2人対称ゲームにおけるジレンマ性と弱支配戦略の存在可否性との関連について  [in Japanese] A Study on the Relation between Dilemma Occurrence and Existence of Weakly Dominant Strategy in a 2-Players Symmetric Game  [in Japanese]

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Author(s)

    • 谷本 潤 TANIMOTO JUN
    • 九州大学大学院総合理工学研究院 Interdisciplinary Graduate School of Engineering Sciences, Kyushu University
    • 相良 博喜 SAGARA HIROKI
    • 九州大学大学院総合理工学府環境エネルギー工学専攻 Department of Energy and Environmental Engineering, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University

Abstract

ジレンマゲームにおけるジレンマ性を「パレート公平戦略が戦略分布上,つねに増加するダイナミクスを持ちえない」ことと定義すると,この条件はゲーム動力学とは無関係にゲーム構造だけから決まる静的影響部分と動力学により決まる動的影響部分との積和の正負性と等価であることがレプリケータダイナミクスから示される.2x2 ゲームでは,このジレンマ性の有無は静的影響だけで決まり,ジレンマ性の存在有無はゲーム動力学上の戦略分布とは無関係である.このことは,2x2 ゲームではパレート公平戦略が他戦略を弱支配できないとジレンマが生起することを意味する.しかし,3 戦略以上のゲームについては,パレート公平戦略が他戦略を弱支配できないからといってつねにジレンマが発生するわけではない.Defining the dilemma game by the proposition, a game cannot sustain the Pareto Equal strategy increasing in its strategy distribution, we deduced that the dilemma substance can be expressed by a productive summation of the static factor and the dynamic factor independently. The static factor means an influence of the game structure on a possible dilemma, which relates to a game structural discrepancy from the situation that the Pareto Equal strategy can be weakly dominant over other strategies. While, the dynamic factor implies an influence of the strategy distribution in the way of game dynamics on the dilemma. In 2x2 game, dilemma existence can be determined only by the static factor, which means if the dilemma occurs or not relates to only the game structural effect but the dynamics. Whereas, in the more-than-three-strategies game, both the static and dynamic factors determine the dilemma existence, but the static factor can not solely explain.

Defining the dilemma game by the proposition, a game cannot sustain the Pareto Equal strategy increasing in its strategy distribution, we deduced that the dilemma substance can be expressed by a productive summation of the static factor and the dynamic factor independently. The static factor means an influence of the game structure on a possible dilemma, which relates to a game structural discrepancy from the situation that the Pareto Equal strategy can be weakly dominant over other strategies. While, the dynamic factor implies an influence of the strategy distribution in the way of game dynamics on the dilemma. In 2x2 game, dilemma existence can be determined only by the static factor, which means if the dilemma occurs or not relates to only the game structural effect but the dynamics. Whereas, in the more-than-three-strategies game, both the static and dynamic factors determine the dilemma existence, but the static factor can not solely explain.

Journal

  • IPSJ journal

    IPSJ journal 47(12), 3343-3351, 2006-12-15

    Information Processing Society of Japan (IPSJ)

References:  16

Codes

  • NII Article ID (NAID)
    110006160091
  • NII NACSIS-CAT ID (NCID)
    AN00116647
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • ISSN
    1882-7764
  • NDL Article ID
    8611248
  • NDL Source Classification
    ZM13(科学技術--科学技術一般--データ処理・計算機)
  • NDL Call No.
    Z14-741
  • Data Source
    CJP  NDL  NII-ELS  IPSJ 
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