Equilibria in Banach lattices without ordered preferences

Economic Theory, 1995

Journal of Mathematical Economics, 1986

Economic Theory

This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence of a continuity hypothesis that is, in principle, non-testable. It identifies topological connectedness of the (choice) set over which the continuous binary relation is defined as being crucial to this question. Referring to the two-way relationship as the Eilenberg-Sonnenschein (ES) research program, it presents four synthetic, and complete, characterizations of connectedness, and its natural extensions; and two consequences that only stem from it. The six theorems are novel to both the economic and the mathematical literature: they generalize pioneering results of Eilenberg (1941), Sonnenschein (1965), Schmeidler (1971) and Sen (1969), and are relevant to several applied contexts, as well as to ongoing theoretical work.

Journal of Mathematical Economics, 1996

This paper is intended as a companion to the paper 'Existence of non-cooperative equilibria in social systems by Prakash and Sertel(l974b) appearing in this volume. It aims to perform two tasks: (1) to give the reader a glimpse at the literature relevant to the existence of equilibria in social systems as it has developed since the writing of the Prakash and Sertel (PS) paper; and (2) to provide a class of examples illustrating where the PS notions of a social system and the non-cooperative equilibrium of a social system generalize the well-known concepts of games, abstract economies and their associated equilibria, showing how the existence theory of PS even today bears economic results beyond where alternative theories are applicable.

Economic Theory, 2008

Radner (1968) proved the existence of a competitive equilibrium for differential information economies with finitely many states. We extend this result to economies with infinitely many states of nature.