The class of continuous semivalues is completely characterized for various spaces of nonatomic games.

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.

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.

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.

Undiscounted nontenninating stochastic games in which the state and action spaces are finite have a value.

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.