A Formal System of Mathematical Programming and Game Theory

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  • Eto Hajime
    東京都国分寺市日立製作所中央研究所

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Other Title
  • 数理計画法とゲーム理論の形成体系
  • スウリ ケイカクホウ ト ゲーム リロン ノ ケイシキ タイケイ

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Description

Some important parts of economics are formally stated in a finite manner in the sense that their syntax is given and that their theorems are proved without resorting to the compactness just under the assumptions the rational numbers and their arithmetical rules are finitely given. Firstly the syntax introduces the linear space spanned over the rational field which is shown to meet the so-called axioms of the linear space. The simplex algorithm of linear programming provides a finite tool to develop the linear algebra and its. geometric representation which, on the contrary, usually in nonfinite systems deduce it. The basic parts of the game theory and non-linear programming are shown to be expressible in a finite manner as well. Economic behaviors besides games are also seen to be expressed by finite mathematics. Lastly it is remarked that the integer programming algorithms as the most powerful tool for finite systems are finite.

Journal

  • Kagaku tetsugaku

    Kagaku tetsugaku 1 45-54, 1968

    The Philosophy of Science Society, Japan

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