An n-Dimensional Intermediate Value Theorem and Its Application to an n-Person Strategic Game

Abstract

Poincaré-Miranda's theorem is an n-dimensional zero-point theorem, which was conjectured by Poincaré [6] and proved by Miranda [5]. Also, Miranda [5] proved its equivalence to Brouwer's fixed point theorem. The author [3] presented an n-dimensional intermediate value theorem by using Poincaré-Miranda's theorem. He applied it to two-person and three-person strategic games with two pure strategies, and showed a range of the payoffs that can be achieved by mixed strategies. In this paper, we extend the result of [3] to an n-person strategic game.