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1999 Fiscal Year Final Research Report Summary

Existence of Nash equilibria for optimum location problems and its applications

Research Project

Project/Area Number 10650062
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionUniversity of Tsukuba

Principal Investigator

KISHIMOTO Kazuo  University of Tsukuba, Institute of Policy and Planning Sciences, Professor, 社会工学系, 教授 (90136127)

Project Period (FY) 1998 – 1999
KeywordsRational Voting Theory / Single Member Constituency / Location Problem / Nash Equilibrium / Two-Party System / Stock Price Changes / Numerical Analysis / Finance
Research Abstract

In the present research, I have proved the following mathematical results in location problems.
1. Under suitable conditions, the two party system is naturally realized under the single member constituency system.
2. There is a Nash equilibrium solution in the optimum location problem in a two dimensional plane by three competitors if all members pursue the top share.
These two results give answers to open problems in the rational voting theory. I have also obtained the following results in related areas.
3. Bid-ask spread is reliably measured by a Kalman filter approach (joint work with Ms. Zheng).
4. Downward bias is reported in the parameter estimation of heteroskedastic time series models. I have found that this bias is substantially amplified if the model is misspecified (joint work with Dr. Chu).
5. There is a sufficient condition for assuring that an eigenvalue is the second largest one.

  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] KIAHIMOTO Kazuo: "Spectral propeties of the operators which appears in the GARCH(1,1) model"Book of Abstracts, ICIAM 99. 50 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Chu Wen-Tseng: "On empirical heteroskedastic properties of Japanese stock price changes"Proceedings of the 9th International AFIR Colloquium 24-27, August 1999, Tokyo, Japan. 131-150 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 岸本一男: "オプションの価格付けと分散評価の問題点"数理モデル化と問題解決シンポジウム論文集. 2000・5. 181-188 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 鄭謙: "売り呼び値と買い呼び値の乖離の計測に対するKalman Filterによるアプローチ"多目的統計データバンク報告書. No.76(印刷中). (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 朱文増: "分散変動時系列データに基準化残差独立性検定を行うことの実証研究での利用可能性の計算機実験による検討"経営財務研究双書. Vol.20. (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] KISHIMOTO Kazuo: "Sufficient conditions for the second largest characteristic value of a non-negative matrix"京都大学数理解析研講究録. (印刷中). (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Wen-Tseng Chu and Kazuo Kishimoto: "On empirical heteroskedastic properties of Japanese stock price changes."Proceedings of the 9th International AFIR Colloquium 24-27, August 1999, Tokyo, Japan. 131-150

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuo Kishimoto: "Option pricing and a problem in estimating historical volatilities (in Japanese)"IPSJ Symposium Series. Vol. 2000, No. 5. 181-188

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qian Zheng and Kazuo Kishimoto: "A Kalman Filter approach for estimating bid-ask spread (in Japanese)"Annual Report on the Multi Use Social and Economic Data Bank. (in press). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Wen-Tseng Chu and Kazuo Kishimoto: "What can we see from the test of independence of the normalized residual sequence of heteroskedastic time series data ? (in Japanese)"Keieizaimu Kenkyu Sosho. Vol. 20(in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] KISHIMOTO, Kazuo: "Sufficient conditions for the second largest characteristic value of a non-negative matrix"Kokyuroku of RIMS. (in press).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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