MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C838D0.EFBAAA00" このドキュメントは単一ファイル Web ページ (Web アーカイブ ファイル) です。お使いのブラウザ、またはエディタは Web アーカイブ ファイルをサポートしていません。Microsoft Internet Explorer など、Web アーカイブをサポートするブラウザをダウンロードしてください。 ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I

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マスタ タイトルの書式設定
マスタ テキストの書式設定
第 2 レベル
第 3 レベル
第 4 レベル
第 5 レベル
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foCAgIB+fn5+fn5+gIB+foCAgICAfoCAfn5+foCAfn5+gIB+fn5+foCAgICAgICAfn5+foCAfoCA gICAgH5+fn6AgICAgICAgH5+foCAgICAgICAgIB+fn5+fn5+fn5+foCAfn5+fn5+gH5+foCAgH6A gICAfn5+foCAgICAgICAfn6AgICAgIB+fn5+fn5+fn5+fn5+gICAgH5+foB+fn5+fn5+fn5+fn5+ gICAfn5+foCAfn5+fn5+fn5+fn5+fn6Afn5+foB+fn5+gIB+fn5+fn6AgICAfn6AgIB+fn6AgICA gICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICA ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
意思決定科学：ゲーム理論１
2007/11/9,Fri.<= /span>〜
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
Contents
3D"*"ケーキを仲良く！
=3D"*"アルゴリズムと解の性質 = ;
3D"*"<= span lang=3DEN-US style=3D'font-size:71%;mso-fareast-language:JA'>The Steinhaus= ’ loan divider procedure
3D"*"<= span lang=3DEN-US style=3D'font-size:71%;mso-fareast-language:JA'>The Banach-Kn= aster last-dimisher procedure
3D"*"ゲーム理論とは何か？
=3D"*"ゲームの定義
2人非協力零和ゲーム
=3D"*"ミニマックス原理と均衡解 = ;
=3D"*"純粋戦略と混合戦略，ミニマックス定理
=3D"*"2人零和ゲームと線形計画
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ケーキを仲良く
　Bob= と Carol にケーキ<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Garamond;mso-= fareast-font-family: "ＭＳ Ｐゴシック"'>（丸々1= 個！）を買ってきた．2人に均等に与えたいのだが，2人は自分の分が相手より小さいと不満を言い，けんかになる．
どうしたらいいだろう?
u仮定：The cake is di= visible: it can be cut at any point without destroying its value.
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C3uDVPLNGmtvFe+C+v5f8/lTV+u4UH7rWeXcyYYjmedQL5ib7YRz7kT3NwGn07KCCgAA ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
ケーキを仲良く
uYou Cut, I Choose !<= span lang=3DEN-US style=3D'mso-fareast-hint:yes;mso-fareast-language:JA'>
•Bobにケーキを切らせ，Carolにケーキを選ばせる
One divid= es,
the other chooses.
ただし，これはこの問題の「解」ではなく「アルゴリ= ズム」！
<= span style=3D'mso-fareast-hint:yes'>u解は…
•Bob divides the cake into two = pieces, between which he is indifferent; and Carol chooses what she considers to be the larger piece.   (from ``Fair Division’’, p.9)
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ケーキを仲良く
u解の持つ2つの性質=
•proportionality (An allocation is proportional.)
&#= 8226;Each thinks he or she recei= ved a portion that has size or value of at least 1/n.
•envy-freeness (An allocati= on is envy-free.)
&#= 8226;Every player thinks he or s= he receives a portion that is at least tied for largest, or tied for most valuable and, hence, does not envy any other player.
プレイヤーが二人の場合は等価
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
ケーキを仲良く
u2<= /span>人の戦略
= •Bob：「均等に切る」「不均等に切る」
= •Carol：「大きいほうを選ぶ｣「小さいほうを選ぶ｣
u= 2人の利得表
<= span style=3D'mso-fareast-hint:yes'>•Bobの利得表
u=
u=
•=
<= span style=3D'color:#4D4D4D;mso-fareast-hint:yes'>•Carolの利得表
2人 非協= 力 <= b>零和ゲーム
 larger cake
smaller cake
不均等に切る
½ cake
½ cake
均等に切る&#= 13;
小cakeとる
大cakeとる
Bob＼Carol
 smaller cake<= /span>
larger cake<= /span>
不均等に切る
½ cak= e
½ cak= e
均等に切る
小cakeとる
大cakeとる
Bob＼Carol=
協力はせずに，<= span style=3D'position:absolute;top:34.78%;left:0%;width:100.0%;height:30.43%'>= 自分の利得最大
（非= 協力的）
自分の利得が相<= span style=3D'position:absolute;top:53.33%;left:0%;width:100.0%;height:46.66%'>= 手の損失（零和）
プレイヤーは2人
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ケーキを仲良く
uミニマックス原理
•Bobの利得表（=3DCarol<= /span>の損失表）
Bob  ：マキシミン戦略= ：　最大（<= b>Max) 最小保証利得（Min）
Carol= ：ミニマックス戦略：最小（Min） 最大保証損失（Max）
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file:///C:/E17059D1/07dmt_5-1.files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
ケーキを仲良く　（３人いたら？）
<= span style=3D'mso-fareast-hint:yes'>uThe Steinhaus’ lone-divider procedure (3 players)&#= 13;
1.Bob がケーキを1/3（とBobが思う通り）に切る = ;
2.Carol = が acceptab= le cake とそうでないものを指摘
• （少なくとも<= span lang=3DEN-US style=3D'font-size:83%;mso-fareast-hint:yes;mso-fareast-language:JA'>1つは accept= able cake があるという条件で）
3.Ted も Carol と同様のことを行う． = ;
4.Case1: Carol(= or Ted)が2個以上acceptable cake がある
• Ted → Carol → Bob の順にケーキを取る = ;
5.Case2= : Carol, Tedとも accept= able cake が高々1個 = ;
• Carol, Tedとも acceptable でないケーキを Bob にあげて，残りのケーキについて2人で[divide-and-choose]を行う．&#= 13;
H. Steinhaus, 1948
call a piece acceptable to a player
if he or she thinks the piece is at least 1/3 of the cake.
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ケーキを仲良く　（３人いたら？）
<= span class=3DBB style=3D'position:absolute;left:-3.94%;top:.49em'>uThe Steinhaus’ loan-divider procedure (3 playes)
<= span class=3DB1B style=3D'position:absolute;left:-3.25%'>•proportional division を保証する各プレイヤーの戦略 = ;
<= span style=3D'font-size:83%'>•Bobはちょうど1/3（とBobが思う） pi= ece に切る = ;
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•Carol, Ted は acceptab= le cake を取る = ;
•
•envy-free ではない = ;
<= span style=3D'font-size:83%'>•case1: Bob, T= ed は誰も妬まないが，Carol は Ted を妬む可能性がある．（Tedが，彼女が考える acceptable cake の大きい方を取る可能性があるので） = ;
<= span style=3D'font-size:83%'>•case2<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 83%;mso-fareast-hint:yes'>：Carol, Ted は誰も妬まないが，Bob は Carol か Ted のいずれかを妬む可能性がある．（Carol と Ted の [divide-and-choose] の結果が Bob から見て 50= -50 に思えない場合，2人のいずれかが1/3以上（とBobが思う）cake <= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 83%;mso-fareast-hint:yes'>を得るので）
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
ケーキを仲良く　（ｎ人いたら？）
uKuhn が = The Steinhaus’ loan-divider procedure (3 playes) を n人版に拡張
• （Frobenius & Konig の combinat= orial theorem に基づくアル<= /span>ゴリズム） = ;
• （4人版は Stei= nhaus も気づいていたらしい） = ;
u
uThe Banach-Knaster last-diminisher procedure
• （Steinhaus が 1948年に2人（彼の学生，ポーランド人）のアイデアを論文の形で発表）
u
u<= /span>……
H.W. Kuhn, 1967
S. Banach-B. Knaster, mid-1940
‥ <= /span>
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ケーキを仲良く
uThe Banach-Knaster last-diminisher procedure  (n players)
•The partners = being ranged A,B,C,…,N. A cuts from the cake an arbitrary part. B has n= ow the right, but is not obliged, to diminish the slice cut off. Whatever he does, C has the right (without obligation) to di= minish still the already diminished (or not diminished) slice,= and so on up to N. The rule obliges the ``last-diminisher’’ = to take as his part the slice he was the last to touch. This partne= r thus disposed of , the remaining n-1 persons start the same g= ame with the remainder of the cake. After the number of partic= ipants has been reduced to two, they apply the classical [divide-and-choose] rule for halving the remainder.     (from ``Fair Division’’, p.35 [Steinhaus’ description 1948 p.102])
S. Banach-B. Knaster, mid-1940
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0022_image019.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAMQAAAAhCAYAAACGLwRaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAL3SURBVHja 7Zw/SBtRHMdvKLTF/tFaoYUOgS5Cl0AXhw4uglPp6FJwLh06FZdyiSY5k4iCYBUHS3HIUKFT7SAk g0MGhxscMgjNICXQDNcQ2gg3XN/3eO84wxETY8qd+X7gCwbiy+P4fd+fhN9XSyaTWj9KJLQpoWmp V0KJdqVSN/O53EOTonrTRDmonqSmfZrst46VOhV6DB+m69o7TEBMsKgmKl47Shsbz6zt7eeudndn fpdKutOuw0PDqVZLFNWTTk6+O0H1BKmag1ZXnzRUPS4u3rB9pvomzTMvjTPatSHEm+Oy8E0Mms9P NPFh+/tvzzCBSuWrN1FCwoptt7w6PT4uuObZ25tzazmdvn0mTit/sbiLWl8I2lm0TObea8O4W19f f+qu7hgIgxJyHWm1LHdxPzh4b2NnyeXGK9gMPENsbcXrllXlkyJDyelp2RF3lV/qOKVhO+FjIcMM rge4M9MQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhNAQhITcEGgBbTZrfCpk KKnXK042O2Z5/RArK4/fpNMjjULhZUP1PhNyXUHHHGoc3aHYDJaXR3+e65hTf+i6NqfSMdCsjfY6 9KHiH03zk9enigEJCTPoAFX1Wi6vue2iqGXDuP9H9lSbMnxgqpfUjUmZVJDIZh98UUkGGFAlHKAP WyUf7Oy8sILSEdDo3SlZoVYzI/3wseUyIWOwwoLcXleqyIOSN5ARoOo1k7nzUQYKoJYfXTqGpstM prgvG2c2KD8HUSCdsnfE+e0HLjVI94iCOWCAo6NNB0dMrDjYcpmfNFhhQQ6orYVBZDNpVxXw1Kex Ysh/UuYoFj/YKLywGkDoM46Y3aw4VLQUugnBHEtLt1IoPGyD/9scNAANEVphGxy0OXABwxkVv8fQ AFRkJuo3By7z+PbgMnlSfgPgeIYLmDyjztMAVCQnjcs8vj1QiYOdzHGBAWIsAiryhrjIHDQANbSG CDIHDUDREBR1BfoH69xaEaYwJWoAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
ケーキを仲良く
<= span style=3D'mso-fareast-hint:yes'>uThe last-dimisher procedure
<= span class=3DB1B style=3D'position:absolute;left:-3.25%'>•proportional division を保証する各プレイヤーの戦略 = ;
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•切るプレイヤーがちょうど1/nと考えるpiece に切ること
•
•envy-freeではない = ;
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•理由：例えば，ゲームを先に抜けたプレイヤーAが，ある段階で切られたケーキが1/nより大きい（とAが思う）ときでもそれを阻止できない．結果として1/nより大きいケーキが誰か（B）に行く（とAが思う）ので，AはBを妬む．
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
ゲーム理論とは何か？
u<= /span>ゲーム的状況　game situations
•複数の意思決定主体（プレイヤー）が存在し，各々目的を= 持ち，その実現を目指して相互に依存しあっている状= 況
•
uゲーム理論　<= span lang=3DEN-US style=3D'font-size:88%;mso-fareast-language:JA'>game theory
•ゲーム的状況を数理モデルを用いて定式化し，プレイヤー間の利害の対立と協力を分析する理論
J. von Neumann & O. Morgenstern
「ゲーム理論と経済行動」（1944）
J= ohn von Neumann (1903-1957)
2004年11月9= 日（火）取得の情報
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ゲーム理論とは何か？
<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uプレイヤー　player
•意思決定し，行動する主体．（2人，3人，…，n人，…，∞）
•例：個人，複数の個人から成る組織，政党，国家，… = ;
•
u戦略　strategy
•プレイヤーが取りうる行動．（有限，無限）
•
u利得と利得関数　payoff
•各プレイヤーの戦略決定後，ゲームは終了し，結果が出る．結果に対する各プレイヤーの何らかの評価値．利得<= span style=3D'font-size: 71%'> payoff，効用 utility．
•
u協力の可能性 = ;
•各プレイヤーは自由に自己の判断で行動．
•協力ゲーム：十分にコミュニケーション可能で，合意の上で戦略を決定．
•非協力ゲーム：各自の独立な判断により，戦略を決定．
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uゲームの表現形式
•展開形　extensive for= m
•
•
•
•
•
•戦略形　strategic for= m，標準形　normal form <= /span>
ゲーム理論とは何か？
6
-4
SA2
1
3
SA1
SB2
SB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
=
A
B
(3,-3)
(-1,4)
(2,-6)
(-2,1)
=
SA1<= /span>
SA2<= /span>
SB1<= /span>
SB1<= /span>
SB2<= /span>
SB2<= /span>
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<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uゲームの定義（戦略形n人ゲーム）
ゲーム理論とは何か？
：= vレイヤーの集合
：= vレイヤーi の= 略集合
：= vレイヤーi の= 得関数
= 各プレイヤーは自己の利得= 最大化を目指し，
Gは全てのプレイヤーの共有= 知識とする．
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u非協力ゲームと協力ゲ= ーム
•各プレイヤーの戦略決定における前提
ゲーム理論とは何か？
1.プ= 激Cヤー間には，各プレイヤーがとるべき戦略について= C強制力のある取り決めは存在しない．
2.
2.
2.全= ﾄのプレイヤー間に，とるべき戦略についての合意が= ｬり立ち，それに基づいて戦略決定する．
拘束的合意が成立しない
拘束的合意が成立
非協力ゲーム
協力ゲーム
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<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uゲームのルール
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>•プレイヤーの数は2人 = ;
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>•各プレイヤーは，独立に戦略を決定（非協力）
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>•プレイヤーの利得の和は，常に零（零和）
•
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>•ゲームは1回限り = ;
•各プレイヤーは戦略決定時に，他のプレイヤーがどの戦略をとるかは知らない = ;
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>•各プレイヤーの取りうる戦略は有限
2人非協力零和ゲーム
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Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0037_image042.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAABkAAAAcCAYAAACUJBTQAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVEjH 7ZYtEsIwEIUjKyuROQIS2SMgOQIyEklOUImsRHIEJBKJrEQikeVt54lO6U8GdmcQiK+TTDr7pdmX mboYo7OmfTTO7YC3lgRwAZmZhKJKsJZk/JpgJqHIgxoUZhKKCoq8mcQiCKMLmkGYkqgFYXJRKwiz L0CwAvehIKT2LGknKLYF135RJtGrSFjwAI4DKVxrSt6CgPEJlGoSFl2wPwXnMj6rSnpBkH404DkX gI8iySA8KBGW30ZY7krJHTcjBK3G52DPo+pLKu2eZDyuuiO5qfekI9zwkoooN5Gk3nzz36G/5Dcl L39IJVb0sWUgAAAAAElFTkSuQmCC ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u利得行列　payoff matrix
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>零和ゲーム，即ち， = ;
• なので，
• とおくと，取りうる戦略と利得の関係を行列Aで表せる
2人非協力零和ゲーム
利得行列
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uExample1： = ;
•<= span lang=3DEN-US style=3D'font-size:64%;mso-fareast-hint:yes;mso-fareast-langu= age: JA'>A君とBさんがトランプで簡単なゲームをしている．双方とも= 予め2枚のカードを持っており，1回だけ1枚のカードを出し，カードの目の差を利得としてもら= えるというゲームである．さて，A君は「スペード の4」「ハートの7」の2枚，Bさん「クラブの2」「ダイヤの10」の2枚のカードを持っていることが互いに分か= っている時，2人はどのようにカードを出すべきか？
2人非協力零和ゲーム
-3
5
ハートの7
-6
2
スペードの4
ダイヤの10
クラブの2
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
3
-5
ハートの7
6
-2
スペードの4
ダイヤの10
クラブの2
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
A君の利得表
Bさんの利得表
ゲームの解： （ハートの7，ダイヤの10）
ゲームの値
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意思決定論　5．ゲーム理論　Part I
uExample2： = ;
•<= span lang=3DEN-US style=3D'font-size:64%;mso-fareast-hint:yes;mso-fareast-langu= age: JA'>A君とBさんがゲームをしている．それぞれ3つずつの戦略があり，A君の利得表は以下の通りである．2人は，各々どんな戦略をとるべきか？
2人非協力零和ゲーム
-3
2
4
sB2
1
2
sA2
0
4
sA3
-1
-2
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0036_image061.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAATgAAAB8CAYAAAD9waykAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOISURBVHja 7dexDYJAHEbxm4baQWQGrKjZgLCCnVMwAgzgBo5g4wYnGFBLMIGYyy//fIXtC+/lDCGEaGaW2Nqm aUKYftyHVbZ4sesutnK4Ybb1iuI4B675Dtxt/GHLNjKL8WorhxtmW6+uyzlwlcAJHFkxEzgTOLJi JnACZ2TFTOAEjqyGmcAJHFkxw0HgBI6smJnACRxZMRM4EziyYiZwAmdkxUzgBI6suGEmcAJHVsNM 4ASOrJiZwAkcWTETOBM4smImcALnYyIrZgIncEZWzARO4MhqmAmcwJEVMxM4gSMrZgIncAJHVswE zgSOrJgJnMAZWTETOIEjq2EmcAJHVsxM4ASOrJgJnMAJHFkxEzgTOLJilkDgzMxS2idw+Skf2ueW 3sjMS/a3ly8OmG3Mqxc4gSMrZgLnBI6smAmcwBlZMRM4gSMrDpgJnMCR1TATOIEjK2YmcAJHVswE zgkcWTETOIHzQZEVM4ETOCMrZgIncGQ1zARO4MiKmQmcwJEVM4ETOIEjK2YC5wSOrJgJnMAZWTET OIEjq2EmcAJHVsxM4ASOrJgJnMAJHFkxEzgncGTFTOAEzsiKmcAJHFkNM4ETOLJihpnACRxZMTOB EziyYiZwTuDIipnACZyRFbM/D5yZWWLzgvOC8xrBzF9UJ3BkxUzgBM7IipnACRxZDTOBEziyYoaD wAkcWTEzgRM4smImcE7gyIqZwAmckRUzgRM4Hx9umAmcwJHVMBM4gSMrZiZwAkdWzATOCRxZMRM4 gfPRkRUzgRM4IytmAidwZDXMBE7gyIqZCZzAkRUzgRM4gSMrZgLnBI6smAmcwBlZMRM4gSOrYSZw AkdWzEzgBI6smAmcwAkcWTETOCdwZMVM4ATOyIqZwAkcWXHAbOfAmZklNi84LzivEcz8RXUCR1bM BE7gjKyYCZzAkdUwEziBIytmOAicwJEVMxM4gSMrZgLnBI6smAmcwBlZMRM4gfPx4YaZwAkcWQ0z gRM4smJmAidwZMVM4JzAkRUzgRM4Hx1ZMRM4gTOyYiZwAkdWw0zgBI6smJnACRxZMRM4gRM4smIm cE7gyIqZwAmckRUzgRM4shpmAidwZMXMBE7gyIqZwAmcwJEVM4FzAkdWzARO4IysmAmcwJEVB8x2 Dlx2yGJZl7ZwE8DeVg83zLbeY2J2fgfOzCyxta/AedaaWbJ/WUEws1T3BH8v19bHtEbcAAAAAElF TkSuQmCC ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uミニマックス原理　minimax principle
<= span style=3D'font-size:86%'>•Example2でプレイヤーAの思考
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•戦略sA1<= /span>を取ったときの最悪の事態は = ;
• min(-2, 4, -1) =3D -2 （プレイヤー<= span lang=3DEN-US style=3D'font-size:83%;mso-fareast-hint:yes;mso-fareast-language:JA'>Bが戦略sB= 1を取る）
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•戦略sA2<= /span>を取ったときの最悪の事態は = ;
• min(2, 2, 1) =3D 1 （プレイヤー<= span lang=3DEN-US style=3D'font-size:83%;mso-fareast-hint:yes;mso-fareast-language:JA'>Bが戦略sB= 3を取る）
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•戦略sA3<= /span>を取ったときの最悪の事態は = ;
• min(4, -3, 0) =3D -3 （プレイヤー<= span lang=3DEN-US style=3D'font-size:83%;mso-fareast-hint:yes;mso-fareast-language:JA'>Bが戦略sB= 2を取る）
2人非協力零和ゲーム
-3
2
4
sB2<= /span>
1
2
sA2<= /span>
0
4
sA3<= /span>
-1
-2
sA1<= /span>
sB3<= /span>
sB1<= /span>
A＼B
最大化プレイヤー
戦略sA2を取る　（最悪でも利= ｾ1が= ﾛ証される）
もっと良い利得を得ることができるのか？
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<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uミニマックス原理　minimax principle
<= span style=3D'font-size:86%'>•Example2でプレイヤーAがBの立場で思考
<= span style=3D'font-size:83%'>•Bが戦略sB1を取ったとき，Aである自分は戦略sA3を取る
• max(-2, 2, 4) =3D 4
•Bが戦略sB2を取ったとき， Aである自分は戦略sA1<= /span>を取る = ;
• max(4, 2, -3) =3D 4
•Bが戦略sB3を取ったとき， Aである自分は戦略sA2<= /span>を取る = ;
• max(-1, 1, 0) =3D 1
2人非協力零和ゲーム
-3
2
4
sB2<= /span>
1
2
sA2<= /span>
0
4
sA3<= /span>
-1
-2
sA1<= /span>
sB3<= /span>
sB1<= /span>
A＼B
戦略sB= 3を取る　（最悪でも損= ｸ1で= ﾏむ）
Aは戦略sA= 2を取る= ﾆき，利得1を得られ，
それ以外の戦略を取ると利得が1以下になる．
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uミニマックス原理 = ;
•<= span lang=3DEN-US style=3D'font-size:86%;mso-fareast-hint:yes;mso-fareast-langu= age: JA'>Example2：
2人非協力零和ゲーム
1
4
4
max
-3
0
-3
4
sA3
1
-2
min
1
-1
sB3
1
max
2
4
sB2
2
sA2
1
min
-2
sA1
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
保証水準 security level
保証水準
security level
マキシミン値
maximin value
ミニマックス値
minimax value
マキシミン原理
maximin principle
〔最大化プレイ= ヤーの行動原理〕 <= /span>
ミニマックス原理
minimax principle
〔最小化プレイ= ヤーの行動原理〕
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<= span style=3D'font-size:88%;mso-fareast-hint:yes'>u均衡点とゲームの値
•2人のプレイヤーがともにミニマックス原理に基づいて行動すると，どうなるのか？
2人非協力零和ゲーム
2人共に勝つことはあり得ない！<= /span>
何らかの意味での均衡に到達
= しかた
ない… <= /span>
やむを
えない…
2人零和ゲームが
「厳密に決定される strictly determined」<= /span>
「厳密に確定的である」
（ sA2<= /span> *, sB= 3 <= /span>*）：ゲームの均衡点 equilibrium point
-3
2
4
sB2<= /span>
1
2
sA2<= /span>
0
4
sA3<= /span>
-1
-2
sA1<= /span>
sB3<= /span>
sB1<= /span>
A＼B
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iVBORw0KGgoAAAANSUhEUgAAACMAAAATCAYAAAAao7T0AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFqSURBVEjH xZYvdMIwEMZPIisnJyMnJycrkZMTe9CH2EMiW1VZOTmJRE5OTiIrkZXIyey+3JUWKGseZY24l6T5 9+t3uUsoyzIaajahJzujaOg6fpu90Z19pWfeMGXb2Dl9cVmyWWfS3mu7cm35lvK8hEszCMYBzGil m1Zsa4WZqhLm4jz0y5iUod4Pa0jdeMNAbp0EgNz3rzzVTRyYqGb+hFFX7DDpFgA9Zwxq5Z0wDPCi roj+E+TECytW6eMIRuVbjwVx4o0Ex8LB6EEtx1SkQ6FPthiVJVsRCkRhpkgZBJ/hvASFWdA9AgdU BdQJrMwD2xaVGD4LDIPkmteNDfwWBEQCaMc2aWddZMV49LMyp2+46TjpAUhCrBgjzDWKt+1r4dIg l6oh4Y0BJof7qeOn+27sStVC/fFKAFNn+L6b22ex2KkkvsV75af1Xin0WdFY01fp+NIByCUcDX5c nUndvFeWZzB13xUu/gUZlibDbdACLgAAAABJRU5ErkJggk== ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0041.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
演習１：
uプレイヤーAの利得表が以下の表で与えられるゲームを考える．プレイヤーA，Bがそれぞれミニマックス原理に基づいて戦略決定をすると，ゲームの解はどうなるか？　（１），（= ２）それぞれの= ゲームについて考えよ
2
0
1
sB2
2
-1
sA2
3
5
sA3
-1
3
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
（１）
2
8
6
sB2
2
1
sA2
3
7
sA3
4
5
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
（２）
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u純粋戦略と混合戦略
&= #8226;Example3：
•<= span lang=3DEN-US style=3D'font-size:75%;mso-fareast-hint:yes;mso-fareast-langu= age: JA'>A君とBさんがゲームをしている．それぞれ3つずつの戦略があり，A君の利得表は以下の通りである．2人は，各々どんな戦略をとるべきか？
2人非協力零和ゲーム
-3
3
2
sB2
1
4
sA2
2
1
sA3
0
-4
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
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u純粋戦略と混合戦略
&= #8226;Example3：
2人非協力零和ゲーム
-3
2
-3
1
sA3
2
3
4
max
1
0
sB3
1
-4
min
3
2
sB2
4
sA2
2
min
1
-4
sA1
max
sB1
A＼B
3D"テキスト=
≠
ミニマックス均衡点が存在しない！？
マキシミン戦略
ミニマックス戦略
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Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAB0AAAAeAQMAAADqyYfiAAAAAXNSR0ICQMB9xQAAAAZQTFRFAAAA /wAAG/+NIgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAACDYAAAg0Ab6QHjwAAAAZdEVYdFNvZnR3YXJl AE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAOElEQVQY02NgIBYwggjJBiAhrQAkuAyABA+IxeMAJPgO AAkhkKwxiFAEKXYGsdxABAuI4DhAtF0AvHEGkfrgVZkAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/dsld0044_image111.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAB0AAAAeAQMAAADqyYfiAAAAAXNSR0ICQMB9xQAAAAZQTFRFAAAA /wAAG/+NIgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAACDYAAAg0Ab6QHjwAAAAZdEVYdFNvZnR3YXJl AE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAOElEQVQY02NgIBYwggjJBiAhrQAkuAyABA+IxeMAJPgO AAkhkKwxiFAEKXYGsdxABAuI4DhAtF0AvHEGkfrgVZkAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0044_image112.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAToAAAAnCAYAAACffYStAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC9SURBVHja 7dSxCcQwFAVBtS5wJ27GilyKS7DRRVfDMgNP8FMFO85j3edxvWZmva17zjnGPgCKdt+EDkgTOiBP 6IA8oQPyhA7IEzogT+iAPKED8oQOyBM6IE/ogDyhA/KEDsgTOiBP6IA8oQPyhA7IEzogT+iAPKED 8oQOyBM6IE/ogDyhA/KEDsgTOiBP6IA8oQPyhA7IEzogT+iAPKED8oQOyBM6IO8vdOvZh5lZb+v5 hW4/Zmbl+QQzy+8DQ81YZ/07tFkAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0044_image113.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAGIAAAAZCAYAAADKQPsMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABaSURBVGje 7dqxDcAgEATBK91fIaVQgs0HpoVPZqWTECGTkjxZZ6+NbFVVeukLzdRvDwKEQIAQCBACAUIgQAgE CIEAIRAgBAKEQIAQCBAXYvvWMrZ9If6Dze4Dcr1u+QsACCYAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0044_image114.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAGsAAAAZCAYAAAA2VdDGAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABnSURBVGje 7dqxCcAwDEVBjZSpsofIwB5BMQZD0qdQ4B78wi59raOuo+oM67hpk5mxF+tSPZs2sGAJFixYsAQL FixYggULFizBggULlmDBggVLsGAJlr7HGn4Std14YT0P1nse4Ue7AXliWqfqBb/ZAAAAAElFTkSu QmCC ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u純粋戦略と混合戦略
&= #8226;Proposition1： 利得行列A=3D[a<= /span>ij]<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";mso-fareast-hint: yes'>が与えられた時，
2人非協力零和ゲーム
ゲームは常に厳密に決定されるとは限らない！
いかなる場合に均衡点が存在し，
ゲームが厳密に確定的であるか？
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0045_image115.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBo4H/AxMAJYhUGM4IYzLmMDAxMDDJgWVYg5mSCsZgYGaEsRqb///+D WXqMElAxbrg6HqYHTA38QkCWGhs/gxTDf5BiBgEg/wCQtQyIHfgZGNqA6rmhangYfBNLMkIqC1IZ GDaA7f7NpPAf4sIJYFtZmBgEQjJzU4sV/FLLFYLycxPzGG7Mf1/+EIgVFD6W2wmlfWABqtMFKuYA 0kZcDxjX8IGclJkF4acxufEwIvETmFZxgvhZWTD1MWxMKPJaLMjyaUxJjBD9EPc1/CPPfYwMIPoD 3J0NjO94QSYkZsH481ghfHR7GEgMB4g94FgFmyvHzQxk5SZWpMJEujjAIpl5cBEuZnQRKwaYLizu YQK5J7gyNyk/h4EhT4hryYknQkT7O44dZMTiRC5oKuACpxSwN6FpQAisFmpXAyMTE1NwZXFJai7D B5C5DEAdigxdEA1A8OSZEAO635nBMgAbW/x+8AIAAA== ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0045_image116.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAXAAAAAnCAYAAAAW5RPEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADASURBVHja 7dTBCYAwFAXBtB6wE5sx1ViCEk+2sDADL/CvOew4j+sBoGN3e845hoADtAg4QJSAA0QJOECUgANE CThAlIADRAk4QJSAA0QJOECUgANECThAlIADRAk4QJSAA0QJOECUgANECThAlIADRAk4QJSAA0QJ OECUgANECThAlIADRAk4QJSAA0QJOECUgANECThAlIADRAk4QJSAA0QJOECUgANE/QK+7n2YmVll 6/4Cvh8zM+vNJ5iZRfcC9iElzlUxnkYAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0045_image117.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAB0AAAAcCAYAAACdz7SqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGlSURBVEjH 7ZQ/SEJRGMXfkPmyp1lGioNFRdQigUsNQeASFE4VNQRBUBA0WLQ15KBrBBE4ttTe1NaUEAWNQUuj Qpj9oSAdTveAhcV7vvueryUcznbv9zvfvd/5lFQqpZhJUTAsNCmhkFQ9mUMuFYXwIJ57R1AyUjCC V48PF45B1XY8ZE6B7LWxtrKA5sdNE9qENqH/CCrW16jQrpFaXHiTgba6ka9XR6jvG6pqmFM9qMys Anqa36wPpPbO9e9SU8uAuw1lAR378by+AJLj0yiZFbej/iiKmoaE7p92dOMwsYYXJ4FshA3VHSRf F85W0ig7AWQDbMR0esW7q+LgFQejESCNswHpyAiwvzOI251je8CNfXyI+zk2YCmnHO+eCO7NovJb NErDNG5rOTC/4QHkGQcZIA3S6FcebW8kjvpQDIWDnHlOaZBGHVmDYuTXY3EUjYA0RGO1WWwYSnkD SMcX8aQHjU7gUWy0Jdla0tDq8jhZ2MZ7LZBGaMhKHUvQ6vK4ZCQIpAEasVrDMpTZE+C72SQqNGD1 vi1oFRzyeHFkFP4/gTaqT0ytsIFMkc6DAAAAAElFTkSuQmCC ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0045_image118.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAS0AAAA9CAYAAAD4Qj/BAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEFSURBVHja 7dTBCcMwEEVBtS5wJ24mOrkUl+CgnFKCH8zAX9gG3jiPdZ3H5zEze/fWNeccYz8Ab7dbJVpAhmgB KaIFpIgWkCJaQIpoASmiBaSIFpAiWkCKaAEpogWkiBaQIlpAimgBKaIFpIgWkCJaQIpoASmiBaSI FpAiWkCKaAEpogWkiBaQIlpAimgBKaIFpIgWkCJaQIpoASmiBaSIFpAiWkCKaAEpogWkiBaQIlpA imgBKaIFpIgWkCJaQIpoASmiBaSIFpAiWkCKaAEpogWkiBaQIlpAimgBKaIFpIgWkCJaQIpoASmi BaSIFpAiWkDKX7TWvR8zs3dv3b9o7WNmVtkXOoplMdaF9qIAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u純粋戦略と混合戦略
•鞍点 saddle point
•行列A=3D[a<= /span>ij]<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Times New Ro= man"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Times New= Roman"; mso-fareast-hint:yes'>において，任意の i,  j に対し， <= /div>
•
•　が成り立つ= とき，（i<= /span>0, = j<= /span>0 ）をこの行列の鞍点といい，ai0j0 を鞍点値という．
2人非協力零和ゲーム
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u純粋戦略と混合戦略
&= #8226;Theorem1：
•（行列）ゲームが厳密に確定的であるための必要十分条件<= span style=3D'position:absolute;top:38.5%;left:15.54%;width:99.43%;height:5.25%= '>は，その利得行列Aに少なくとも= 1つの鞍点が存在すること．またこのとき，鞍点が均衡点．
2人非協力零和ゲーム
•最適戦略　optimal strategy
•均衡点（i*= ,<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'> j*）は鞍点なので，プレイヤーAが戦略 i*= を用いると，プレイヤーBがいかなる戦略をとっても少なくともv<= /span>(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>A<= /span>) = を得ることができ，また，Bが戦略 j* を取る限り，Aは戦略を変えても利得を増加させることはできない．
戦略 i* が<= span lang=3DEN-US style=3D'mso-fareast-hint:yes;mso-fareast-language:JA'>Aの最適戦略 <= /div>
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u純粋戦略と混合戦略
&= #8226;Theorem2：
•厳密に確定的な零和ゲームにおいて，均衡点が複数ある場合，各均衡点の値は等しい．また，(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>i<= /span>*, j<= /span>*), (i<= /span>0, = j<= /span>0) = が均衡点ならば，(<= span lang=3DEN-US style=3D'font-family:"Times New Roman";mso-ascii-font-family:= "Times New Roman"; mso-hansi-font-family:"Times New Roman";mso-fareast-language:JA'>i<= /span>*, j<= /span>0), (i<= /span>0, = j<= /span>*)= も均衡点である．
2人非協力零和ゲーム
均衡戦略は交換可能
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Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAABsAAAAgCAYAAADjaQM7AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGLSURBVEjH vZchk4NADIWRSCQSWYk8iUSerKysrESCOllZiURWIlcikScrT/YncMnkdWbLbXtsyVa8mVKW+Ug2 +xKipmmid2nZomhKSXuSgSbSgN8VKVsNA6Ql/ZBOpIKFex+4/iJdSD1p8xKMHjyQvkm7hdGXpJHh XjB6oCYdSYnXnkRTjLS2i2AA1asKgbLhArpS0atUnmTm4IShGDjnqRIsRsXmLtifN1EAcsUOdzBE xeUbqx9kyVZuw/isVEFcI5q2pM6GjXZulWEJ6Sq/rYtgnohg7sIMCDuKI4nBngLDKqkLBcdY6ihv h1XPnFoJtpcW9cA0lWG1SBqgCQxrJSgxzGsIq7JgbIXZ7YJbehkIlPOhtu3qk3QOeaDnLUbdH7FF l1uPtG+oRzc/VvObZ4Yq7tVgF55rThyXDp3/tJVhPke6Fm4w6WYrQMa1/48eyBDhzhNUYrDNfSfi BCe/R8+Ln6zl4uqwNn35wwJv28FlDF6gxuxv8D8X1lblK8Y6MwWMu4aTFz4j+i9uBBDUyURmjQAA AABJRU5ErkJggk== ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0048_image146.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAABsAAAAgCAYAAADjaQM7AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGASURBVEjH vZetloMwEIWRSCSyEomsRPYRKpErV1YWVVlZiewjVCIrkUgkkkfozpSbPWkKJSEdxD2HAyRfJvOT SVAUReCiIHhEpNR13HOsxeQx6YfUkB6knlRrzyVp6wWjCULSkdSSLqRkwsqcdIcSZxgN2mD1DAst t3cL6w/WMICquVV+gJ54kbMwBsCizRKQATxMwuCjytbZFkCeK5uCnT7t9wJYDB9GLzB8aG2DwQF4 1P0nYpVh3b8R6mXHH74Nw9yc9PnwTKWHI1ACBBgnfalgv6SzIIzztlWwK2kvBdPdNJoPArB6cNeQ C4kw7GnQ6rBVt3GNAGmHqDRKigCID9hehX7GWykI2/Pu6eWq16uzWLnCizNXEgFQCENC84jpBGAv pXDU3C8GRqOfJqbJjW//oc33llJj7djdN1jQ1F5sWrkUVSXyAJUuTWqKrM8dINwG3sYssmm/IwRN jdXGE//ttP92vheLFL1+h5ypIHW5uOHon+3MloRzBjlfm/4AJrAR8rC1jv8AAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0049.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u純粋戦略と混合戦略
&= #8226;Example3：
2人非協力零和ゲーム
-3
3
2
sB2
1
4
sA2
2
1
sA3
0
-4
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
完全予見は不可能！
決断は下さねばならない！
主体的な賭，
最適な賭の確率
期待効用原理
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iVBORw0KGgoAAAANSUhEUgAAACAAAAAOCAYAAABO3B6yAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB1SURBVEjH Y2hsbGQYSMww7Bzwn4FBYMBDAOiI+UCcMJAOEADi+1CcMCBpAGixARB/B+L/+BxC0wQGtDQC6oD/ uBwCU9iAppDWGOQQBXqEAHI0wPB8mOW0TgOwhIjVYno4YD8+i2mdDfsJWUzTkpAYiwdNXQAAHIK1 a1Q7AUAAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0050.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u純粋戦略と混合戦略 = ;
•Example3：
2人非協力零和ゲーム
-3
3
2
sB2<= /span>
1
4
sA2<= /span>
2
1
sA3<= /span>
0
-4
sA1<= /span>
sB3<= /span>
sB1<= /span>
A＼B
p1
p2
p3
q1
q2
q3
プレイヤーBが各戦略をとったときの，プレ= CヤーAの期待効用
よって，Bが各戦略を(q1,q2= ,q3)の確率でとったときの，Aの期待効用
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u純粋戦略と混合戦略 = ;
•Example3：
2人非協力零和ゲーム
-3
3
2
sB2<= /span>
1
4
sA2<= /span>
2
1
sA3<= /span>
0
-4
sA1<= /span>
sB3<= /span>
sB1<= /span>
A＼B
p1
p2
p3
q1
q2
q3
プレイヤーAが各戦略をとったときの，プレイヤーBの期待効用
Aが各戦略を(p1,p2,p3= )の確率でとったときの，Bの期待効用
= まとめると，プレイヤーA, B= がそれぞれ確率(p1,p2,p3= ), (= q1,q2,q3= )で各戦略をとったとき，
各プレイヤーの期待効用は以下のようになる．
また，このとき明らかに，以下が成り立つ．
プレイヤーAは期待効用最大化！
プレイヤーBは期待損失最小化！
純粋戦略
pure strategy
混合戦略
mixed strategy
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file:///C:/E17059D1/07dmt_5-1.files/slide0051_image191.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAAF8AAAAkCAYAAADvqeb3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABuSURBVGje 7duxCcAwDEVBrS7wJl4mrjyKR0hQZghKcw++we31ijnWnuO6rXNrZ2ZEfdRbmcOHD1/w4Qs+fMGH L/jwBR++4MMXfPiCD1/w4cOHDx++4MMXfPiCD1/w4esz/HVcirRfppwXvx77Zw9fzu+tdJsPMgAA AABJRU5ErkJggk== ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0052.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u支配戦略 = ;
•Example3：
2人非協力零和ゲーム
-3
3
2
sB2
1
4
sA2
2
1
sA3
0
-4
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
3D"テキスト=
><= /b>
3D"テキスト=
><= /b>
3D"テキスト=
><= /b>
-3
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A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
>
>
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A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
支配する
dominate
被支配戦略
支配戦略
戦略の支配 domination of strategies =
プレイヤー i の戦略 h, k について，
戦略 h が戦略 k を支配するとは，
任意の　　　　　　　に対して，<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Garamond;mso-= fareast-font-family: "ＭＳ Ｐゴシック";mso-hansi-font-family:Garamond;font-size:75%;display:non= e'>
が成立すること．
被支配戦略除去の原理
「支配される戦略は用いない」
<= span style=3D'font-family:Garamond;font-size:75%;color:#00CC00;mso-fareast-hint= :yes'>•＝だと「同等<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Garamond;mso-= fareast-font-family: "ＭＳ Ｐゴシック";mso-hansi-font-family:Garamond;font-size:75%;mso-fareast= -hint:yes'>」
<= span style=3D'font-family:Garamond;font-size:75%;color:#00CC00;mso-fareast-hint= :yes'>•≧かつ≠
だと「弱支配」
補足）通常は，被弱支配戦略は
除去しない→　共有地の悲劇
補足：被支配戦略除去の原理による均衡点が存在
→　ゲームは= x配可解 dominance solvable=
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u最適混合戦略 = ;
•Example3：
2人非協力零和ゲーム
-3
3
sB2<= /span>
1
sA2<= /span>
2
sA3<= /span>
sB3<= /span>
A＼B
p2
p3
q2
q3
p2
E1
1
0
5/7
q2
E1
1
0
1/7
9/7
Aの最適戦略 p*=3D(<= span lang=3DEN-US style=3D'font-size:75%;mso-fareast-language:JA'>0, 5/7, 2/7)
Bの最適戦略 q*=3D( = 0, 1/7, 6/7)
(p*,q*)：均衡解
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Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u最適混合戦略 = ;
•Example3：
2人非協力零和ゲーム
-3
3
sB2<= /span>
1
sA2<= /span>
2
sA3<= /span>
sB3<= /span>
A＼B
p2
p3
q2
q3
player B
player A
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意思決定論　5．ゲーム理論　Part I
2人非協力零和ゲーム
-3
3
sB2<= /span>
1
sA2<= /span>
2
sA3<= /span>
sB3<= /span>
A＼B
p2
p3
q2
q3
player A
player B
5/7
1/7
u最適混合戦略 = ;
•Example3：
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u混合戦略の意味 = ;
&= #8226;p*,q* の確率のくじをつくって，引いていずれかに決する方法が，なぜ合理的な決定方法なのか？
2人非協力零和ゲーム
-3
3
sB2<= /span>
1
sA2<= /span>
2
sA3<= /span>
sB3<= /span>
A＼B
p2
p3
q2
q3
Aの最適戦略 p*=3D(0, 5/7, 2/7)
Bの最適戦略 q*=3D( 0, 1/7, 6/7)
<= span style=3D'font-size:86%'>•player A は S= A2<= /span>なら 3， SA3<= /span>なら 2 が望ましいが， = ;
•　　　　　　　　　　　　　 の確率で望ましくない= 結果になる．
しまった！
•このような状況も全て考慮に入れた上で，最適戦略が決定された！
しかし，これは事後的
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演習２：
uプレイヤーAの利得表が以下の表で与えられるゲームを考える．プレイヤーA，Bがそれぞれ期待効用原理に基づいて戦略決定をすると，ゲームの解はどうなるか？
3
-2
sB2
-3
sA2
4
sA1
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
（１）
1
2
3
sB3
3
4
1
sB2
3
4
sA2
2
2
sA3
4
3
sA1
sB4
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
（２）
5
1
sB2
-1
sA2
3
sA1
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
1
3
2
sB2
0
-1
sA2
-2
2
sA3
4
3
sA1
sB3
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
（３）
（４）
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uミニマックス定理 = ;
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>プレイヤーA, Bの純粋戦略
•
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>プレイヤーAの利得行列
2人非協力零和ゲーム
•プレイヤーA, Bの混合戦略
= 得関数
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iVBORw0KGgoAAAANSUhEUgAAACkAAAAOCAYAAACyyTV4AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB4SURBVEjH Y2hsbGQY7HhgLGX4LzDoHQl16HwgThjsjhQA4vtQnDAoHQl1qAEQfwfi//gcO/CZguF/BNSR/3E5 FqawAU3hYMAgxyoMlpBEjnIYng9z4GBIk7DMg9Vxg8WR+/E5bjAUQf2EHDfgNQ4xjhs0RdCwcSQA VyZ4R9h/JIEAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uミニマックス定理
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>プレイヤーAの保証水準
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<= span style=3D'font-size:86%;mso-fareast-hint:yes'>•プレイヤーBの保証水準
2人非協力零和ゲーム
p を操作して期待利得= 最大
q を操作して期待損失= 最小 <= /span>
<= span class=3DB1B style=3D'position:absolute;left:-4.45%'>•Proposition2
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Pw17oTjZDT8DG25sBaXGyvIjxt6a2d1KOIo94aP8w45KmIVSsDncqpkYBtsLrbA4mmbztsZGLKpx e1ociav9Y8neFoNKDkwV44a7koye1DCWMpijrJdgrrjL6FM5P2D0aRiKZO8wCxp9qhGHIRlUXr4L KoQRfaCKvsCTN0rziO7wXAGhoKMSlaj8s/IHdY4OlU7/TaIAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0061.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
<= span style=3D'font-size:88%;mso-fareast-hint:yes'>uミニマックス定理
&= #8226;Theorem3 =
•
•　また，これを成立させ= る戦略の組（p*, q*）を均衡点<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>といい，均衡点における利得 v(A) をゲームの値という．
2人非協力零和ゲーム
J. von Neumann, 1928
•Theorem4
戦略の組（p*, q*）が均衡点であるための必要十分条件は， （p*, q*）が関数 = E(p, q) の<= /span>鞍点であること．即ち，
が= ｬ立すること．
均衡点における<= span style=3D'position:absolute;top:52.94%;left:0%;width:100.0%;height:47.05%'>= 戦略が最適戦略 <= /span>
Aがp*の時，<= /span>Bはq<= /b>*にするのが損失最小 <= /span>
Bがq*の時，<= /span>Aはp*にするのが利得最大
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uミニマックス定理 = ;
&= #8226;Theorem5 =
• <= /span> v(A) がゲームの値， （p*, q*）が均衡点であるための必要十分条件は = ;
•
•　 が成立すること．
2人非協力零和ゲーム
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2人非協力零和ゲーム
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text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
uミニマックス定理 = ;
&= #8226;Example5：一般の2×2ゲーム
2人非協力零和ゲーム
a22
a21
sA2
a12
sB2
a11
sA1
sB1
A＼B
p1
p2
q2
q1
= 鞍点が存在すればそれが均衡点．
なければ，混合戦略を考えるが，
このとき，必ず E(p,sB) と E(p,sB)  及= び E(sA1,q) と E(sA2,q) は交点を持つ．
均衡点=
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9aldmw1hdNfhuhmakw4xgWNmvWr9FNiolrboP8DVqplt1xkGwgRtJSUCZU/Fss1Tx/WHSp5GtSdM 0MZVfbUPbLRubohJgEH68shetSdM2UQFl7uoGmHSIqaQZ/WW5gkTZPKGhDDB9IIGbM8gP19Dm6x2 +NAtOAMX2wWDEHdEIoOrtmXuEBPDmt4euNNEIjOmOyJZIIb9149Va3q/oL8OS/jcjqg8W/g8Lj7+ AZ50NfMKtsrBAAAAAElFTkSuQmCC ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0065.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
演習３：
uプレイヤーAの利得表が以下の表で与えられるゲームを考える．プレイヤーA，Bがそれぞれ期待効用原理に基づいて戦略決定をすると，ゲームの解はどうなるか？
3
-2
sB2
-3
sA2
4
sA1
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
（１）
（２）
5
1
sB2
-1
sA2
3
sA1
sB1
A＼<= span lang=3DEN-US style=3D'mso-fareast-language:JA'>B
------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u2人零和ゲームと線形計画法
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>プレイヤーAの利得行列と混合戦略 p
2人非協力零和ゲーム
まとめると…　
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u2人零和ゲームと線形計画法
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 86%;mso-fareast-hint:yes'>プレイヤーBの利得行列と混合戦略 q
2人非協力零和ゲーム
まとめると…　
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0qlT5n8nTx5dWYfQmv4Pss1pAEIxZmMAAAAASUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u2人零和ゲームと線形計画法
2人非協力零和ゲーム
<= span class=3DB1B style=3D'position:absolute;left:-3.5%'>•Theorem6
（= o），（Ｄ）の最適解が（p*, u*），（q*, w*）のとき，（p*, q*）= が= Qームの均衡点であり，v:=3D u*= =3D w*がゲームの値である
プレイヤーAの問題 （Ｐ）
プレイヤーBの問題 （D）
主・双対
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u2人零和ゲームと線形計画法
•Example6：じゃんけん
2人非協力零和ゲーム
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マキシミン戦略
ミニマックス戦略
<= span style=3D'font-family:Garamond;font-size:75%;mso-fareast-hint:yes'>u両プレイヤーとも，支配戦略は存在しない．
<= span style=3D'font-family:Garamond;font-size:75%;mso-fareast-hint:yes'>u純粋戦略ではミニマックス均衡点は存在しない．
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7drBCYAwEEXBLcmq7GOxQEtJCWsiaAUeVpgHH0KOmWuijq1qD+u7MzNjLe4L9W36wIIlWLBgwRIs WLBgCRYsWLAEC5YHgSVYsARLsGAJlr7FGn4Qtd54sZ6D9Z9H+NEuPc6P2RvtAKAAAAAASUVORK5C YIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
u2人零和ゲームと線形計画法
•Example6：じゃんけん
2人非協力零和ゲーム
0
-4
7
=
4
-7
0
2
-2
0
=
A＼B
自己双対線形計画問題 self-dual LP
(p1*, = p2*, = p3*)=3D(0.53= 8462, 0.153846, 0.307692),  = u*=3D0
 (q1*, q2*, q3*)=3D(0.538462, 0.153846, 0.307692),  w*=3D0
p1
p2
p3
q1
q2
q3
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iVBORw0KGgoAAAANSUhEUgAAANEAAAAzCAYAAAAJtu1mAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAClSURBVHja 7dOxCcAwDEVBjeQRrS28VUbxCAkqnF6pUtzBB6PS8GKsdcecZtbblZlRizoAPdWNiEBEICIQEYhI RCAiEBGICETkR0BEICIQEYgIEBGICEQEIgJEBCICEYGIABGBiEBEICJARCAiEBGICBARiAhEBCIC RAQiAhGBiAARgYhARCAiEJGIQEQgIhARiEhEICL4SUS7DmbW2n4jOg8z+7YHTIj8tBmygbMAAAAA SUVORK5CYIJ= ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定論　5．ゲーム理論　Part I
演習４：
u硬貨合せゲーム = ;
u 　プレイヤーA, Bが各々100円硬貨を投げて表・裏の出た組合せによって勝ち負けを決めるゲームを考える．両方とも表，あるい= は両方とも裏がでたらAの勝ちとし，<= span lang=3DEN-US style=3D'font-size:63%;mso-fareast-hint:yes;mso-fareast-language:JA'>BはAに100円を支払う．逆に2枚の硬貨の出た面が違う場合はBの勝ちとし，AはBに100円を支払う．このゲー= ムの値はどうなるか？　期待効<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 63%;mso-fareast-hint:yes'>用原理の観点で考察せよ． = ;
u
u市場シェアゲーム<= /span>
u 　2大自動車メーカーA社とB社は，各々RV車を販売している．市場でシェア争いにしのぎを削っていた．現状では，いずれも200万で販売しているが，= 今後の戦略として，それぞれ価格を「据え置く」か「10%引き」とするかがある． = ;
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 64%;mso-fareast-hint:yes'>両社とも「据え置く」場合の純利益が，Aが600億円で, Bが400億円， = ;
•Aが据え置き，Bが10%引きだと，Aが300億円で，Bが700億円， = ;
•Aが10%引き，Bが据え置くだと，Aが450億円で，Bが550億円，
•<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 64%;mso-fareast-hint:yes'>両社とも10%引きで販売すると， Aが700億円で，Bが300億円 = ;
u が見込まれる．それぞれの最適戦略はどうなるか？
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参考文献
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>uS.J. Brams & A.D. Taylor, = ``Fair Division’’, Cambridge Univ. Press (1996)
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u鈴木光男「ゲーム理論入門」共立出版（1981,2003（新装版）） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u鈴木光男「新ゲーム理論」勁草書房（1994） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u岡田章「ゲーム理論」有斐閣（1996） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u今野浩「線形計画法」日科技連（1987） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u中山幹夫・武藤滋夫・舟木由喜彦「ゲーム理論で解く」有斐閣（2000）
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u武藤滋夫「ゲーム理論入門」日本経済新聞社（2001） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u逢沢明「ゲーム理論トレーニング」かんき出版（2003）
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>u今井春雄・岡田章編著「ゲーム理論の応用」勁草書房（2005） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>uR.アクセルロッド「つきあい方の科学」ミネルヴァ書房= （1998）
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ICFpbXBvcnRhbnQ7fQ0KYTphY3RpdmUNCgl7Y29sb3I6IzQ0OEM4RSAhaW1wb3J0YW50O30NCmE6 dmlzaXRlZA0KCXtjb2xvcjojNkI1NjUzICFpbXBvcnRhbnQ7fQ0K ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/script.js Content-Transfer-Encoding: quoted-printable Content-Type: application/javascript; charset="shift_jis" function LoadSld() { var sld=3DGetObj("SlideObj") if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } var g_HLinkArray =3D new Array(); =20 function IMapAreaObj( areaObj, coords ) { this.areaObj =3D areaObj; this.coords =3D coords; } function InitHLinkArray() { var appVer =3D navigator.appVersion; var msie =3D appVer.indexOf ( "MSIE " ) var ver =3D 0; if ( msie >=3D 0 ) ver =3D parseInt ( appVer.substring( msie+5 ) ); linkNum =3D 0; for (i=3D0; i 4 ) ) g_HLinkArray[linkNum++] =3D new IMapAreaObj( areaObj, ParseCoords( ar= eaObj.coords ) ); } } function ScaleHyperlinks( factor ) { =20 for ( ii=3D0; ii< g_HLinkArray.length; ii++) { coordsStr=3D""; imaObj =3D g_HLinkArray[ii]; for ( jj=3D0; jj < imaObj.coords.length-1; jj++ ) coordsStr +=3D (imaObj.coords[jj]*factor) + ","; coordsStr +=3D (imaObj.coords[jj]*factor); imaObj.areaObj.coords =3D coordsStr; } } function ParseCoords( coordsStr ) { var numArray =3D new Array(); var i =3D curPos =3D commaPos =3D 0; while ( ( commaPos =3D coordsStr.indexOf(",", curPos) ) !=3D -1 ) {=20 numArray[i++] =3D parseInt( coordsStr.substr( curPos, commaPos ) ); curPos =3D commaPos + 1; } numArray[i] =3D parseInt( coordsStr.substr( curPos ) ); return numArray; } function PlaySound( href, loop ){ href=3D unescape(href); if( window.event ) window.event.cancelBubble =3D true; pptSound.src =3D href; pptSound.loop =3D loop ? -1 : 0; } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"スライド ショーの最後です。 クリックすると終了します。"= , SCREEN_MODE=3D"Frames", gIsEndShow=3D0, NUM_VIS_SLDS=3D55, SCRIPT_HREF=3D= "script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0018.htm",1,-1,1),new hrefList("slide0002.htm",1,-1,1),new hrefList("= slide0019.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("s= lide0025.htm",1,-1,1),new hrefList("slide0026.htm",1,-1,1),new hrefList("sl= ide0021.htm",1,-1,1),new hrefList("slide0027.htm",1,-1,1),new hrefList("sli= de0028.htm",1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slid= e0023.htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("slide= 0031.htm",1,-1,1),new hrefList("slide0032.htm",1,-1,1),new hrefList("slide0= 034.htm",1,-1,1),new hrefList("slide0053.htm",1,-1,1),new hrefList("slide00= 37.htm",1,-1,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("slide003= 5.htm",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0038= .htm",1,-1,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide0040.= htm",1,-1,1),new hrefList("slide0042.htm",1,-1,1),new hrefList("slide0041.h= tm",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new hrefList("slide0044.ht= m",1,-1,1),new hrefList("slide0045.htm",1,-1,1),new hrefList("slide0046.htm= ",1,-1,1),new hrefList("slide0047.htm",1,-1,1),new hrefList("slide0048.htm"= ,1,-1,1),new hrefList("slide0049.htm",1,-1,1),new hrefList("slide0050.htm",= 1,-1,1),new hrefList("slide0051.htm",1,-1,1),new hrefList("slide0052.htm",1= ,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide0055.htm",1,= -1,1),new hrefList("slide0056.htm",1,-1,1),new hrefList("slide0057.htm",1,-= 1,1),new hrefList("slide0058.htm",1,-1,1),new hrefList("slide0059.htm",1,-1= ,1),new hrefList("slide0060.htm",1,-1,1),new hrefList("slide0061.htm",1,-1,= 1),new hrefList("slide0062.htm",1,-1,1),new hrefList("slide0063.htm",1,-1,1= ),new hrefList("slide0064.htm",1,-1,1),new hrefList("slide0065.htm",1,-1,1)= ,new hrefList("slide0066.htm",1,-1,1),new hrefList("slide0069.htm",1,-1,1),= new hrefList("slide0068.htm",1,-1,1),new hrefList("slide0067.htm",1,-1,1),n= ew hrefList("slide0070.htm",1,-1,1),new hrefList("slide0071.htm",1,-1,1),ne= w hrefList("slide0029.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"次へ",sPrev=3D"前へ",sEnd=3D"スライド ショーの終了",sFont=3D"= lＳ 明朝",sArrow=3D"矢印",sFreeform=3D"フリーフォーム",sRect=3D"四角形",sOv= al=3D"楕円" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="shift_jis" 意思決定論　5．ゲーム理論　Part I ------=_NextPart_01C838D0.EFBAAA00 Content-Location: file:///C:/E17059D1/07dmt_5-1.files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis"
 ノ= ート
スラ= Cド ショー
アウトライン
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