1999 Fiscal Year Final Research Report Summary
Existence of Nash equilibria for optimum location problems and its applications
| Project/Area Number |
10650062
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KISHIMOTO Kazuo University of Tsukuba, Institute of Policy and Planning Sciences, Professor, 社会工学系, 教授 (90136127)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Rational Voting Theory / Single Member Constituency / Location Problem / Nash Equilibrium / Two-Party System / Stock Price Changes / Numerical Analysis / Finance |
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| 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.
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