Mathematical and numerical research on evolutionary games that describe population concentration and outflow

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K05005
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Osaka Prefecture University
• Principal Investigator: TABATA Minoru 大阪府立大学, 工学(系)研究科(研究院), 教授 (70207215)
• Co-Investigator(Kenkyū-buntansha): 江島 伸興 京都大学, 高大接続・入試センター, 特定教授 (20203630)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 経済地理学 / 核周辺モデル / 賃金方程式

Outline of Final Research Achievements

Spatial economics is an interdisciplinary area between economics and geography. Its purpose is to study the allocation of resources over space and the location of economic activity. Among many important nonlinear models in the NEG, one of the most fundamental models is the Krugman's Core-Periphery model. Each equilibrium of the continuous model is defined as a solution to the wage equation, which is a singular nonlinear integral equation. The wage equation is quite a new kind of integral equation that has not been fully studied mathematically. We must note that the wage equation has a singular double nonlinear structure in the sense that the equation contains a nonlinear integral operator whose integral kernel itself is expressed by another nonlinear integral operator with a singularity. It is difficult to prove the existence of solutions to the wage equation. In this study we prove the existence of solutions to the wage equation under the most general assumption.

Free Research Field

応用数学