Adv. Math. Econ. Volume 2, pp.119-135 (2000)

Fixed point theorems and the existence of economic equilibria based on conditions for local directions of mappings

Akira Yamazaki
Graduate School of Economics, Hitotsubashi University, Kunitachi, Tokyo, 186-8601, Japan

A mathematical model of a directed graph with stochastic transfers is presented. It will be used to analyze the optimality (or "competitiveness" ) properties of a network of transactions involving risky transfers of assets in an economic system. These properties are discussed in a model with some specific directed graph structures which result in a decompositon of the graph into parts with "narrow" linkage.

stochastic transfer, network economy, directed graph, efficinecy, competitiveness