This paper provides simple proofs of a theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem.

This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that...

In this paper I study a class of two-player games, in which both players’ action sets are [0,1] and their payoff functions are continuous in joint actions and quasi-concave in own actions. I show that a no-improper-crossing condition is both necessary and sufficient for a finite subset A of <InlineEquation ID="Equ1"> <EquationSource...</equationsource></inlineequation>