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パロンドのパラドックスを生成するパラメータ空間の凸領域
http://hdl.handle.net/10271/2754
http://hdl.handle.net/10271/2754f1b4f006-b845-448d-86e3-86b4a1510de4
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
kiyo28_01.pdf (355.8 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
|---|---|---|---|---|---|---|---|---|
| 公開日 | 2014-07-30 | |||||||
| タイトル | ||||||||
| タイトル | パロンドのパラドックスを生成するパラメータ空間の凸領域 | |||||||
| 言語 | ||||||||
| 言語 | jpn | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | Parrondo’s paradox | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | generalized random walk | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | mixed strategy | |||||||
| キーワード | ||||||||
| 主題Scheme | Other | |||||||
| 主題 | convexity | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | departmental bulletin paper | |||||||
| その他のタイトル | ||||||||
| その他のタイトル | A Convex Domain in the Parameter Space that Generates Parrondo’s Paradox | |||||||
| 著者 |
野田, 明男
× 野田, 明男
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| 書誌情報 |
浜松医科大学紀要. 一般教育 巻 28, p. 1-9, 発行日 2014-03-28 |
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| 出版者 | ||||||||
| 出版者 | 浜松医科大学 | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | The author proposed, in his classes for medical students at Hamamatsu, a study of Parrondo’s paradox described in these books [1], [2] and [3]. This paradox interested them and their naïve discussions in the classes stimulated him to investigate the class of all Parrondo’s games from a viewpoint of generalized random walks ([4]. The game consists of two basic games A and B of the same type. Suppose that a player repeats the game and observes the partial sum S X n k k n = = Σ1 at time n. Then, if Sn is a multiple of 3, she plays game A to get the next result Xn+1 that takes on one of the two values, +1(win) and –1(loss); otherwise she plays game B to get the result ′+ Xn 1 in like manner. We can therefore parametrize such a game by means of the expectations of games A and B, which we put E(Xn+1 ) = –α,E(Xn′+1 ) = β (–1 <α,β < 1). Our main result is Theorem 4 which asserts that Sn /n converges (in the weak sense) to the value δ1=3{2β –α(1+β2)}/(9+β2–2αβ) as n→∞. Hence we see that the game is favorable or unfavorable for a player according to δ1 > 0 or δ1 < 0. Since the domain given by α < 2β / (1+β2), 0 ≤ β <1, is convex, we now explain how one can generate Parrondo’s paradox. Indeed, noting that the mixed strategy of game I with α1, β 1 and game II with α2, β 2 becomes the game having the parameter α = (α +α ) / ,β = (β + β ) / 1 2 1 2 2 2, we generate various examples of α i, βi (i =1,2) in the final section, such that the inequality αi > 2βi / (1+β i2) holds for each i, whereas we have the inverse inequality α < 2β /(1+ β 2 ) satisfied by the mixed strategy. Applying the theory of generalized random walks developed in [4], we can also solve the ruin problem for every Parrondo’s game; we thus understand his paradox from another point of view. | |||||||
| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 09140174 | |||||||
| NII書誌ID | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AN10032827 | |||||||
| フォーマット | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | application/pdf | |||||||
| 著者版フラグ | ||||||||
| 出版タイプ | VoR | |||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||
