{"created":"2023-06-20T15:48:06.468344+00:00","id":2630,"links":{},"metadata":{"_buckets":{"deposit":"06d59915-9642-41bc-824e-ca8c27e5dfbf"},"_deposit":{"created_by":2,"id":"2630","owners":[2],"pid":{"revision_id":0,"type":"depid","value":"2630"},"status":"published"},"_oai":{"id":"oai:hama-med.repo.nii.ac.jp:00002630","sets":["6:14:50"]},"author_link":["7765"],"item_2_alternative_title_1":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"A Convex Domain in the Parameter Space that Generates Parrondo’s Paradox"}]},"item_2_biblio_info_5":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2014-03-28","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"9","bibliographicPageStart":"1","bibliographicVolumeNumber":"28","bibliographic_titles":[{"bibliographic_title":"浜松医科大学紀要. 一般教育"}]}]},"item_2_description_30":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_2_description_9":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Abstract"}]},"item_2_publisher_6":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"浜松医科大学"}]},"item_2_source_id_19":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"09140174","subitem_source_identifier_type":"ISSN"}]},"item_2_source_id_23":{"attribute_name":"NII書誌ID","attribute_value_mlt":[{"subitem_source_identifier":"AN10032827","subitem_source_identifier_type":"NCID"}]},"item_2_version_type_32":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"野田, 明男"}],"nameIdentifiers":[{"nameIdentifier":"7765","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-08-27"}],"displaytype":"detail","filename":"kiyo28_01.pdf","filesize":[{"value":"355.8 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"kiyo28_01.pdf","url":"https://hama-med.repo.nii.ac.jp/record/2630/files/kiyo28_01.pdf"},"version_id":"6e8183ac-f54b-4a83-9702-bdb649909a61"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Parrondo’s paradox","subitem_subject_scheme":"Other"},{"subitem_subject":"generalized random walk","subitem_subject_scheme":"Other"},{"subitem_subject":"mixed strategy","subitem_subject_scheme":"Other"},{"subitem_subject":"convexity","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"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","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"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"}]},"item_type_id":"2","owner":"2","path":["50"],"pubdate":{"attribute_name":"公開日","attribute_value":"2014-07-30"},"publish_date":"2014-07-30","publish_status":"0","recid":"2630","relation_version_is_last":true,"title":["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"],"weko_creator_id":"2","weko_shared_id":-1},"updated":"2023-06-20T17:05:38.173876+00:00"}