Publications by Type: Journal Articles

Kohlberg E, Neyman A. Asymptotic Behavior of Nonexpansive Mappings in Uniformly Convex Banach Spaces. American Mathematical Monthly. 1981;88 :698-700. 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.

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

Stochastic Games have a value.

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.

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

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