不完全市場一般均衡的存在性問題

Abstract

Brouwer不動點定理是證明完全市場一般均衡存在性的關鍵。然而 [4] 指出在不完全市場下，一般均衡未必存在。本篇論文中我們綜合 [2]、[6] 的方法，利用Grassmannian流形的mod 2尤拉示性數不變的特性，得到類似的不動點定理，進而證明了不完全市場下，條件較弱的「假均衡」(Pseudo-equilibrium) 存在。論文最後討論一般均衡的普遍性，即一般均衡存在的經濟體是一稠密的開集合。

Brouwer’s fixed point theorem is critical to the existence of general equilibria in a complete market. However, [4] pointed out that in an incomplete market, a general equilibrium does not always exist. In this paper, following [2] and [6], we use the invariant property of mod 2 Euler number of Grassmannian manifold to derive a fixed-point-like theorem, and therefore, prove the existence of a weaker “pseudo-equilibrium”. At last, we discuss the genericity of general equilibria, that is, the economy in which the equilibria exist is an open and dense set.