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Study of parabolic systems with discontinuous nonlinearities arising in game theory

Research Project

Project/Area Number 24740083
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionUniversity 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
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsゲーム理論 / 放物型方程式 / 不連続な非線形項 / 安定性 / 進行波解
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.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (2 results)

All 2013 2012

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (1 results)

  • [Journal Article] The wave equation with a discontinuous coefficient depending on time only: generalized solutions and propagation of singularities2013

    • Author(s)
      H. Deguchi, G. Hoermann and M. Oberguggenberger
    • Journal Title

      Pseudo-Differential Operators, Generalized Functions and Asymptotics, Operator Theory: Advances and Applications

      Volume: 231 Pages: 323-339

    • DOI

      10.1007/978-3-0348-0585-8_18

    • ISBN
      9783034805841, 9783034805858
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] The wave equation with a discontinuous coefficient depending on time only: generalized solutions and propagation of singularities2012

    • Author(s)
      Hideo Deguchi
    • Organizer
      International conference "PDE, Microlocal and Time-frequency Analysis"
    • Place of Presentation
      University of Novi Sad, Serbia
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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