Equilibrium points of nonatomic games over a nonreflexive Banach space

Nonreflexive Banach Ssd Spaces

In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions. 0 Introduction In this paper, we unify three different lines of investigation: the theory of SSD spaces as expounded in [11] and [13], part of the theory of strongly representable multifunctions ...

Anonymity in Nonatomic Games

A proximal point method in nonreflexive Banach spaces

We propose an inexact version of the proximal point method and study its properties in nonreflexive Banach spaces which are duals of separable Banach spaces, both for the problem of minimizing convex functions and of finding zeroes of maximal monotone operators. By using surjectivity results for enlargements of maximal monotone operators, we prove existence of the iterates in both cases. Then w...

On Nonatomic Banach Lattices and Hardy Spaces

We are interested in the question when a Banach space X with an unconditional basis is isomorphic (as a Banach space) to an order-continuous nonatomic Banach lattice. We show that this is the case if and only if X is isomorphic as a Banach space with X(i2). This and results of Bourgain are used to show that spaces HI (Tn) are not isomorphic to nonatomic Banach lattices. We also show that tent s...

Equilibrium Points in N - Person Games

* This note arose from consultations during the tenure of a John Simon Guggenheim Memorial Fellowship by MacLane. ' Whitehead, J. H. C., "Combinatorial Homotopy I and II," Bull. A.M.S., 55, 214-245 and 453-496 (1949). We refer to these papers as CH I and CH II, respectively. ' By a complex we shall mean a connected CW complex, as defined in §5 of CH I. We do not restrict ourselres to finite com...