Study of parabolic systems with discontinuous nonlinearities arising in game theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740083
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: University of Toyama
• Principal Investigator: DEGUCHI Hideo 富山大学, 大学院理工学研究部(理学), 准教授 (30432115)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ゲーム理論 / 放物型方程式 / 不連続な非線形項 / 安定性

Outline of Final Research Achievements

The concept of Nash equilibrium has played a central role as a solution concept in game theory. However, when a game has multiple Nash equilibria, the players face a problem which equilibrium they should play. To treat this problem, Hofbauer (1999) introduced the concept of spatial dominance by means of the stability of a constant stationary solution, which corresponds to a Nash equilibrium, to a reaction-diffusion system. That a Nash equilibrium is spatially dominant means that if it initially prevails on a large finite part of the space, then it takes over the whole space in the long run. In this research project we investigated the selection criterion of spatial dominance.

Free Research Field

偏微分方程式論