Budget Deficit

%A Abraham Neyman %A Tim Russo %XWe 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.

%B Center for the Study of Rationality, Hebrew University. %G eng %0 Journal Article %J Notices of the AMS %D 2006 %TAumann Awarded Nobel Prize

%A Abraham Neyman %B Notices of the AMS %V 53 %P 44 - 46 %G eng %0 Journal Article %J Econometrica %D 2006 %TOptimal Use of Communication Resources

%A Abraham Neyman %A Olivier Gossner %A Penelope Hernandez %XWe 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.

%B Econometrica %P 1603 - 1636 %G eng %0 Journal Article %J Mathematics of Operations Research %D 2004 %TAsymptotic Values of Vector Measure Games

%A Abraham Neyman %A Rann Smordinsky %XThe 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.

%B Mathematics of Operations Research %P 739 - 775 %G eng %0 Journal Article %J Dynamiques de Communication %D 2004 %TDynamiques de Communication

%A Abraham Neyman %A Gossner Olivier %A Penelope Hernandez %B Dynamiques de Communication %V 55 %P 509 - 516 %G eng %0 Generic %D 2003 %TOnline Information Transmission

%A Abraham Neyman %A Olivier Gossner %A Penelope Hernandez %G eng %0 Book Section %B Kluwer Academic Publishers %D 2003 %TFrom Markov chains to stochastic games

%A Abraham Neyman %E Abraham Neyman %E Sylvain Sorin %B Kluwer Academic Publishers %7 2003 %I Kluwer Academic Publishers %C Dordrecht / Boston / London %P 9--25 %G eng %0 Book Section %B Kluwer Academic Publishers %D 2003 %TStochastic games: Existence of the minmax

%A Abraham Neyman %E Abraham Neyman %E Sylvain Sorin %B Kluwer Academic Publishers %I Kluwer Academic Publishers %P 173--193 %G eng %0 Book Section %B Kluwer Academic Publishers %D 2003 %TReal algebraic tools in stochastic games

%A Abraham Neyman %E Abraham Neyman %E Sylvain Sorin %B Kluwer Academic Publishers %I Kluwer Academic Publishers %P 58--75. %G eng %0 Book Section %B Stochastic Games %D 2003 %TStochastic games and nonexpansive maps

%A Abraham Neyman %E Abraham Neyman %E Sylvain Sorin %B Stochastic Games %I Kluwer Academic Publishers %P 397--415. %G eng %0 Journal Article %J International Journal of Game Theory %D 2003 %TA value on `AN

%A Abraham Neyman %A J. F. Mertens %XWe 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.

%B International Journal of Game Theory %P 109-120 %G eng %0 Manuscript %D 2003 %TOnline Concealed Correlation by Boundedly Rational Players

%A Abraham Neyman %A Gilad Bavly %XIn 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.

%B Center for the Study of Rationality, DP336 %P DP-336 %G eng %0 Manuscript %D 2003 %TOnline Matching Pennies

%A Olivier Gossner %A Penelope Hernandez %A Abraham Neyman %XWe 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.

%B Center for the Study of Rationality, Discussion Paper 316 %G eng %0 Book %D 2003 %TStochastic Games and Applications

%A Abraham Neyman %A Sylvain Sorin %7 NATO ASI series %I Kluwer Academic Publishers %G eng %0 Book Section %B Handbook of Game Theory, with Economic Applications %D 2002 %TValues of Games with Infinitely Many Players

%A Abraham Neyman %E Roberth J. Aumann %E sergiu hart %B Handbook of Game Theory, with Economic Applications %I North-Holland %C Amsterdam %V 3 %P 2121--2167. %G eng %0 Journal Article %J Israel Journal of Mathematics %D 2001 %TValues of Non-Atomic Vector Measure Games

%A Abraham Neyman %XMuch 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.

%B Israel Journal of Mathematics %V 124 %P 1-27 %G eng %0 Journal Article %J Games and Economic Behavior %D 2000 %TRepeated games with bounded entropy

%A Abraham Neyman %A Daijiro Okada %XWe 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.

%B Games and Economic Behavior %V 30 %P 228--247 %G eng %0 Journal Article %J International Journal of Game Theory %D 2000 %TTwo-person repeated games with finite automata

%A Abraham Neyman %A Daijiro Okada %XWe 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.

%B International Journal of Game Theory %V 29 %P 309--325 %G eng %0 Journal Article %J Israel Journal of Mathematics %D 1999 %TA strong law of large numbers for nonexpansive vector-valued stochastic processes

%A Elon Kohlberg %A Abraham Neyman %B Israel Journal of Mathematics %V 111 %P 93-108 %G eng %0 Journal Article %J Econometrica %D 1999 %TCooperation in Repeated Games when the Number of Stages is not Commonly Known

%A Abraham Neyman %XIt 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

%B Econometrica %V 67 %P 45--64 %G eng %0 Journal Article %J Games and Economic Behavior %D 1999 %TStrategic entropy and complexity in repeated games

%A Abraham Neyman %A Daijiro Okada %XWe 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.

%B Games and Economic Behavior %V 29 %P 191--223 %G eng %0 Journal Article %J International Journal of Game Theory %D 1998 %TEquilibria in Repeated Games with Incomplete Information: The General Symmetric Case

%A Abraham Neyman %A Sylvain Sorin %XEvery 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.

%B International Journal of Game Theory %V 27 %P 201--210 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1998 %TFinitely Repeated Games with Finite Automata

%A Abraham Neyman %XEvery 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.

%B Mathematics of Operations Research %V 23 %P 513--552 %G eng %0 Journal Article %J International Journal of Game Theory %D 1997 %TCorrelated Equilibrium and Potential Games

%A Abraham Neyman %XAny 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.

%B International Journal of Game Theory %V 26 %P 223--227. %G eng %0 Book Section %B Cooperation: Game-Theoretic Approaches, NATO ASI Series %D 1997 %TCooperation, Repetition and Automata

%A Abraham Neyman %E sergiu hart %E Andreu Mas-Colell %B Cooperation: Game-Theoretic Approaches, NATO ASI Series %V 155 %P 233--255 %G eng %0 Journal Article %J Kluwer Academic Publishers %D 1997 %TEquilibria in Repeated Games with Incomplete Information: The Deterministic Symmetric Case

%A Abraham Neyman %A Sylvain Sorin %B Kluwer Academic Publishers %P 129--131. %G eng %0 Book %D 1995 %TGames and Economic Theory: Selected Contributions in Honor of Robert J. Aumann

%A Abraham Neyman %A sergiu hart %I The University of Michigan Press %C Michigan %G eng %0 Book Section %B Game-Theoretic Methods in General Equilibrium Analysis %D 1994 %TValues of Games with a Continuum of Players

%A Abraham Neyman %E Jean-Francois Mertens %E Sylvain Sorin %B Game-Theoretic Methods in General Equilibrium Analysis %I Kluwer Academic Publishers %C Amsterdam %P 67--79 %G eng %0 Journal Article %J Game-Theoretic Methods in General Equilibrium Analysis %D 1994 %TValue of Games with a Continuum of Players

%B Game-Theoretic Methods in General Equilibrium Analysis %V 77 %P 67--79 %G eng %0 Book Section %B Game-Theoretic Methods in General Equilibrium Analysis %D 1994 %TAn Axiomatic Approach to the Equivalence Phenomenon

%A Pradeep Dubey %A Abraham Neyman %E Jean-Francois Mertens %E Sylvain Sorin %B Game-Theoretic Methods in General Equilibrium Analysis %I Kluwer Academic Publishers %C Dordrecht / Boston / London %V 77 %P 137--143 %G eng %0 Journal Article %J Journal of Economic Theory %D 1994 %TAn Equivalence Principle for Perfectly Competitive Economies

%A Abraham Neyman %A Pradeep Dubey %XFour 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.

%B Journal of Economic Theory %V 75 %P 314-344 %G eng %0 Journal Article %J Games and Economic Behavior %D 1991 %TThe Positive Value of Information

%A Abraham Neyman %XIt 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.

%B Games and Economic Behavior %V 3 %P 350-355 %G eng %0 Journal Article %J Journal of Mathematical Economics %D 1990 %TOn Non-Atomic Weighted Majority Games

%A Abraham Neyman %A Ezra.Einy %B Journal of Mathematical Economics %V 19 %P 391-403 %G eng %0 Book %D 1990 %TGame Theory and Applications

%A Abraham Neyman %A T. Ichiishi %A Y. Tauman %7 Academic Press %I Harcourt Brace Jovanovich, %G eng %0 Journal Article %J Journal of Economic Theory %D 1989 %TLarge Symmetric Games are Characterized by Completeness of the Desirability Relation

%A E.Einy %A Abraham Neyman %B Journal of Economic Theory %V 148 %P 369-385 %G eng %0 Journal Article %J Games and Economic Behavior %D 1989 %TUniqueness of the Shapley Value

%A Abraham Neyman %XIt 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.

%B Games and Economic Behavior %V 1 %P 116-118 %G eng %0 Journal Article %J Journal of Mathematical Economics %D 1988 %TValues of Vector Measure Games: Are They Linear Combinations of the Measures?

%A Abraham Neyman %A sergiu hart %B Journal of Mathematical Economics %V 17 %P 31-40 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1988 %TWeighted Majority Games have an Asymptotic Value

%A Abraham Neyman %B Mathematics of Operations Research %V 13 %P 556-580 %G eng %0 Journal Article %J The Shapley Value, A. Roth (ed.), Cambridge Univ. Press %D 1988 %TPayoffs in Non-Atomic Games: An Axiomatic Approach

%A Abraham Neyman %A Pradeep Dubey %B The Shapley Value, A. Roth (ed.), Cambridge Univ. Press %P 207-216. %G eng %0 Journal Article %J The Shapley Value, A. Roth (ed.), Cambridge Univ. Press %D 1988 %TValues of Smooth Non-Atomic Games: The Method of Multilinear Approximation

%A Abraham Neyman %A Dov Monderer %B The Shapley Value, A. Roth (ed.), Cambridge Univ. Press %P 217-234 %G eng %0 Journal Article %J Journal of Economic Theory %D 1987 %TPower and Public Goods

%A Robert J. Aumann %A M. Kurtz %A Abraham Neyman %B Journal of Economic Theory %V 42 %P 108-127 %G eng %0 Journal Article %J Economic Letters %D 1986 %TA Counter-Example to the Folk Theorem with Discounting

%A F. Forges %A J. F. Mertens %A Abraham Neyman %B Economic Letters %V 19 %P 227-229 %G eng %0 Journal Article %J Economic Letters %D 1985 %TBounded Complexity Justifies Cooperation in the Finitely Repeated Prisoner's Dilemma

%A Abraham Neyman %B Economic Letters %V 19 %P 227-229 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1984 %TDiagonality of Cost Allocation Prices

%A Leonard J. Mirman %A Abraham Neyman %B Mathematics of Operations Research %V 9 %P 66-74 %G eng %0 Journal Article %J Econometrica %D 1984 %TPayoffs of Non-Atomic Markets: An Axiomatic Approach

%A Pradeep Dubey %A Abraham Neyman %B Econometrica %V 52 %P 1129-1150 %G eng %0 Journal Article %J Israel Journal of Mathematics %D 1984 %TRepresentation of Lp-Norms and Isometric Embedding in Lp-Spaces

%A Abraham Neyman %B Israel Journal of Mathematics %V 48 %P 129-138. %G eng %0 Journal Article %J Mathematics of Operations Research %D 1984 %TSemi-Values of Political Economic Games

%A Abraham Neyman %XThe class of continuous semivalues is completely characterized for various spaces of nonatomic games.

%B Mathematics of Operations Research %V 10 %P 390-402 %G eng %0 Journal Article %J Journal of Mathematical Analysis and Applications %D 1983 %TConvergence in Hilbert's Metric and Convergence in Directions

%A E. Kohlberg %A Abraham Neyman %B Journal of Mathematical Analysis and Applications %V 93 %P 104-108 %G eng %0 Journal Article %J Journal of Mathematical Economics %D 1983 %TPrices for Homogeneous Cost Functions

%A Leonard J. Mirman %A Abraham Neyman %XThe 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.

%B Journal of Mathematical Economics %V 12 %P 257-273 %G eng %0 Journal Article %J Review of Economic Studies %D 1983 %TVoting for Public Goods

%A Robert J. Aumann %A M. Kurtz %A Abraham Neyman %XIt 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.

%B Review of Economic Studies %V 50 %P 677-693 %G eng %0 Journal Article %J International Journal of Game Theory %D 1982 %TNim-Type Games

%A D. Gale %A Abraham Neyman %B International Journal of Game Theory %V 11 %P 17-20 %G eng %0 Journal Article %J Journal of Mathematical Economics %D 1982 %TIntegrals of Production Sets with Restricted Substitution

%A Abraham Neyman %A Werner Hildenbrand %XIt 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.

%B Journal of Mathematical Economics %V 9 %P 71-82 %G eng %0 Journal Article %J Proceedings of the National Academy of Sciences %D 1982 %TStochastic Games have a Value

%A J. F. Mertens %A Abraham Neyman %XUndiscounted nontenninating stochastic games in which the state and action spaces are finite have a value.

%B Proceedings of the National Academy of Sciences %V 79 %P 2145-2146 %G eng %0 Journal Article %J Annals of Probability %D 1982 %T Renewal Theory for Sampling without Replacement %A Abraham Neyman %B Annals of Probability %V 10 %P 464--481 %G eng %U https://projecteuclid.org/download/pdf_1/euclid.aop/1176993870 %N 2 %0 Journal Article %J Game Theory and Mathematical Economics %D 1981 %TMinimax Theorems for Undiscounted Stochastic Games

%A J.-F. Mertens %A Abraham Neyman %B Game Theory and Mathematical Economics %P 83-87 %G eng %0 Journal Article %J Israel Journal of Mathematics %D 1981 %TDecomposition of Ranges of Vector Measures

%A Abraham Neyman %B Israel Journal of Mathematics %V 40 %P 54-64 %G eng %0 Journal Article %J Israel Journal of Mathematics %D 1981 %TAsymptotic Behavior of Nonexpansive Mappings in Normed Linear Spaces

%A Elon Kohlberg %A Abraham Neyman %XLet 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.

%B Israel Journal of Mathematics %V 38 %P 269-275 %G eng %0 Journal Article %J American Mathematical Monthly %D 1981 %TAsymptotic Behavior of Nonexpansive Mappings in Uniformly Convex Banach Spaces

%A Elon Kohlberg %A Abraham Neyman %B American Mathematical Monthly %V 88 %P 698-700 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1981 %TSingular Games have Asymptotic Values

%A Abraham Neyman %XThe 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.

%B Mathematics of Operations Research %V 6 %P 205-212 %G eng %0 Journal Article %J International Journal of Game Theory %D 1981 %TStochastic Games

%A J. F. Mertens %A Abraham Neyman %XStochastic Games have a value.

%B International Journal of Game Theory %V 10 %P 53-66 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1981 %TValue Theory without Efficiency

%A Abraham Neyman %A Pradeep Dubey %A Roberth J. Weber %XA 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.

%B Mathematics of Operations Research %V 6 %P 122--128 %G eng %0 Conference Proceedings %B Game Theory and Related Topics %D 1979 %TAsymptotic Values of Mixed Games

%A Abraham Neyman %B Game Theory and Related Topics %P 71-81 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1979 %TThe Partition Value

%A Abraham Neyman %A Yair Tauman %B Mathematics of Operations Research %V 2 %P 236-267 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1977 %TContinuous Values are Diagonal

%A Abraham Neyman %XIt 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.

%B Mathematics of Operations Research %V 2 %P 338-342. %G eng %0 Conference Paper %B Cahiers du Centre d'Etudes de Recherche Operationelle %D 1976 %TThe Limiting Behavior of the Shapley Value in a Class of Games with Many Players

%A Abraham Neyman %B Cahiers du Centre d'Etudes de Recherche Operationelle %V 18 %P 161 %G eng %0 Journal Article %J Mathematics of Operations Research %D 1976 %TThe Existence of Non-Diagonal Axiomatic Values

%A Abraham Neyman %A Yair Tauman %B Mathematics of Operations Research %V 1 %P 246--250 %G eng