The Neural Networks Realization of Quasi-Gradient System to Search for Equilibrium Solutions in Game Theory and Their Dynamical Behavior

• HORIE Ryota

  Faculty of Science and Technology, Keio University

• AIYOSHI Eitaro

  Faculty of Science and Technology, Keio University

• MIYANO Kippei

  Faculty of Science and Technology, Keio University

Bibliographic Information

Other Title

• ゲーム理論的均衡解探索のための疑似勾配系モデルのニューラルネットワーク実現とその挙動
• ゲーム リロンテキ キンコウカイ タンサク ノ タメ ノ ギジ コウバイケイ モデル ノ ニューラル ネットワーク ジツゲン ト ソノ キョドウ

Abstract

Mutually coupled plural Neural Networks (N.N.) modules are proposed from the view point of noncooperative game theory. First, new dynamical models, which is called “Quasi-Gradient System”, to search the Nash Equilibrium (NE) points under [0, 1] -interval or nonnegative constraints are proposed. The stability of the proposed searching models is analyzed by the linearization approach. In addition, relations between the Lotka-Volterra's ecological model or the population genetics model and the proposed searching models are indicated. Second, new mutually coupled plural N.N. modules are introduced to realize the proposed searching model for problems with quadratic objective functions. the asymmetric Hopfield type N.N. can be regarded as a special class of the proposed N.N. modules. Last, by simulations for simple problems, the biffurcations in dynamical behavior such as converging to different NE points, cyclic state transition with no NE points and other exceptional cases are shown.

Journal

• Transactions of the Institute of Systems, Control and Information Engineers

  Transactions of the Institute of Systems, Control and Information Engineers 12 (11), 680-690, 1999

  THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)

Keywords

• noncooperative game theory
• Nash equilibrium
• neural networks
• Lotka-Volterra equation

Details

• CRID: 1390001205165606400
• NII Article ID: 10004473721
• NII Book ID: AN1013280X
• DOI: 10.5687/iscie.12.680
• ISSN: 2185811X
• ISSN: 13425668
• NDL BIB ID: 4898579
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4898579
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed