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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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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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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
2007/30,Fri. 〜
------=_NextPart_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_5-2.files/slide0031.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
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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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;
|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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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
|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
つまり，相= 手が純粋戦略を取ってきたときだけの自分の混合戦略を考えて期待利得を求めるやり方では，均衡解を求められない
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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:/E17059D2/07dmt_5-2.files/slide0039_image061.png Content-Transfer-Encoding: base64 Content-Type: image/png iVBORw0KGgoAAAANSUhEUgAAABwAAAAOCAYAAAA8E3wEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAI NgAACDQBvpAePAAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAB5SURBVDjL Y2hsbGSgJyZJcUNDgwRdLARalADE6zs6OjhoaiHUovtA/B6IFWgWpEgW/YdiB5rEIRaL/tfX1xdQ PdGAggvdIhrhBmTfgSydj0WRA02zBRaLqZZg8KZSNIvPUyNLEJUPkSxeTteSBmqxAl2LNrqXpdTA AKYCgiQKkkbFAAAAAElFTkSuQmCC ------=_NextPart_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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;
Bがq*をとるなら= A= はp*がベスト
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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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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>
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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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補足：2人非協力零和ゲーム
|2人非協力零和ゲームのNash均衡点 = ;
|例：プレイヤーAの利得表
4
-1
sA= 2
-2
3
sA= 1
sB= 2
sB= 1
Ａ＼Ｂ
p1
p2
q1
q2
p1
q1
0
1
1
3/5
1/2
プレイヤーＡ=
の最適応答
Nash均衡点
プレイヤーＢ=
の最適応答
p1
E
1
0
1/2
1
E
1
0
3/5
q1
零和ゲームの場合は=
<= span style=3D'font-family:Impact;font-size:58%;mso-fareast-hint:yes'>Ø最適応答戦略
<= span style=3D'font-family:Impact;font-size:58%;mso-fareast-hint:yes'>Øミニマックス戦略=
いずれの考え方でも均衡解を求= められるよ
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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:/E17059D2/07dmt_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=
協力ゲームへの転換
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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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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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_5-2.files/slide0057_image243.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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_5-2.files/slide0057_image244.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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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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Y5g5cybH9OnTHUB0Y2Mjw1DBDFOnTrUAOnz/tGnT/gPp60B6OVCsYrB7BoUDdLABECcAHd+P5pn1 QPEGkGc6OjoEaOEQUgOJoAJsngHi+9T2DNCcAlDsU83hRHrmO6WemThxogRQ/3ug3gyaORyHxRpA SyOAuB3NM9tBngFiD5Dj8JkBCghojC4nlHRomoFweOY5Ls9AQ/07LG+B9A+Iw4n0zHtkzyDlo//Q pBMxKByOI88oAB0YAHI41CP/0XA/etIZVGUzKBawOBqEz4M8NugcDgpNUImE5NDnQIfOByUTXBl6 wB0NzZDnoWm8AlTU0rU4pCB9G5DTtBgyjapRhw80BgBA/bk+N4KruAAAAABJRU5ErkJggk== ------=_NextPart_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_5-2.files/slide0058.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
(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:/E17059D2/07dmt_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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QBRpqTIFRY6RI3CEpYOGmnIlaNLlAKuQmbHICSjYYsae5/n+ngX+7dcBoyb2zQE9EMXXLPSiqbc1 MR6BVBuoIZ87GM8KCuhbNzUULz1pzNhqLIi3BmaDg3cr0dpBuosTJJXlCKYLbGRNTEdUJFUn08QP U7I+srsErKXgERz4N5LmmzglcG9SgYeNcLikYwDme7M7f7OzcaWNOd6LSXcPwNXntYksXj/U/tds EHSjy4GzP66qS6iDNg8DuTgQRQhMOAM0AOzcVutog1y0Q6MPW/72550Al+4nJdNCWUoAAAAASUVO RK5CYIJ= ------=_NextPart_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_5-2.files/slide0051_image345.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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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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<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=3D= a/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 <= span style=3D'font-family:"ＭＳ Ｐ明朝";mso-fareast-font-family:"ＭＳ Ｐ明朝";m= so-fareast-hint: yes'>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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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=3D40, 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("= slide0034.htm",1,-1,1),new hrefList("slide0033.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= 68.htm",1,-1,1),new hrefList("slide0035.htm",1,-1,1),new hrefList("slide005= 3.htm",1,-1,1),new hrefList("slide0044.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.h= tm",1,-1,1),new hrefList("slide0038.htm",1,-1,1),new hrefList("slide0050.ht= m",1,-1,1),new hrefList("slide0052.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("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_01C838D1.07C6AB80 Content-Location: file:///C:/E17059D2/07dmt_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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