Publications by Type: Journal Articles

1981
Kohlberg E, Neyman A. Asymptotic Behavior of Nonexpansive Mappings in Normed Linear Spaces. Israel Journal of Mathematics. 1981;38 :269-275.Abstract

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

Paper
Neyman A. Singular Games have Asymptotic Values. Mathematics of Operations Research. 1981;6 :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.

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

Stochastic Games have a value.

Paper
Neyman A, Dubey P, Weber RJ. Value Theory without Efficiency. Mathematics of Operations Research. 1981;6 :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.

Paper
1979
Neyman A, Tauman Y. The Partition Value. Mathematics of Operations Research. 1979;2 :236-267. Paper
1977
Neyman A. Continuous Values are Diagonal. Mathematics of Operations Research. 1977;2 :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.

Paper
1976
Neyman A, Tauman Y. The Existence of Non-Diagonal Axiomatic Values. Mathematics of Operations Research. 1976;1 :246--250. nondiagonal.pdf

Pages