MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C70A43.F7C35A10" 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_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II

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マスタ タイトルの書式設定
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マスタ タイトルの書式設定
マスタ サブタイトルの書式設定
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<フッター>&= #13;
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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_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II
意思決定科= 学：　ゲーム理論２
情報学部　= 堀田敬介
2006/11/17,Fri. 〜
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Contents
|2人非協力非零和ゲーム
|定義：ゲームのルール，双行列 = ;
|例：囚人のジレンマ，面会ゲーム，恋人達のジレンマ= ，…
|最適応答，Nash均衡点
|Nash均衡点と線形相補性問題（LCP） = ;
|戦略形ゲームの社会・経済問題への応用例
------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0032.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 II
2人非協力非零和ゲーム&#= 13;
<= span style=3D'font-size:88%;mso-fareast-hint:yes'>|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 = ;
|各プレイヤーは，独立に自分の戦略を決定（非協力）
|プレイヤーの利得の和は一定とは限らない（非零和）
|
<= 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= [がどの戦略をとるかは知らない
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>|純粋戦略の数は有限
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2人非協力非零和ゲーム&#= 13;
|双行列ゲーム
|利得関数 = ;
|
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>|利得行列
プレイヤーBの戦略（n個）の利得= （右側）
= プレイヤーA
の戦略（m個）=
の利得（左側）
= 双行列
和が零（一定）という条件はない（非零和）
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2人非協力非零和ゲーム&#= 13;
|例１：恋人達のジレンマ battle of sexes
|ある一組のカップルがデートをしたいと思っている
|男性は野球観戦を希望し，女性は映画鑑賞がしたい
|各々が好きなものを見るより一緒にいることの方が大= 事
(1,2)
(-1,-1)
映画
(-1,-1)
(2,1)
野球
映画
野球
男＼女
性の戦い，男女の戦い，逢引きのジレンマ，…
互いに支配戦略は持たない=
ミニマックス原理に従うと，互いにどちらの戦略でも良い？=
　（または各戦略のマックスが大きくなる方を選ぶ！？）
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AE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAm0lEQVQoz2NgoAsQYDDAEAECJjQ+H4KvAJVnPSfznvWc YIEelM9nqOTCZ2jcYQjlsygqabAoCnIkMvB/gPD5BEB8R6B0fROILyQB40PVq4D4TnD1ak4gfosK 1Pzi3c+BeE4FSD07koNvoHnAAx8f6PoJKD5jYLiALH+AgSEAxk4AYgcIBfe5A6pZDA1IfAc0PlAj UwOqW5ipFnEA46UZ8SoRO/YAAAAASUVORK5CYIJ= ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0055.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 II
2人非協力非零和ゲーム&#= 13;
|例１：恋人達のジレンマ battle of sexes
|零和ゲームの時と全く同じやり方で，混合戦略でミニマックス原理に基づき期待利得最大= ｻをしてみると…
(1,2)
(-1,-1)
映画
(-1,-1)
(2,1)
野球
映画
野球
男＼女
p1
p2
q1
q2
ところが…
Bが　　をと= るならAは　　ではなく(1,0)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Impact;mso-fa= reast-font-family: "ＭＳ Ｐゴシック";mso-hansi-font-family:Arial;font-size:75%;mso-fareast-hi= nt:yes'>にする方が期待利得が高くなる！
Aが　　をと= るならBは　　ではなく(0,1)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Impact;mso-fa= reast-font-family: "ＭＳ Ｐゴシック";mso-hansi-font-family:Arial;font-size:75%;mso-fareast-hi= nt:yes'>にする方が期待利得が高くなる！
均衡しない！
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|最適応答対応 best response correspondence
•Ｂの戦略　　　　　　に対するＡの最適応答の集合
•
•
•
• を，プレイヤーＡの最適応答対応<= 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'>とよび， = ;
• = ;
• を，プレイヤーＡの最適応答集合とよぶ
|Definition 最適応答と最適応答対応 = ;
|最適応答 be= st response
•プレイヤーＡの戦略　　　　　　が，プレイヤーＢの= 戦略　　　　　　に対する最適応答であるとは，以下が成り立つこと
2人非協力非零和ゲーム&#= 13;
純粋戦略の場合
混合戦略の場合
純粋戦略
の場合
混合戦略
の場合
2人零和ゲームでは，=
ミニマックス原理は
最適応答原理に帰着
最適応答原理
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file:///C:/E17059D2/06dmt_5-2.files/slide0039_image061.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAABwAAAAOCAYAAAA8E3wEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB5SURBVDjL Y2hsbGSgJyZJcUNDgwRdLARalADE6zs6OjhoaiHUovtA/B6IFWgWpEgW/YdiB5rEIRaL/tfX1xdQ PdGAggvdIhrhBmTfgSydj0WRA02zBRaLqZZg8KZSNIvPUyNLEJUPkSxeTteSBmqxAl2LNrqXpdTA AKYCgiQKkkbFAAAAAElFTkSuQmCC ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II
プレイヤーＡの（純戦略での）最適応答=
　　sB1<= /span> → max{7,8,4} =3D 8
　　sB2<= /span> → max{0,6,3} =3D 6
　　sB3<= /span> → max{5,2,6} =3D 6
|最適応答と最適応答対応 = ;
•プレイヤーＡ，Ｂが各々最適応答をとる場合，その組= の集合は
•
• となる
2人非協力非零和ゲーム&#= 13;
(6,2)
(3,1)
(4,5)
sA= 3
(2,7)
(6,6)
(8,0)
sA= 2
(5,5)
(0,8)
(7,7)
sA= 1
sB= 3
sB= 2
sB= 1
Ａ＼Ｂ
= |例：
プレイヤーＢの（純戦略での）最適応答=
　　sA1<= /span> → max{7,8,5} =3D 8
　　sA2<= /span> → max{0,6,7} =3D 7
　　sA3<= /span> → max{5,1,2} =3D 5
互いに最適応答なら均衡する
（　　　　なら均衡）
　　　　　　　より，
純粋戦略のみでは
均衡しない
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2人非協力非零和ゲーム&#= 13;
|Definition Nash均衡点 Nash equilibr= ium point
|（混合）戦略の組　　　　　が次の条件を満たすとき= ，　　　　　をNash= 均= t点とよぶ
|Theorem 1
|（混合）戦略の組　　　　が互いに最適応答であるな= らばNash均衡点であり，逆も成り立つ．即ち，Nash均衡点の集合をEとすると，&#= 13;
Nash均衡点は，零和ゲー= = ムの均衡点（鞍点）を含む=
一般的な概念
|Theorem 2
|（混合）戦略の組　　　　　がNash均衡点であるための必要十分条件は&#= 13;
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2人非協力非零和ゲーム&#= 13;
|2人非協力非零和ゲームのNash均衡点
p1
p2
q1
q2
プレイヤーＡ，Ｂが混合戦略をとった際の期待利得
Theorem 2 より，=
=
　　Nash均衡点
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2人非協力非零和ゲーム&#= 13;
|2人非協力非零和ゲームのNash均衡点 = ;
|プレイヤーＡの最適応答について
故に，　　　　　　　　となるため= には，
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------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II
2人非協力非零和ゲーム&#= 13;
|2人非協力非零和ゲームのNash均衡点 = ;
|プレイヤーＢの最適応答について
故に，　　　　　　　　となるため= には，
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AGogjd8wESOujavi/klAS8jS3zFNBoRacIG83cq+SuHvMldDeg8r0KUZ//DYEqcXhOghZ4nH9d32 gKe6+5cf/QJGazKtoxsYJQAAAABJRU5ErkJggk== ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II
2人非協力非零和ゲーム&#= 13;
|2人非協力非零和ゲームのNash均衡点 = ;
|例：
(6,1)
(3,4)
sA= 2
(2,7)
(6,5)
sA= 1
sB= 2
sB= 1
Ａ＼Ｂ
p1
p2
q1
q2
p1
q1
0
1
1
4/7
3/5
プレイヤーＡ=
の最適応答
プレイヤーＢ=
の最適応答
= Nash均衡点
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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 II
2人非協力非零和ゲーム&#= 13;
(6,1)
(3,4)
sA= 2
(2,7)
(6,5)
sA= 1
sB= 2
sB= 1
Ａ＼Ｂ
EA(p,q)
EB(p,q)
= EA(p,(4/7,3/7))= =3D30/7
EB((3/5,2/5), q)=3D23/5
p1
q1
0
1
1
4/7
3/5
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2人非協力非零和ゲーム&#= 13;
|Theorem 3
|（混合戦略まで拡大すると，）双行列ゲームには，少= なくとも1つNash均衡点が存在する = ;
|
|Theorem 4 （cf. Theorem 2）
|（混合）戦略の組　　　　　がNash均衡点であるための必要十分条件は= ，　　　　　が写像　　　　　　　　　の不動点であ= ること．即ち，
戦略の組が均衡点であるための必要十分性（Theorem 2, 4など）=
の証明は，「Brouwerの不動点定理」「角谷の不動点定理」などから
------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0049_image183.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjA4wK/AxMAJYn0MZgQxmNcyMjAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgUmA7wCwFZamz8DFIM/0GKGQRAtgFZy4C4gZ+B4RjQMG6oGh4G38SSjJDKglQG hgCw3b+ZGv5BXDgBZCkDCxODQEhmbmqxgl9quUJQfm5iHsON+e/LHwKxgsLH8n+caTYsQHW6QNUc QNqIq4HRhw/kJC1NGP8GD8goDTh/LweqfD07qvwmZkYU+ShGCB/VfXuYGElyHyMDiP6A5M4ZvCAT CuD2MHOA+IVw/g8mVH4BA0Q9xB0K/2HhxEhiOEHcwQh1xwNGWXD4OGnC+OfZQHxHTfT4oNS/xtwg E4Lg/rnFCuFjiXcmkD3BlblJ+TkMDEu5uJK/fBQi0j8NjPJcICO2wO3pYgHxz8H5OkwQeS5oKuQC p1RwcoOmQSGwWVC3NDAyMTEFVxaXpOYy2IDsZQDqUGToAmsAEQJfhBjQ/cwM1g8AHYXBL3ADAAA= ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0049_image184.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjB4wKHAxMgJYl0IYWQAMphrGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMCkwPOISALDU2fgYphv8gxQwCQP4BIGsZEC/gYGA4BjSMG6qGh8E3sSQjpLIg lYEhAGz3b6aGfxAXTgBZysDCxCAQkpmbWqzgl1quEJSfm5jHcGP++/KHQKyg8LG8litNhQWoTheo Gmg4gxFXA6MSB0irZiWMP4cNxNeA862ZUeVfM0LkUe3fw8RIkv2MDCD6A5I7YthBJhTA7ckHm1gI tUfhP8yfjCT6E2IPI9SeB4wPWUEmOFXC+NZgEx0r0cOTUv98ZwGZEAT3jxsDhI8l3phA9gRX5ibl 5zAw/OfiCv/yUYhI/zQwPgbHz5ZKLmgq4QKnJHBygKYRIbBaqF0NjExMTMGVxSWpuQwqIHMZgDoU GbrAGkCEwBchBnQ/MYP1AwDTOTFwEAMAAA== ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0048.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 II
演習１：
|次の双行列ゲームのNash均衡点を求めよ
(-2 , 2)<= /span>
( 6 ,  -8)
sA= 2
( 4 ,  6)
(-24, 12)=
sA= 1
sB= 2
sB= 1
Ａ<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 71%;mso-fareast-hint:yes'>＼Ｂ<= /div>
------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0054.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 II
Coffee Brake!
|John F. Nash (1928- ) =
|紹介サイトの情報 = ;
|
|
|
•
|
|A Beautiful Mind
いずれも2004年11月9= 日（火）取得の情報
<= span style=3D'font-family:Impact;font-size:75%'>=3D"*" Non-Cooperative Games Nash [pdf]
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2人非協力非零和ゲーム&#= 13;
|例２：囚人のジレンマ prisoner’s dilemma
|２人の凶悪犯が別個に取り調べを受けている<= span style=3D'font-family: "ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴシック";font-size:86%;= display:none'>
|現状では証拠不十分で軽い罪でしか起訴できないため= ，２人とも3年
|各囚人は司法取引を持ちかけられ，応じた方は1年，応じない方は10年，ただし，２人ともが応じた場合は２人とも8年
(8,8)
(1,10)
自白
(10,1)
(3,3)
黙秘
自白
黙秘
A＼B
※司法取= 引：被告が自分の罪を認める代わりに罪を軽くしてもらうこと
= 注意：値が小さい方が嬉しい！
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最適応答原理に従ってまじめに計算しても…
2人非協力非零和ゲーム&#= 13;
|例２：囚人のジレンマ= prisoner= fs dilemma
(8,8)
(1,10)
自白
(10,1)
(3,3)
黙秘
自白
黙秘
A＼B
注意：値が小さい方が嬉しい！
各プレイヤーとも，「自白」が支配戦略！　結果として，= （自白，自白）がNash均衡点であり，ゲームは支配可解
最適応答原理に従って考えても…，
p1
p2
q1
q2
p1
q1
0
1
1
注意：±逆で計算
明らかにもっと良い解がある=
Pareto最適でない！
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Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0044.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 II
2人非協力非零和ゲーム&#= 13;
|Nash均衡点が最適戦略か？=
|2人零和ゲーム
•ミニマックス戦略が最適戦略！ = ;
<= span style=3D'font-size:86%;mso-fareast-hint:yes'>|2人非零和ゲーム = ;
<= span style=3D'font-size:83%'>•Nash均衡点が最適戦略を与= えるわけではない！
<= span style=3D'font-size:83%;mso-fareast-hint:yes'>•ゲームの値が異なる複数の均衡点が存在する場合がある！
<= span style=3D'font-size:83%'>•Nash均衡点は，必ずしもPareto= 最適ではない！
行動の指針を与えてくれる
最適応答原理は不十分かも…！？=
（しかし他に適切なものがあるか？）
•得られる解の状態を示すことで，何らかの= 均衡戦略を= とるべきことを教える= •<= /span>均衡状態が複数あることを示すことで，戦略決定判断= が困難であることも教える
非協力ゲーム
Nash均衡点の精緻化
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2人非協力非零和ゲーム&#= 13;
|例３：面会ゲーム = ;
|遠く離れている２人が至急会う必要がある
|今居る場所は互いにわかっており，会いに行くか，相= 手が来るのを待つかの選択が出来る．（途中で会うことは= ない）
(0,0)
(10,6)
待つ
(6,10)
(-6,-6)
行く
待つ
行く
A＼B
p1
q1
0
1
1
3/11
3/11
Nash均衡点=
（（0,1）<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>1,0））,
（（3/11,8/11）,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>3/11,8/11））,
（（1,0）<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>0,1））
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2人非協力非零和ゲーム&#= 13;
p1
q1
0
1
1
3/11
3/11
EA(p,q)
EB(p,q)
= EA(p,(3/11,8/11))=3D30/11 <= /span>
EB((3/11,8/11), q)=3D30/11
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VAbYYrk2olriWj1dIyASFGoCbLFce3uLxLVd3lifSFCoD7DFcm1ojcS1Nm+8TyQoQEnj2pBaiWtd dIWDbVCAksa18Sv3C1x7nK5vEAlMezgwvy3Xxq86IHDtabq+QSQoPB6Y35Zr4zI6BK49T94JIkHh 6cD8tlwbl3lQ4NrLdH2DSFB4PrCysFwbu+aQwLXXaVaCSFB4OTC/LdfG5nQLXBtGswNEgsLrgflt uTYmV+LaKJodIBIUhgWyg+Xa6PwjAtfG0ZwGkaAwKkAHy7X3C48JXJtKcwtEgsK4AB0s15LWHhe4 NofmNIgEhakBOliuvVcicW0x7S+IBIU5ATpYro1aJ3Et1XvPJxIUFgfoYLk2suy0wLU1NDNBJChA SePaOxvOCFwrpNwAIkFhTYAtlmvDK84KXCuj9wpEggKUNK4N2yhxbTMRAUSCQlmALZZrQ6skrtUR EUAkKGwOsMVybchmiWvbiS0gEhTqAmyxXBtcLXGt2ZvkEwkKUNK4NnCrxLVOukbBNihASePamNR2 gWuP0LwCkcC0BwMz1HJtdJrEtSdoNIgEhUcCM9RybfSqToFr/ej6BpGg8ERgtOXa+xkS116g6xtE gkK/wPy2XEvK7BK4NoCubxAJCi8E5rflWlKWxLU3iEkgEhQGBOa35dp7OT0C14bT9Q0iQeGNwMrC cm1U3lGBa0k0K0EkKAwPzG/LtXcLJK5NoPEgEhSSAvPbcm1kocS1GTQ7QCQoTAjMb8u1d9aeFLg2 n+Y0iASFGYHsYLk2vOSUwDX8RVEQCQrzA3SwXHt7ncS1VTS3QCQoLAvQwXLtrTKJazl0vkAkKKwK 0MFy7c1yiWvFdK5AJChASePakAqJaxXeRJ9IUCgO0MFy7fVKiWs1RAQQCQpQ0rg2cJPEtXpiC4gE hZoAWyzXXq2SuLabrhMQCQr1kb85EOTay5slru33pvlsgwKUzOi//C2rv/wtq7/8Lau//C2rP83f svrL36r5/9Pfqom9ujSC2C0mer+N+suev+Ut5vJstn8PFq/If10WszKsNs8b5KihZ/568mMxf/Ha vKL/xWvM3LDqSm+2o4qe+Uvno2L++iheOd9fvMbcDmsWUMtqFvDrcKOUmD01r+h/8drOwk1R53tT 5Hx/RGuh6LOJV+S/eD3VezRyvT4WxYDHeIvp3lO8xXSvr7MFeuEtZnnP8hYzveecLdAzfy28P28x J0JQbGFe752wyBvKWyyM/FVRbIFeeIvFlPXNX7weGfUXr0dGfHcMb7GUWnaLpfw6rozJkb+rPTnq 72pPjuSchZG/FrbI2QK98BaZ9A6Ft8j0ljtboGf+4npG5O97Z0T9fe+MyLWUG3HGPGcL9MJbFFPe DG+xltbkdgv0wlus87byFqXUsluU8uu9E8q9j3iLMmrZLcr49d4JlV5jxNMbnS0q+PXetO0TXvRf vMYr8fzF6zJeo9irEK/gKrzHuQqj/95Vp3cf0eVO5+9dXejvYX268XcNuGtATVJNkv3+Jf7f+P3/ AJpJ149OaQEA ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0057.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 II
2人非協力非零和ゲーム&#= 13;
|例４：弱虫ゲーム  chicken game
|２人の人間が２台の車をそれぞれ運転する
|２人は，お互いに向かって車を走らせる
|２台ともそのまま走り続ければ，やがてぶつかり死ぬ= ため，直前で回避してよい． = ;
|しかし，相手より先によけた（進路を変えた）プレイ= ヤーは「チキン」と罵られ，臆病者のレッテルを貼られる
(-5,-5)
(9,0)
避けない
(0,9)
(2,2)
避ける
避けない
避ける
A＼B
------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0057_image234.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAABkAAAAgCAYAAADnnNMGAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF/SURBVEjH Y2hsbGTAhYHAAogdiMAWeM3BY4ECMzPTbz11yfeEMAc7yw98FuG1RFiQ6/Oj4zX/CWGQRSAfjVoy asmoJaOWjFoyaC2BVjz/0bGKvMg3YixxtFT+ik0/FxdLKopPRIS4Ty7si/hJjKGE8P4Vmf/FRXnv AS0SQLEEJCAqxP3k2Lociiy4srvkv4Ks0AugeRpY4wQkAVIAUkiuJSa6Mm8Febj88EY8Hw9HqI2p wltyLEgON/sgKszTSlTqAikEaSDFgkmNgb+Ehbh3kJSEgQnh4Mz2kF/EWLBhduJ/MWGey8Dg5iA1 n3AALbq1fVEqXgvObin4Lysl8BSUr0jOjLAMKSXO9wpXQrh9sOK/lqr4a7Ibd0gWORhpS78GGYhu ia+z9gdYhqPIEhAW5OOojAkw/ohsQXWu8zdgRM8lRj9RloBTnAjP8uZiD3Axs3Jq7H9BAa7zxOol 2hJQQgCloClNgf9BJQOsyKCqJVCLJHi52G8jFxlUt4RcDAAcgu7UHWSpzAAAAABJRU5ErkJggk== ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0057_image235.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAANEAAABTCAYAAAABQuI8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHRSURBVHja 7dy7DYJgFIDRvzKsYMcOLsA01m5gGMPEUUxwAAZgCxpjYqEIig/UQjBWHJKvoL25h2tlCCGc6g51 pcLRDMzli3atm02apqF5KkmDKp4RbZuXsdfMIq8qvWQu3VZZdkO0hggiiCCCCCKIIIIIIogggggi iCCCCCKIIIIIIogggggiiCCCCCKIIIIIIogggggiiCCyJBBBBBFEEEEEEUQQQQQRRIIIIogggggi iCCCCCKIIBJEEEEEEUQQQQQRRBCNB5Gk/j0QLedLn5f8+sV1kT9faHPozGMBEUQQQQQRRBBBBBFE EEEEEUQQQQQRRBBBBBFEEEEEEUQQQQQRRBBBBBFEEEEEEUQQQQQRRBBBBBFEEEEEEUQQQQSRZYEI IogggggiiCCCCCKIILIoEEEEEUQQQQQRRBBBBBFEgqgPIkn+Rtglcon8nIMIIogggggiiCwLRBBB BBFEEEEEEUQQQQSRJYEIIogggggiiCCCCCKIIBJEEEEEEUQQQQQRRBBBBJEggggiiCCCCCKIIIII IogsjblABBFEEEEEEUQQQQQRRBAJIogg+h+ieBpXySwZfdEkagZT6i1z6bZvZ5LfEUkaVHFB5DxL v3UGb53XqcuUdSMAAAAASUVORK5CYIJ= ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0037.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 II
2人非協力非零和ゲーム&#= 13;
|例４：弱虫ゲーム  chi= cken game
(-5,-5)
(9,0)
避けない
(0,9)
(2,2)
避ける
避けない
避ける
A＼B
p1
q1
0
1
1
5/12
5/12
Nash均衡点=
（（0,1）<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>1,0））,
（（5/12,7/12）,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>5/12,7/12））,
（（1,0）<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>0,1））
= EA(p,(5/12,7/12))= =3D10/12
EB((5/12,7/12), q)=3D10/12
(9,0)<= /div>
(0,9)<= /div>
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2人非協力非零和ゲーム&#= 13;
|例１：恋人達のジレン= マ battle of sexes
(1,2)
(-1,-1)
映画
(-1,-1)
(2,1)
野球
映画
野球
男＼女
p1
q1
0
1
1
2/5
3/5
Nash均衡点=
（（1,0）<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>1,0））,
（（3/5,2/5）,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>2/5,3/5））,
（（0,1）<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>,（<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:75%;mso-fareast-language:JA'>0,1））
EA(p,(5/12,7/12))= =3D1/5
EB((5/12,7/12), q)=3D1/5
(2,1)<= /div>
(1,2)<= /div>
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2人非協力非零和ゲーム&#= 13;
|例５：純粋戦略全ての= 組合せがNash均衡
(4,4)
(8,4)
sA2
(4,8)
(8,8)
sA1
sB= 2<= /span>
sB= 1<= /span>
A＼B
友情ルール：自分の利得が同じならば，= 相手の利得が大きい方の戦略を選ぶ
Nash均衡点の精緻化
全ての戦略の組がNash均衡点！
（s= A１,sB1）が均衡点となる
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3D"テキスト=
弱支配
2人非協力非零和ゲーム&#= 13;
|例６：共有地の悲劇 （囚人のジレンマのn人拡張版） = ;
|数軒の酪農家が共有の牧草地を所有している．各酪農= 家が先を争って牛を放牧し，自分の利益最大をはかる限り，牛の数を= 増やし続けると，待っているのは共有地の荒廃という悲劇である．
<= span style=3D'font-size:71%;mso-fareast-hint:yes'>|単純なモデルでの考察
<= span style=3D'font-family:"Times New Roman";font-size:75%;mso-fareast-hint:yes'= >•酪農家は4 (i=3D1,2,3,4)
<= span style=3D'font-family:"Times New Roman";font-size:75%;mso-fareast-hint:yes'= >•酪農家iが放牧する牛の数 qi
<= span style=3D'font-family:"Times New Roman";font-size:75%;mso-fareast-hint:yes'= >•各酪農家は32
<= span style=3D'font-family:"Times New Roman";font-size:75%;mso-fareast-hint:yes'= >•酪農家iの収益をxiとし，xi =3D qi{16−(q1 + q2 + q3 + q4)}2 qi
12
10
6
0
7
15
12
7
0
6
18
14
8
0
5
21
16
9
0
4
24
18
10
0
3
27
20
11
0
2
6
6
4
0
9
30
22
12
0
1
33
24
13
0
0
0
0
8
2
9
3
5
1
8
i＼others
たくさん放牧すると収益が減る！
= Nash均衡点
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file:///C:/E17059D2/06dmt_5-2.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 II
Nash均衡点と線形相補性問題
|Definition 戦略的同等性 = ;
|ゲームGのNash均衡点がG’のそれであり，かつその逆も成立するとき，2つのゲームは戦略的に同等であるという
|Theorem 5
|2つの双行列ゲームG, G’において，任意の要素について，
|
|
| という関係があるとき，GとG’は戦略的に同等である
= |例：
(5,-2)
(-2,4)
sA2
(0,2)
(3,-1)
sA1
sB= 2<= /span>
sB= 1<= /span>
A＼B
(9,-4)
(-5,14)
sA2
(-1,8)
(5,-1)
sA1
sB= 2<= /span>
sB= 1<= /span>
A＼B
3D"左右矢印=
戦略的同等
G
G’
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MR6BVBuoIZ87GM8KCuhbNzUULz1pzNhqLIi3BmaDg3cr0dpBuosTJJXlCKYLbGRNTEdUJFUn08QP U7I+srsErKXgERz4N5LmmzglcG9SgYeNcLikYwDme7M7f7OzcaWNOd6LSXcPwNXntYksXj/U/tds EHSjy4GzP66qS6iDNg8DuTgQRQhMOAM0AOzcVutog1y0Q6MPW/72550Al+4nJdNCWUoAAAAASUVO RK5CYIJ= ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0059.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 II
Nash均衡点と線形相補性問題
|Nash均衡点を求める
Nash均衡点
= Th.2
= Th.5
ただし，
ただし，
とおく
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Nash均衡点と線形相補性問題
|Proposition 1= 相補性 complementarity
Nash均衡点=
が存在する
まとめ= ると…
を満たす　　　　　　　　　　が存在 <= /span>
が成立
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file:///C:/E17059D2/06dmt_5-2.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 II
Nash均衡点と線形相補性問題
|LCP, Linear Complementarity Problem
を満たす解
がNash均衡点
ただし，
B=3D-AだとLP　⇔　零和= ゲーム
Lemke法（M≧0）<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Impact;mso-fa= reast-font-family: "ＭＳ Ｐゴシック";mso-hansi-font-family:Arial;font-size:83%;display:none'>=
内点法（M：<= span lang=3DEN-US style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-= hansi-font-family: Arial;font-size:83%;mso-fareast-language:JA'>PSD,P0,…）<= /div>
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戦略形ゲームの応用　（岡田章『ゲーム理論』p.49-59等）
|応用例１：クールノー複占市場
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|2i=3D1,2）が同質な財を生産し，同一市場に供給している <= /span>
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|企業iの供給量qi ( ≧0) p=3Dmax{a−b(q1 + q2), 0}, (a,b>0)
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|企業iの費用関数 Ci(qi)=3D ci qi , (0<ci<a)
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|企業iの利潤関数π<= 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";font-size:47%;position:relative; top:.37em;mso-text-raise:-25%;mso-fareast-language:JA'>i (q1, q2)=3Dpqici qi
限界費用
各企業は利潤最大化したい！
クールノー・ナッシュ均衡<= span style=3D'font-family:Impact;mso-ascii-font-family:Impact;mso-hansi-font-fa= mily: Arial;font-size:75%'> Cournot-Nash equilibrium
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|企業i（=3D1,2）の企業j（≠i）に対する最適応答対= 応 <= /div>
= p＞0
= p＝0
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iVBORw0KGgoAAAANSUhEUgAAADMAAAAdCAYAAAAHB1RsAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAECSURBVFjD 7ZihDsIwEIYneYxJJBKJRCJ5BCSPwBQStSwdAskjIBDIkbEFieQRJiePu61NFgKkbBlU/OJPK67d fff3Js4LgsCzUabomsWUsE5OSVFhcvRsYXJF9ywk3zb+V2IYAgxgAAMYwAAGMIABDGAAAxjAAMYB mHRL8zSiybOsPhrS+NXZrmoFw4fWjUFCIpdoFWdFo0bSfqpoelG04gLsq0GIxPU0DMlj2n0Nc1Q0 EGd0goVcwvsN7xfVWk9KSnGQdRAYiW+C9i0bR2YaoDRuVP1TV1uqE7ETS7FcgP/ZP29dkCTFAQ1w M9UWONbQtR/BR2dMs7uYdOtnBhjAdNcD+bXo1QIdgVwAAAAASUVORK5CYIJ= ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0051_image336.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAADMAAAAdCAYAAAAHB1RsAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAELSURBVFjD 7ZihC8JQEMaNRqPRaDQajUaj0Wg0Gl0yikHGm8Fo9A8wGJW5sWg0LhqNn3ePJ25DkU0H27jwcWxw 8P3uu1euZllWrSqqDMhHmLPCzFO4+ApbV2Hi2uiVOhmC6DMMQSGiwHewoTr2VuiWbs3IeEObp6Q0 kIMj1Z2p+pugF56N0UmhU5o3Q+bbZN6mGprUBpwQr6JJLDCAB6pzd40h9xQOhs1pk0+9Vi8koFZs RemN0f+pAeZE77HeP4qHmBqGjF150mw0qW+9e4X6u75/iAeaCSaZQBEkMAIjMAIjMAIjMAIjMAIj MAIjMAJTABh9eeHzUk6HicxSuKWHWaKZ11Hip4NGZFse3+AXNmbQJRIAAAAASUVORK5CYIJ= ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.files/slide0062.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 II
戦略形ゲームの応用
|応用例１：クールノー= 複占市場
q1
q2
0
の場合
クールノー・ナッシュ均衡点
各企業の利潤
財の価格
パレート最適ではない
例：c1=3Dc2の時，q1=3Dq2=3D(a-c)/4b= とした方が，どちらの企業もより多くの利潤が得られる
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戦略形ゲームの応用
|応用例２：寄付金ゲーム
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|ある町の町長が，公共事業のため，n人の住人に寄付を募る
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|各住人は，寄付額 0円〜1000 を自分の好きな分だけ寄付 <= /span>
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|寄付総額の2n人の住人に均等に
|i (=3D1,…,n) の戦略（寄付額）： = xi 0≦xi≦1000） <= /span>
|i (=3D1,…,n) の利得関数：
n>2= の<= 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'>時，戦略 xi*=3D0 が，他の戦略 xi >0 に対する支配戦略となる！
戦略の組 x*=3D(0,…,0) が唯一の均衡点， = ;
即ち，誰も寄付しない= ！
寄付はいくら集まるだろう？
パレート最適ではない
全ての住人が1000円寄付すると，全ての住民の利得は1000円であり，均衡点より望ましい
しかし，x=3D(1000,…,1000)= では，どの住民も裏切る動機を持つ
ただ乗り free-riding：<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:Impact;mso-fa= reast-font-family: "ＭＳ Ｐゴシック";mso-hansi-font-family:Arial;font-size:83%;display:none'>=
他人の貢献を利用して個人的利益を得る行為
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file:///C:/E17059D2/06dmt_5-2.files/slide0064.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 II
戦略形ゲームの応用
|応用例３：電力消費ゲーム
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|ある都市で，n人の住人がクーラーを所持．暑い日の出来= 事
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|各住人i (=3D1,…,n)の戦略と，その費用，及び効用は，
<= span style=3D'font-family:"Times New Roman";font-size:75%;mso-fareast-hint:yes'= >•戦略：低温設定（xi=3Dα)，電力消費1000W，効用U
<= span style=3D'font-family:"Times New Roman";font-size:75%;mso-fareast-hint:yes'= >•戦略：中温設定（xi=3Dβ)，電力消費500W，効用u （U>u>0) =
<= span style=3D'font-family:"Times New Roman";font-size:71%;mso-fareast-hint:yes'= >|この都市の停電確率は，総電力量をQとしたとき，
停電臨界点
|節電する住人の数をs (0≦s≦n)
<= span style=3D'font-family:"Times New Roman";font-size:75%'>•Q(s) :=3D 500s + 1000(n-s)=3D1000n-500s
|住人i の効用は
<= span style=3D'font-family:"Times New Roman";font-size:75%'>• 
減少関数Q(s)について，Q(s’)≦c≦Q(s’-1) を満たすs’が= 唯一定まり，0≦s*≦s’-2, s*=3Ds’を満たす全てのsが均衡点
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7dTRCYAwEAXBtJ4y7ElIKZagxi9bWJiBd3AN7DiPe727zcwstzXnHGM/APTsfgs5QJiQA8QJOUCc kAPECTlAnJADxAk5QJyQA8QJOUCckAPECTlAnJADxAk5QJyQA8QJOUCckAPECTlAnJADxAk5QJyQ A8QJOUCckAPECTlAnJADxAk5QJyQA8QJOUCckAPECTlAnJADxAk5QJyQA8QJOUCckAPECTlAnJAD xAk5QJyQA8QJOUCckAPE/UN+7cfMzHK7vpDvY2Zm3T3nXYhRYB9ISwAAAABJRU5ErkJggk== ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II
戦略形ゲームの応用
|応用例３：電力消費ゲ= ーム
s
Q
0
1000n
n
s’-1
s’
s’+1
s’-2
均衡点
均衡点
c
都市停電！=
<= span style=3D'font-family:Impact;font-size:75%;mso-fareast-hint:yes'>•<= /span>全住人の効用は0． = ;
•1人の住人だけ設定を変えても効用は0のままなので均衡状態
都市停電せず=
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>•低温設定住人の効用U
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>•中温設定住人の効用u
•中温設定の1人でも低温に変更<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 75%;mso-fareast-hint:yes'>すると停電（効用がu→0)より均= 衡状態
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avR8vMmdXBl1PjNsNxcUEHG/PdUZdZ7eMXou1vPQu6n7sW6XFxQScb/jZ+t362O537r+ufHHp1sR r2ddCCgi4n4HBjyo4ngd9ZN8p86NJTOdCI8wQiERbz1IILd4jg7GLzmjbg/G2zyDa3Zc1FBExF85 UO/A1o0ngoZCIu638aSO+oR/qAaFRuy/IoKIQcQiBhGLGEQsYhAxiFjEIGIRg4gBEYOIRQwiFjGI GEQsYhCxiEHEIobvP+Lnf8WbPC3TsqxP69GfsVxOxFXs6TZiNE/LtCzr87qbJ98UEbFlWd9eHwHs sAMYYwT94QAAAABJRU5ErkJggk== ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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 II
戦略形ゲーム
|囚人のジレンマ型ゲー= ム
(T1, T2)
(B1, W2)
D
(W1, B2)
(S1, S2)
C
D
C
A＼B
ただし，Bi (best) > Si (second) > = Ti (third) > Wi (worst)
=
さらに=
=
も満たすならば，『標準的な囚人のジレンマ型ゲーム』 とよばれる
２人のプレイヤーが互いに相手と異なる戦略を交互に取る，即ち，=
(C,D)→(D,C)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-famil= y:"ＭＳ Ｐゴシック"; font-size:67%;mso-fareast-hint:yes;mso-fareast-language:JA'>→(C,D)<= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:= Impact; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:Arial;font= -size:67%; mso-fareast-hint:yes;mso-fareast-language:JA'>→…
とするときの期待利得が，協調行= 動(C,C)<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴ= Vック";font-size: 67%;mso-fareast-hint:yes'>の利得より小さい状況
→ Nash均衡は (D,D)
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戦略形ゲーム
|演習：
|身近な所，あるいは社会において，囚人のジレンマと= 同じ状況となっていると思われる例を２つ上げよ．<= span style=3D'font-family: "ＭＳ Ｐゴシック";mso-fareast-font-family:"ＭＳ Ｐゴシック";font-size:86%;= mso-special-format: lastCR;display:none'>
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参考文献
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>|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'>|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'>|岡田章「ゲーム理論」有斐閣（1996） = ;
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>|今野浩「線形計画法」日科技連（1987） = ;
<= span style=3D'font-size:75%'>|R. Axelrod, 松田裕之訳「つきあい方の科学」ミネルヴァ書房（1998）
<= span style=3D'font-size:75%;mso-fareast-hint:yes'>|…… <= /span>
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<ヘッダー>= ;
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<日付/時刻>
マスタ テキストの書式設定
第 2 レベル
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第 5 レベル
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<#>
プレイヤーＡについて
　○π1(q1,q2)は上に凸の2次関数．全範囲= では頂点で最大値をとる．=
　○π1(0,q2)=3D0
　○q2=3Da/b の時は π1(q1,q2)= <0 であり，q= 2=3D(a-c1)/b のときπ1= (q1,q2)=3D0となる．
　○従って，0<=3D q2 <=3D (a-c1)/b までは，この2次関数上の頂点= がプレイヤーＡの最適応答であり，(a-c1)/b <=3D q2 <=3D a/b までは q1=3D0が最適応答とな= る．= 　○また，q2 >=3Da/b では，線形関数-c1q1となるが，最大値は常にq1=3D0の時0である．
　○以上をまとめると，表記の通りとなる．
プレイヤーＢについても同様．
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cnRpY2FsLWFsaWduLXNwZWNpYWw6YmFzZWxpbmU7DQoJbXNvLWZhcmVhc3QtbGFuZ3VhZ2U6SkE7 DQoJbXNvLWFuc2ktbGFuZ3VhZ2U6RU4tVVM7fQ0KYTpsaW5rDQoJe2NvbG9yOnJlZCAhaW1wb3J0 YW50O30NCmE6YWN0aXZlDQoJe2NvbG9yOiNDMTI3MjcgIWltcG9ydGFudDt9DQphOnZpc2l0ZWQN Cgl7Y29sb3I6I0E4OTI1NCAhaW1wb3J0YW50O30NCn== ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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=3D39, 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("slide0030.htm",1,-1,1),new hrefList(= "slide0031.htm",1,-1,1),new hrefList("slide0032.htm",1,-1,1),new hrefList("= slide0033.htm",1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("s= lide0055.htm",1,-1,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("sl= ide0041.htm",1,-1,1),new hrefList("slide0040.htm",1,-1,1),new hrefList("sli= de0042.htm",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new hrefList("slid= e0045.htm",1,-1,1),new hrefList("slide0046.htm",1,-1,1),new hrefList("slide= 0047.htm",1,-1,1),new hrefList("slide0049.htm",1,-1,1),new hrefList("slide0= 048.htm",1,-1,1),new hrefList("slide0054.htm",1,-1,1),new hrefList("slide00= 35.htm",1,-1,1),new hrefList("slide0053.htm",1,-1,1),new hrefList("slide004= 4.htm",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0056= .htm",1,-1,1),new hrefList("slide0057.htm",1,-1,1),new hrefList("slide0037.= htm",1,-1,1),new hrefList("slide0058.htm",1,-1,1),new hrefList("slide0038.h= tm",1,-1,1),new hrefList("slide0050.htm",1,-1,1),new hrefList("slide0052.ht= m",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("slide0051.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("slide0067.htm",1,= -1,1),new 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 II ------=_NextPart_01C70A43.F7C35A10 Content-Location: file:///C:/E17059D2/06dmt_5-2.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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