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<日付/時刻><= span lang=3DEN-US style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"= ＭＳ Ｐゴシック"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"ＭＳ Ｐゴ= Vック";font-size: 56%;mso-fareast-language:JA;mso-special-format:lastCR'>
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------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
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意思決定科学： ゲ= ーム理論３
情報学部　堀田敬介=
2006/1= 2/1,Fri.
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charset="shift_jis" 意思決定科学： ゲーム理論3
Contents
n協力ゲームの理論
–2人交渉ゲーム&#= 13;
–結合戦略，実現可能集合
–<= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";font-size:120%;mso-fareast-lang= uage: JA'>Nash交渉解&#= 13;
–提携ゲーム，提携と配分
–コア，安定集合，シャープレイ値=
n
n投票ゲーム
–投票力指数
nシャープレイ・シュービック指数&#= 13;
nバンザフ指数&#= 13;
nディーガン・パックル指数
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協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal;mso-fareast-h= int: yes'>n<= /span>2人交渉ゲーム
–交渉問題（bargaining problem）
n= 交渉を行う　←何らかの共通の認識をもつ
n= 共通の認識を明確に定義し，交渉のルールと解を求める
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–例：恋人達のジレンマ
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n事前に話し合いを行う
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–ジャンケンで勝った方，強く主張した方，くじ引き，etc…
( 1, 2)
(-1,-1)
映画
(-1,-1)
( 2, 1)
野球
映画 <= /div>
野球 <= /div>
男＼女<= span style=3D'font-weight:normal;color:#996600;mso-special-format:lastCR;displa= y: none'>
–結合純= 略（joint pure strategy）
n（野球，野球），（野球，映画），（映画，野球），（映画，映画= j
–結合混= 戦略（joint mixed strategy）
n　
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協力ゲー= の理論
n結合混合戦略と実現可能集合
–双行列　G=3D(aij,bij) (i=3D1,2,…,m, j=3D1,2,…,n)
–結合混合戦略
n= 結合純戦略(i,j)がとられる確率を zijとしたと= ｫの確率分布
n
n
n= 結合（混合）戦略集合： Z=3D{z}
<= span style=3D'font-family:"Century Schoolbook";font-size:111%;color:black;mso-f= areast-hint: yes'>–二人の期待利得
<= span style=3D'font-family:"Century Schoolbook";color:black;mso-fareast-hint:yes= '>n　
<= span style=3D'font-family:"Century Schoolbook";font-size:111%;color:black;mso-f= areast-hint: yes'>–実現可能集合（到達可能集= ）
<= span style=3D'font-family:"Century Schoolbook";color:black;mso-fareast-hint:yes= '>n　
u
v
非協力ゲームの
実= ｻ可能集合 <= /span>
非協力ゲームの
Nash均衡点 <= /span>
協力ゲームの
実現可= \集合
（非協力ゲームの<= /span>
実現可能集合の
凸包となっている）
例：恋人達のジレンマ
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ABwAgAAAAP8A/wI3hI+JoZ3BnIyy0fouPnqDvoEY5D3lcnJitU6p0TrkG1vvV3+oR+XwXyLNeBAf rIgMIX3J0/BUAAA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n交渉の基準点
成功 <= /div>
失敗 <= /div>
交渉
利得 <= /div>
利得＝最悪の場合でも保証される利得
　　　＝maximin値=
<= ![if !ppt]>3D"テキスト
≧ <= /div>
決裂 <= /div>
<= span style=3D'font-family:"Century Schoolbook";font-size:111%;color:black;mso-f= areast-hint: yes'>–例：恋人達のジレンマ　
成功 <= /div>
失敗 <= /div>
交渉 <= /div>
決裂 <= /div>
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>•= デート成立
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>•<= /span>家に帰って不貞寝　   (c1,c2)=3D(0= ,0)
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>•<= /span>非協力ゲームをやる　(c1,c2)=3D(1= /5,1/5)
交渉が不成功に終わったとしても期待= ﾅきる保証水準
＝交渉の基準点
交渉の基準点
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Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n2<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; font-weight:normal;mso-fareast-hint:yes'>人交渉ゲーム
–演習：
( 2, 3)
( 9, 0)
sB2
( 0, 9)
( 6, 7)
sA1
sB2
sB1
A＼B
<= span style=3D'font-family:"Century Schoolbook";font-size:111%;color:black;mso-f= areast-hint: yes'>1.（協= 力）実現可能集合を描いてみよう
<= span style=3D'font-family:"Century Schoolbook";font-size:111%;color:black;mso-f= areast-hint: yes'>2.この= ゲームを協力ゲームの出発点として，交渉の基準点を考えよう
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協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal;mso-fareast-h= int: yes'>n交渉問題の要素と定式化
–プレイヤーの集合 N <= /i>=3D {<= /span>1,2,…,n}
–&= #13;
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–交渉の基準点 = c =3D (= c1, c2,…, cn) =
–&= #13;
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–実現可能集合 S =3D {= = x =3D (= x1, x2,…, xn) }
<= span style=3D'font-family:"Century Schoolbook"'>nSの満たすべき性質
–1. = n次元Euclid空間の有= E閉凸集合
–2. = 基準点 c は= S <= /i>に含まれる
–3. = S には，任意の i について= Cxi>ci なる点を少なくとも1つ含む
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–交渉問題 ( N, S, = c ) = ;
–&= #13;
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–交渉の妥結点 = s =3D (= s1, s2,…, sn) =
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n交渉問題 (N, S, = c) が与えられたとき，全てのプレイヤーが納得する S に属すた= ｾ一つの点 = s が選び出されたとき，その点 s
–&= #13;
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–交渉解 F： (N, S, = c) → = s
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n交渉問題 (N, S, = c) が与えられたとき， (N, S, = c) に
n　対してただ一つの妥結点 s を対応さ= ｹるルール
交渉不成立の場合の保証水準
※プレイヤーに <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>= c の共通認識があるとき，= cを交渉の基準点とよぶ
（ここでは c は所与とする）
交渉のル= [ルが共通認識となっていれば，基準点を定め= 骭渉となる！
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協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal;mso-fareast-h= int: yes'>n<= /span>交渉の妥結点の満たすべき公準（そ= ﾌ1）–公準1：個人合理性
n= x が個人合理的　⇔　 xi≧ci  (i=3D1,…,n)
nF(N, S, = c) の妥結点 s が個人合= 搏Iのとき，F <= /i>は個人合理的であるという
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–公準2：強個人合理性
nx が強個人合理的　⇔　 xi>ci  (i=3D1,…,n)
<= span style=3D'font-family:"Century Schoolbook"'>nF(N, S, = c) の妥結点 s が強個人= 理的のとき，F <= /i>は強個人合理的であるという
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–公準3：パレート最適性（共同合理性，効率性）
n交渉の妥結点 F(N, S, = c) =3D = = s はパレート最適でなければならない
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–公準4：弱パレート最適性
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n交渉の妥結点 F(N, S, = c) =3D = = s は弱パレート最適でなければならない
交渉成立時は，交渉不成立時に保証され= 髣得 = c より多くの利得が保証さ= 黷ﾋばならない
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協力ゲー= の理論
n交渉領域–T <= /i>=3D { = = s∈S <= /i>| = x ≧ = c }<= /b><= b>
–例：
<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; font-size:90%;color:#996600;mso-special-format:lastCR;display:none'> <= /span>
<= /span>
= <= /span>
1
3
2
min
4
4
( 4, 2)
( 4, 6)
( 6, 2)
sB2
2
min
( 4, 1)
sB3
( 2, 3)
sB2
3
max
( 8, 4)
sA1
max
sB1
A＼B
各々のmaximinを=
交渉の基準点 c =3D (4, 3)
とする
T
c
公準1より T≠φ
公準3よりパレート最適
x2 = ｰc2
x1 = ｰc1
x2
x1
o
2
4
6
8
2
1
3
4
5
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協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal'>nNash交渉解–Nash積
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
<= span style=3D'font-family:"Century Schoolbook"'>–Nash交渉解
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n交渉問題 (N, S, = c) のNash交渉解は= CNash積を最大にする S の点 = s
各プレイ= п[について，基準点からの利得の= 摯ｪの積
Nash交渉解は= C利得の測定法から独立なので，プレイヤー毎に利得を正一次変換しても変わらない．
（効用の個人間比較を排除）=
基準点を 0= に変換して
考えることが出来る
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Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0012_image081.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhswBlAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQCy AGIAgAAAAGYzAAL/hI+py50Bg5u02ouz3pzJ83XiSJbmCSnpybbu24XLCtf2jcqNjvf+/+A5aMCi 8SWsEI/MZmapSTqnVIP0ea1qfdBRdwuufUvZsNmLG5/X2J+a3YvI5/Q6/WjP6/f8vv/fByco+DZo yFR4qOhWtuh4k/go6RI5aUnWeKkpUrnpidH5KToROmqqknmqGrTaelHqOgob+zlLu2l7e5mrO8nb +/gLvCg8fFhsPIicDLfMvOb8bBYtDUZdrXWNTaW97dTtjZgafjxOrmx+3pyuDs3ePv0Oby0/n11v z42f/73PL/5PEriASPwRBDLwIIuECk0wbEjiIUROBifakGhxA8aMXG04uvP4EWQ8kSNJ0jN5EuU9 lStZ6nP5EmY/mTNpArSJpyJOUDp3Wti4EyhOoTaJ0jQqEylMpS6ZsnSqEipKqSapkrQqEitIrR65 cvSaEaxFQGTLmj2LNq1atQUAADs= ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0012_image082.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKQAOAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAm AAkAgAAAAGYzAAIfhG+By+0b1Jv0xFhzu1h7wIXiSJIJ96Vnp35s68JPAQA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal'>nNash交渉解–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–例：
( 4, 6)
( 2, 3)
sB2
( 4, 2)
( 6, 2)
sB2
( 4, 1)
( 8, 4)
sA1
sB3
sB1
A＼B
基準点 c =3D (4, 3) とする
 ↑= 各々のmaximi= n = ;
c
x1
x2
x2 ｰc2
x1 ｰc1
s
演習：= y1=3D1/2= x1という正一次変換
　　を施して考えてみよう！
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>•<= /span>共同合理性（パレート最適）を満たす部分= は？
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>•<= /span>基準点 c は？= 3;
　さらに z1=3Dy1-2, z2=3Dx2-3 としたとき，
<= span style=3D'font-family:"Century Schoolbook";font-size:89%'>•Nash解はどう書けるか？
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>•<= /span>妥結点を求めもとの問題の妥結点を出そう= ！ <= /div>
o
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------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
nNash交渉解–例：交渉力（bargaining power）
x2 ｰc2
x1 ｰc1
s
( 1, 2)
(-1,-1)
映画
(-1,-1)
( 2, 1)
野球
映画 <= /div>
野球 <= /div>
男＼女<= span style=3D'font-weight:normal;color:#996600;mso-special-format:lastCR;displa= y: none'>
u
v
<= span style=3D'font-family:"Century Schoolbook"'>•a <= /i>> <= /span>b <= /i>の時（プレイヤーAの方が交= ﾂ力が強い）
<= span style=3D'font-family:"Century Schoolbook";visibility:hidden'>•<= /span>
<= span style=3D'font-family:"Century Schoolbook"'>•a <= /i>< <= /span>b <= /i>の時（プレイヤーBの方が交= ﾂ力が強い）
<= span style=3D'font-family:"Century Schoolbook";visibility:hidden'>•<= /span>
<= span style=3D'font-family:"Century Schoolbook"'>•a <= /i>=3D b <= /i>の時（双方の交渉力が等しい）
Nash交渉解：<= /span> (u*,v*) =3D (3/2, 3/2)=
c
o
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協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal;mso-fareast-h= int: yes'>n<= /span>交渉の妥結点の満たすべき公準（そ= ﾌ2）–公準5：利得の正一次変換からの独立性
n= 利得を測定する単位や尺度を変えても本質的に変わらない=
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–公準6：対称性
n例えば，２人交渉問題(S)において，『交渉領域 S が= y=3Dx <= /i>に関して対称ならば，ルール <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>F <= /i>による妥結点における２人の利得が等しい』 を満たす
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n一般には，実現可能集合 S の任意の置換 π(S) =3D = { π(x) | x∈S } に対し，『π(S) =3D = S　⇒　Fi(S) =3D = Fj(S) for = all i, j』 を満たす
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–公準7：無名性（匿名性）
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n交渉問題 (N, S, = 0) において，
n F[π(S)] =3D= π[F(S)]
基準点を c=3D0 と出来る<= /span>
　プレイヤーの番号を付替えても，<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>交渉領域が変化しないとき，全ての<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>プレイヤーの受け取る利得が同じ<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-special-format:lastCR;display:none'> <= /div>
　プレイヤーの番号を付替えた時，<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>交渉領域が変化したとしても，妥結= 点におけるプレイヤーの受け取る<= /span>= 利得が番号の付け方に独立，例え<= /span>= 匿名にしても変わらない
=
S’
S
o
x1
x2
無名性
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協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal;mso-fareast-h= int: yes'>n<= /span>交渉の妥結点の満たすべき公準（そ= ﾌ3）–公準8：無関連な代替案からの独立性
n= 交渉問題 (N, S, = 0) と妥結点 s において= C
n T⊂S, F<= /i>(S)∈T　⇒　F(S)∈ F(T)
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–公準9：全体と部分との整合性
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n交渉問題 (N, S) の解 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>F <= /i>について，F(T)=3Dt <= /i>とする．M⊂N を考え，妥結点 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>t <= /i>の N-M 人の利得を固定し，Mのプレイ= п[だけの交渉問題 (M, S) を考える．このとき，解 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>F <= /i>によって M のプレイヤーの利得は，(N, S) でも (M, S) でも変わらない= D
交渉の場を (S, c) から (T, c) に変えても妥結点 s は変わらない
整合性を持たないと，プレイヤー<= /span><= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>が色々な部分集合に分かれて交<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>渉が始まってしまう！
=
T
S
o
x1
x2
独立性
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協力ゲー= の理論
nNash交渉解の一意性–Nashの定理　(1950)
n= ２人交渉問題のNash交渉解は= C次の5つの公準を満たす唯一の解
–個人合理性（公準1），パレート最適性（公準3），利得測定法からの独立性（公準5），対称性（公準6），無関連な代替案からの独立性（公準8）= 3;
–
–Rothの定理 (1977)
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n任意の交渉問題において，Nash交渉解は次の4つの公準= 満たす唯一の解
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; font-size:89%;mso-fareast-hint:yes'>強個人合理性（公準2），利得測定法からの独立性（公準5），対称性（公準6），無関連な代替案からの独立性（公準8）
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n任意の交渉問題において，次の3つの公準
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; font-size:89%;mso-fareast-hint:yes'>利得測定法からの独立性（公準5），対称性（公準6），無関連な代替案からの独立性（公準8）= 3;
nを満たすのはNash解か，非= 意解 F(S) =3D = = c =3D <= /span>= 0 のみ．
n
–Lensbergの定理 (1985)&#= 13;
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n任意の交渉問題において，Nash交渉解は次の5つの公準を満たす唯一の解
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; font-size:89%;mso-fareast-hint:yes'>個人合理性（公準1），パレート最適性（公準3），利得測定法からの独立性（公準5），無名性（公準7），全体と部分との整合性（公準<= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-family:"Century S= choolbook"; mso-hansi-font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint: yes;mso-fareast-language:JA'>9）
------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n交渉の妥結点の満たすべき公準（その4<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; font-weight:normal;mso-fareast-hint:yes'>）
–公準10：個人単= ｲ性
n= 2つの交渉= 竭 (N, S, = c)，(N, T, = c) において，解Fが個人単調
n T⊃S, かつ M(T)i=3DM(S)i (i=3D1,2)　⇒　Fi(T)≧Fi(S) (i= =3D1,2)
交渉問題の理想点：
M(S)=3D(M(S)1,M(S)2)
M(S)1：交渉領域S内でのプレイヤーiの利得上限（最大= ﾀ度額）
= •<= /span>公準8への批判
<= span style=3D'font-family:"Century Schoolbook";font-size:78%'>•Nash解は公準10を満たさないという批判
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal'>nKalai & Smorodinsky解<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>–交渉領域Sのパレート最適解集合と，交渉基準点cと理
–　想点M(S)とを結ぶ直線との交点を妥結点とするルール
<= span style=3D'font-family:"Century Schoolbook"'>–Kalai&Smorodinskyの定理(1975)
<= span style=3D'mso-fareast-hint:yes'>n任意の2人交渉問題において，Kalai&Smorodinsky解
n は次の5つの公準を満たす唯一の解
<= span style=3D'font-size:89%;mso-fareast-hint:yes'>–個人合理性（公準1），パレート最適性（公準3），利得測定法からの独立性= i公準5），対称性（公準6），個人単調性（= 公準10）
T
S
o
x1
x2
交渉領域がSからTに拡大したのに，Nash解ではプレイヤー2の利得が減少！
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Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n例題–→ [例題6.1] [= 2] p.151〜=
–→ [例題6.2] [2] p.155〜=
------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0040.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
A市
B市
C市
協力ゲー= の理論
n提携と配分
–例題：ゴミ処理場建設（[数学セミナー](2004/8) p.32〜）
n3市が各々独自に建設　…　A=3D5億円，B=3D3億円，C=3D2億円= 3;
n共同施設の建設　…　A+B=3D7.2億円，B+C=3D4.8億円，C+A=3D6.6億円，A+B+C=3D8億円
例えば，A市とB市はそれぞれ独自に建設する（5億＋3億＝8億）よりも，= 携して共同施設を建設（7.2億）した= ﾙうが安い．
→　0.8億円の得= するということ！
協力関係を結んだプレイヤーのグループ＝提携 =
提携が作られることによって得られる便益の値を与える関= 数＝特性関数 = ;
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Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n<= /span>提携と配分
–定義：提携ゲーム
n<= /span>ゲームのルール
n （１） プレイヤー <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N <= /i>=3D {<= /span>1,2,…,n}
n （２） <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N <= /i>の任意の部分集合は提携可能
n （３） 譲渡可能効用が存在し，提携内で別払い可能
n 　〔別払いのあるゲーム（games with sidepayment） 〕
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n任意の提携 S にたいし= C実数値を対応させる関数 v(S) が存在
–v ：特性関数（characteristic function）
–v(S) ：提携 S のもつ提= g値
プレイヤ= [の間で利得を自由に譲渡可能
譲渡可能効用(transformable utility)
が存在 ＝ 利得の一部をプレイヤー間で自由に譲渡でき，Ａ→Ｂへ譲渡したときの，Ａの損失とＢの利得が等しい
(N, v) ： 提携形ゲーム （coalitional game）
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A市
B市
C市
協力ゲー= の理論
n提携と配分
–例題：ゴミ処理場建設（[数学セミナー](2004/8) p.32= 〜）
n3市が各々独自に建設　…　A=3D5億円，B=3D3億円，C=3D2億円= 3;
n共同施設の建設　…　A+B=3D7.2億円，B+C=3D4.8億円，C+A=3D6.6億円，A+B+C=3D8億円
プレイヤ= [の集合： N =3D {= A, B, C}
実現可能= ﾈ提携： 2N =3D { φ, {A}, {B}, {C}, {A,B}, {B,C}, {C,A}, {A,B,C} }
特性関数： v(φ) =3D v({A}) =3D v({B}) = =3D v({C}) = =3D 0
　v({A,B}= ) =3D (5+3)ｰ7.2 =3D 0.8
　v({B,C}= ) =3D (3+2)ｰ4.8 =3D 0.2
　v({C,A}= ) =3D (2+5)ｰ6.6 =3D 0.4
　v({A,B,= C}) =3D (5+3+2)ｰ8 =3D = 2
vが優加法的(supperadditive)
　= 互いに素な任意の提= g S, T について以= ｺが成立する特性関数v
= v({A})+= v({B})= =3D0 < 0.8=3Dv({A,B})
v({B})+= v({C})= =3D0 < 0.2=3Dv({B,C})
v({C})+= v({A})= =3D0 < 0.4=3Dv({C,A})
v({A,B}= )+v({C})= =3D0.8 < 2=3Dv({A,B,C})
v({B,C}= )+v({A})= =3D0.2 < 2=3Dv({A,B,C})
v({C,A}= )+v({B})= =3D0.4 < 2=3Dv({A,B,C})
相交わらない2つの提携は，各々別個に行<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>動するより共に行動した方が得られる便益= = が大きい（小さくはならない）ということ= <= /div>
だから提携すればよい
問題は「配分」をどうするかとなる
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協力ゲー= の理論
n<= /span>提携と配分
–<= span style=3D'mso-fareast-hint:yes;color:#996633'>定義：配分（imputation）
n<= /span>提携形ゲーム (N, v)
n<= /span>プレイヤー i の利得 xi　利得ベク= gル = x =3D (<= /span>x1 , x2 ,…, xn ) =
n<= /span>実現可能集合 R
n
n
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n実現可能集合の点 x が交渉領= 謔ﾉあるための条件
n （１） = ﾂ人合理性　xi ≧ v({i}) = ;
n （２） <= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; text-shadow:auto;mso-fareast-hint:yes;color:red'>全体合理性<= span style=3D'font-family:"Century Schoolbook";mso-ascii-font-family:"Century S= choolbook"; mso-hansi-font-family:"Century Schoolbook"'> 　=
各プレイ= п[の利得は単独行動で獲得可能な値以上
準配分 (preimputation)
全体合理性を満たす利得ベクトル
配分 (imp= utation) =
　個人合理性と全体合理性を満たす利得ベクトル
全プレイ= п[の協力で得られる値= v(N)は，全て配分されねばならない
全体合理= ｫを満たす利得ベクトルは実現可能領域でパレート最適になっている
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Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
A市
B市
C市
協力ゲー= の理論
n提携と配分
–例題：ゴミ処理場建設（[数学セミナー](2004/8) p.32= 〜）
n3市が各々独自に建設　…　A=3D5億円，B=3D3億円，C=3D2億円= 3;
n共同施設の建設　…　A+B=3D7.2億円，B+C=3D4.8億円，C+A=3D6.6億円，A+B+C=3D8億円
プレイヤーの集合： N =3D {A, B, C}
実現した提携の例： {A,B,C} 　その特性関数の値：v({A,B,= C}) =3D (5+3+2)ｰ8 =3D = 2
（１） = ﾂ人合理性　xi ≧v({i})
（２） = S体合理性
配分の例： （xA, xB, xC）＝（1, 0.5, 0.5）=
　　（１）個人合= 理性を満たしている： xA≧v({A})= =3D0，xB≧v({B})= =3D0，xC≧v({C})= =3D0
　　（２）全体合= 理性を満たしている： xA+xB+xC =3D v({A,B,= C}) =3D 2
配分の例： （xA, xB, xC）＝（0.6, 0.8, 0.4）=
　　（１）個人合= 理性を満たしている： xA≧v({A})= =3D0，xB≧v({B})= =3D0，xC≧v({C})= =3D0
　　（２）全体合= 理性を満たしている： xA+xB+xC =3D v({A,B,= C}) =3D 2
•<= /span>どんな配分がよい？
<= span style=3D'font-family:"Century Schoolbook";font-size:89%;mso-fareast-hint:y= es'>•<= /span>どんな配分が考えられる？
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Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTgAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABQBI ABoAgwAAAAAAAAYFBQMDAwsKCgsJCgoICQgHBwcGBgkICAkHCAcGBwUEBAECAwECAwECAwTTUIRJ KwU46827/6AmDIQnhWiqBSkrDkVXuGrt0VeW05hkdDybEBAkbnhB33B5Oxp1K84h8ANdJkssJhfF cYrTqrVo0xKLLK+TgzigyDoLGRdUozkFRIsZNdahcxsEem9PhltyQE9/W4dQGgglIS5wNWZIR4EZ kW+UaZVWa1yOjRkHYhwJk3x9lhkGCh8GhB+gZa4YBQuyA7G1rF97GAQDcnKoX7bAIQzGcjHL0dLT 1NXWhUCeytfAatysZk5p39F0lH7ky9rn4+l83obb7rXmO/N8EQA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0042_image188.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhqwA2AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACp ADQAgQAAAJnMAP///wECAwL/hI9pwe0Po5y02otzVryrKITiSJbmiabqyrauC3le89b2jec63MgA vQsKh8SioJdgGJfMprPEOASe1Kp1F/hdt9wuSukNi63gsflMLKPX7Jq6DY+b3vJ6nG7Po/H6fpjv F3gFKFjoRGiYWISo2Ig15RhpxChZ2UJpmfkFqdn5gukZChraOUqaaXpamaoaydra+AqbKDtbWGsb iJvbt8ub5/tbFyx8x1lceoxsmaW1zNz8o/x8G40ARN0b5eOQDefg0yHhXRURfv6hob7OPrFlgR4v P09fPz89CW6/z9/vf7/kwb+BBAsSxHdDn8GFDBuiQ8hCoMOJFCtK+aTQosaNGwYhipDIMaTIgQgz jjyJ0h4nkClbupRn8mW8AgA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n<= /span>例題
–多数決ゲー= =
n<= /span>プレイヤーは3人 N =3D {1,2,3}
n= 12万円が贈= 轤黷ﾄきた．多数決で分け，多数派が全てとって良い．
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n提携集合 2N
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n多数派の提携　{1, 2}, {1, 3}, {2, 3}, {1, 2, 3}
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n特性関数
n v(φ) =3D = 0, v({i})=3D0= (i=3D1,2= ,3), v({1,2}= )=3Dv({2,3}= )=3Dv({3,1}= )=3D12, v({1,2,3})=3D12
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n提携値
n v =3D (= v(S) | S⊂N <= /i>) =3D<= /span> ( 0, 0= , 0, 0, 12, 12, 12, 12 )
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n利得ベクトルの集合
n X =3D {= = x =3D (= x1, x2, x3) } ⊂ R3
例1：提携 {1,2} が成立　→　x =3D (= 6, 6, 0)
例2：提携 {1,3} が成立　= ｨ　= x =3D (= 6, 0, 6)
ゲームの結果として考えられる利得ベクトルの集合
K =3D { (6, 6, 0), (6, 0, 6),= (0, 6, 6) }
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協力ゲー= の理論
nコア（core）
配分の集合
X = =3D { = x = =3D (= x1, <= /b>…, xn) }=
＝ 交渉領域
ゲーム (N,v)
ある配分= ﾉ到達 <= /span>
交渉
–配分の支配<= /span> =
n提携 S において，配分 x が配分y を支配するとは，次の2条件が成立すること =
n
n （１） 有効条件　：
n
n （２） 選好条件　：
提携 S は x の有効集合（effective set）=
つまり，提携 S にとって，配分 x は S の力だけで実現可能！
　交渉の過程で，ある提携にとって= x配される配分は，= その提携によって拒否され，排除= ｳれる．
支配されない配分が残る
コ= A
提携 S にとって，配分 y を支配す= 髞z分 = x が存在するとき，
「提携 S は配分 = y を拒否する（block）」
or
「配分 y は提携 S にとって<= /span>改善可能」
という
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DoqXMlpgYLFRAQImUD4AIPNhyWUoe/4M+nKAzKQ3cx4UOrVo0qxNn2asGjRm1q1fn4otejRt2q45 B8A9e/fu3pJ/pw4ufLjtHcZl606enDji5quhW5cumDpy69GXr6rOnTv2vr+3h4e+Ib369ezbu3/v 4Lx8AAUAADs= ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
nコア–ゲーム (N, v) において，いかなる配分にも支配されない配分の集合
n<= /span>コア（別定義）
–ゲーム (N, v) が優加法的であるとき，提携合= 理性を満たす配分の集合
提携合理性<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:78%;mso-fareast-hint:yes'>（個人合理性の拡張）
　任意の提携 S について= ﾈ下を満たす配分
vが優加法的(supperadditive)
　互いに素な任意の提携 S, T について以下が成立する特性関数v
= 補足：Theorem
　各プレイヤーのとりうる純戦略が有限な協力ゲームの特= 性関数は優加法的
　　　　　　　　を提携 S の配分 = x に対する不満とよぶ．
コアとはいかなる提携に対しても不満を= 与えない配分の集合
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協力ゲー= の理論
n<= /span>例題
–3人ゲーム= ﾌコア
<= span style=3D'font-family:"Century Schoolbook"'>nN =3D (1, 2, 3)
<= span style=3D'font-family:"Century Schoolbook"'>nv(φ) =3D = 0, v({1}) = =3D v({2}) = =3D v({3}) = =3D 0,
n v({1, 2= }) =3D a3, v({2, 3}) =3D a1, v({3, 1= }) =3D a2,　（ただ= ｵ，0≦ai ≦1, i<= /i>=3D1,2= ,3）
n v({1, 2, 3}) =3D 1
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>nゲームの配分 x =3D (x1, x2, x3) とすると， xi ≧0 <= /i>(i=3D1,2,3), x1+x2+x3=3D1
A
B
C
x
x1
x2
x3
正三角形<= /span>ABCが，このゲームの配分の集合 X を表す
x1+x<= i>3= ≧a2
x2+x<= i>3= ≧a1
x1+x<= i>2= ≧a3
x1
x2
x3
120°
120°
120°
The= orem
　3人ゲーム= iN, v）のコアが空出な= ｢ための必要十= 分条件は，v({1,2}= )+v({2,3}= )+v({3,1}= )= ≦2v({1,2,= 3})
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Theorem
　本質的定和n人ゲーム（N, v）のコアは空
n演習：
–以下の各ゲーム（全て優加法的）において，v <= /i>を全て書き出し，コアを見つけよう．ただし，v(N)=3D1,= v(φ)=3D0 = とする．
= 211;（１） 3人定和ゲ= [ム（[4] p.= 25 例3.2）=
n= 一定量の資金を3人の多数決で分ける．多数派提携が資金の全てを獲得．
–v({1,2,3}) =3D v({1,2}= ) =3D v({2,3}= ) =3D v({3,1}= ) =3D 1
–v({1}) =3D v({2}) = =3D v({3}) = =3D v(φ) =3D = 0
–→　コア C(v) =3D = φ
n
–（２） 3人拒否権= Qーム（[4] p.= 26 例3.3）=
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n一定量の資金を3人の多数決で分ける．多数派提携が資金の全てを獲得．
nただし，プレイヤー1には拒否権があり，資金の獲得にはプレイヤー1の協力が必要．即ち，プレイヤー2，3だけでは資金の獲得不可能．
–v({1,2,3}) =3D v({1,2}= ) =3D v({1,3}= ) =3D 1
–v({2,3}) =3D v({1}) = =3D v({2}) = =3D v({3}) = =3D v(φ) =3D = 0
–→ コア C(v) =3D { (1,0,0) }
協力ゲー= の理論
1
2
3
1
2
3
2,3が1との提携をめぐって競争すると，1が全部を得てしまう
•<= /span>加法的（additive） ⇔= 3;
<= span style=3D'font-family:"Century Schoolbook";font-size:78%;mso-fareast-hint:y= es'>•<= /span>非本質的（inessential） ⇔ 加法的 v を持つ協力ゲーム<= /span>
•<= /span>本質的（essential） ⇔ そうでない協力ゲ= [ム <= /div>
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oX9eUIP3EWjR8HxUFmjs14P+8BCxEYP61xH1NTWB0XlQUQ5O+GfQgTslmBi2g4XpN1dbCAxdmDsm mH6q4BBleAnjEBiIQxmjkIFtqIZdqITDMBJ16BjQgX65sIfCAh10CIi1E2iDSIiDs4aIWH26cIiL 6AyO+Ij+IImSEAgAOw== ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n演習：
= 211;（３） 家購入ゲーム
player1
p= layer2
player3
player4
x1
x2
x3
x4
x2 + x3 = =3D100
（x1 + x4 = =3D100）
x1 + x4<= /i>=3D70
（x2 + x3<= /i>=3D130）
p : player1 ⇔ pla= yer3
q : player2 ⇔ pla= yer4
取引価格
x1 = =3D p <= /i>− 1000
x2 = =3D q −  900=
x3 = =3D 1150 − p
x4 = =3D 950 − q
 120 ≦ p-q= ≦ 150=
100= 0 ≦  p  ≦ 115= 0
  900 ≦  q  ≦ 950=
x1 = + x3 = =3D150
x2 = + x4 = =3D 50
とすると…
C(v) =3D { x∈X |x1 + x3 = =3D 150,  x2 + x4<= span style=3D'mso-spacerun:yes'>  =3D 50,  x1 = + x4 = ≧70,  x2 = + x3 = ≧ 100 }
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------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0036_image296.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABM AAEAgAAAAAAA/wIHjI+py+3vCgA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0036_image297.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhVgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABU AAEAgAAAAP8AAAIIjI+py+0PVQEAOw== ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
nコアの存在条件（線形計画法に基づく）–ゲーム (N, v) において，コアが非空となる必要十分条件
(P)
(D)
(P), (D)共に実行可能で最適解 = z*, w* を持ち，z* =3D w*．
また，『z*≦v(N) ⇔ コアが非空』
The= orem
　ゲーム（N, v）において，非空なコアが存在するための必要十分条件は，双対問題(D)の制約を満たす非負ベクトルγSに対し
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協力ゲー= の理論
n仁（nucleolus） （Schmeidler,1969）
–提携 S と= 配分 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>= x=3D(x1,…,xn) について
n&#= 13;
= 211;　を「配分x <= /span>に対して提携S が持つ不満」という
配分 x に対して= C全員集合N <= /i>と 空集合φを除く 2n-2 個の提携の不満の量を大きい順に並べる．
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
n
–2つの配分<= /span> = x，y について
= 211;　　「x は y より受容的である」とは，以下が成り立つこと．
R= 11;
R= 11;
n
R= 11;それよりも許容的な配分が存在しない配分を仁という
【注：コアでは　　　　　　　= 　より不満は常に0か負】
　コアは複数存在したり，空集合だったりする． 　仁は，常にただ一つの配分を与える解である． 　コアが非空のときは，仁はコアに含まれる．
【注：全員集合= の不満e(N,x)=3D0 （∵）全体合理性）= 3;
　　　 空集合の不満 e(φ,x)=3D0  （∵）v(φ)=3D0）　　】
3D"テキスト
＝
3D"テキスト
＝
3D"テキスト
＝
3D"テキスト
＜
…<= /span>
　不満の量を大きい順に比較していき，最初に異なるところで小さい方が好ま<= /span>しい（＝許容的）と考える
最大不満= の= 最小化
acceptable
excess
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DsF9ERRu+OGIJ6744ow37vjjkEcu+eSUR3AfA5hnrvnmnHfu+eeghy76cuikl2766Qzcl8DqrLfu +uuwxy777LTXbvvtuOeuewL3KeD778AHL/zwxBdv/PHIJ6/88sw3r8B9C0Qv/fTUV2/99dhnr/32 3Hfv/ffgL3AfAeSXb/756Kev/vrst+/++/DHL//8BBxo//3456///v+FAAA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0044.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n仁–例題：ゴミ処理場建設（[数学セミナー](2004/8) p.32= 〜）
n3市が各々独自に建設　…　A=3D5億円，B=3D3億円，C=3D2億円= 3;
n共同施設の建設　…　A+B=3D7.2億円，B+C=3D4.8億円，C+A=3D6.6億円，A+B+C=3D8億円
A市
B市
C市
= e({A,B}= ,= x)=3Dv({A,B}= )ｰ(xA+xB)=3D0.= 8ｰ(xA+xB) =
= e({B,C}= ,= x)=3Dv({B,C}= )ｰ(xB+xC)=3D0.= 2ｰ(xB+xC) =
= e({C,A}= ,= x)=3Dv({C,A}= )ｰ(xC+xA)=3D0.= 4ｰ(xC+xA) =
= e({A},<= /span>= x)=3Dv({A})<= /span>ｰxA=3DｰxA
= e({B},<= /span>= x)=3Dv({B})<= /span>ｰxB=3DｰxB
= e({C},<= /span>= x)=3Dv({C})<= /span>ｰxC=3DｰxC
ただし，全体合理性から
xA+xB+xC=3Dv(N)=3D2<= /span>
min.
s.t.
最適値：ε*=3Dｰ0.6
最適解：(xA,xB,xC)=3D(0.8,0.6,0.6)
3D"テキスト
最大不満最小化 <= /span>
費用分担問題における仁の= 応用
「滑走路使用料の決定」（= 岡田p.360参）
最小コアを求めるLP
任意の配分 x について，不満がε=3Dｰ0.6に一致する提携 S を除く．= 3;
　　　（e(S,x)=3Dｰ0.6  となる S を除く）
そのうえで，同様のLPを作って解く．以下，この繰り返し．
例では= 3;
より，e({A,B},x)=3De({C},x)=3Dｰ0.6なので，提携{A,B}と{C}の式を除く．
= LPを有限回繰り返し解くこと= で仁を得る
min.
s.t.
最適値：ε*=3Dｰ0.7
最適解：(xA,xB)=3D(0.7,0.7)
唯一配分の仁
(xA,xB,xC)=3D(0.7,0.7,0.6)
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file:///C:/E17059D3/06dmt_5-3.files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
<= span style=3D'font-family:"Century Schoolbook";font-weight:normal;mso-fareast-h= int: yes'>n<= /span>シャープレイ値（Shapley value）–提携に対するプレイヤーの貢献度をもとに= ｵた解
–プレイヤーが1人ずつ加わり全員提携を作る順列を考える
–プレイヤーが加わることにより新たに獲得できる量を貢献度とする
= 211; 全員提携の順列が{1,2,= …,i-1,i,= …}のとき，
= 211; <= /span>i番目に加わるプレイヤーの貢献度 ＝ v({1,2,…,i-1,i})v({1,2,…,i-1})
<= span style=3D'font-family:"Century Schoolbook"'>–n!個の全ての順列が当確率= で起こるときの，プレイヤーの貢献度の期待値をそのプレイヤーのシャープレイ値という
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>nプレイヤー i のシャー= vレイ値
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
–
<= span style=3D'font-family:"Century Schoolbook";font-size:90%;color:#72974B; mso-color-index:5;mso-fareast-hint:yes'>–補足：シャープレイ値は= 4つの公準を満たす唯一の解である
<= span style=3D'font-family:"Century Schoolbook";font-size:90%;color:#72974B; mso-color-index:5;mso-fareast-hint:yes'>–補足：vが優加= 法的なら個人合理性も満たし配分となる
公準1：全体合理性
公準2：ナルプレイヤーの零評価
公準3：対称性
公準4：加法性
<= ![if !ppt]>
∈
S
i
プレイヤー i を含む提携 S を固定したとき，<= /span>
　提携 S-{i} のメンバー数＝|S|-1
　N/S のプレイヤー数＝n-|S|
より，提携 S-{i} +{i}+N/Sの順列の総数は(|S|-1)!(n-|S|)!通り．<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:56%;mso-fareast-hint:yes'>故に i が最後に参加して提携 S となる確率が(|S|-1)!(n-|S|)!/n!
… <= /span>
… <= /span>
i
S-1
n-|S|
　シャープレイ値も仁と同様，唯一の解を与える 　コア・仁が「不満」をもとにしているのに対し，シャープレイ値は「貢献度」をもとにした解
コアに含まれるとは限らない
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NCqReRK0ev0KNixSmBHEmj2L1kWtrmnbunWracLbuXTTxmBbtwjWvXwpfH2Qt0MDUlADiwVZJ6vh JsgUL8bpzPFjBE5dTd4a+bKOyn0ka+YcSzPjZZ4vg85TevJpWqLVZm69kzTs2I1nQ5Ztmwvu3C53 865Zu+7e18JXX0p92Dgk5GYRI2J+1jmq1tJDwx6sDfrc6rp+F4mmPa9yOOGFE/c+vpf3n0/LP/YQ qvB6qX3r289aAAA7 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
nシャープレイ値–例題：ゴミ処理場建設（[数学セミナー](2004/8) p.32= 〜）
n3市が各々独自に建設　…　A=3D5億円，B=3D3億円，C=3D2億円= 3;
n共同施設の建設　…　A+B=3D7.2億円，B+C=3D4.8億円，C+A=3D6.6億円，A+B+C=3D8億円
3.0
4.2
4.8
合計
0.0
2.0
1.8
C←B←A
0.0
1.6
0.4
C←A←B
0.2
0.0
1.8
B←C←A
1.2
0.0
0.8
B←A←C
0.4
1.6
0.0
A←C←B
1.2
0.8
0.0
A←B←C
C
B
A
= S体提携
= ﾌ順列
貢献度
v(φ) =3D v({A}) =3D v({B}) =3D v({C}) =3D 0
v({A,B}) =3D (5+3)ｰ7.2 =3D 0.8= 3;
v({B,C}) =3D (3+2)ｰ4.8 =3D 0.2= 3;
v({C,A}) =3D (2+5)ｰ6.6 =3D 0.4= 3;
v({A,B,C}) =3D (5+3+2)ｰ8 =3D 2=
各プレイヤーのシャープレイ値
シャープレイ値に= 謔髣B一の配分
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協力ゲー= の理論
n安定集合（stable set） 〔or 解（solution），von Neumann-Morgenstren解〕 <= /span>
–例題（再掲）： 3人定和ゲーム
n= 一定量の資金を3人の多数決で分ける．多数派提携が資金の全てを獲得．
–v({1,2,= 3}) =3D v({1,2}) =3D v({2,3}= ) =3D v({3,1}= ) =3D 1
–v({1}) = =3D v({2}) = =3D v({3}) = =3D v(φ) =3D = 0
–→　コア C(v) =3D φ
でも…
現実には交渉の決着がつき，配分がある範囲に収まるので= は？
例：提携{1,2}<= /span>が成立　→　配分 x =3D (0.5, 0.5, 0)
結局，K =3D { (0.5, 0.5, 0), (0.5, 0, 0.5), (0, 0.5, 0.= 5) } のいずれかで決着！
〔互いに支配関係にない．また， (0.4, 0, 0.6) などは (0.5, 0.5, 0) <= /span>に支配される．〕
n<= /span>安定集合（stable set）–配分の集合Xの部分集= Kが以下の性質を満たす時，Kを安定集合という
&#= 8211; （１） 内部安定性（internal stability）
&#= 8211; 　　　x∈K, y∈K →　x, y は互いに支配関係にない= 3;
&#= 8211; （２） 外部安定性（external stability）
&#= 8211; 　　　Kに属さない任意の配分は，Kに属す少なくとも1つの配分に支配される
------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0022_image364.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAr ABsAgQAAAAAA/5nM/wECAwJuhI8Joe0PTZixWhSEoLe7rG2MR0phyJUXeGqpNcXyHLftC7H2zp94 o+sJdz/M8NgrLpBM4sjYjPqeS6nVNQpeo7WtlKP1Jqlh8Y1qMvOUZbEyrcZWaHSZ8K2Cn/NzG55/ oPMHGChHuDJ4iKEIUAAAOw== ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
協力ゲー= の理論
n<= /span>安定集合
–Dom = x :=3D {= = y | = y∈X, = x dom <= /span>= y } ：配分 x に支配さ= 黷髞z分の集合
–Dom A = :=3D ∪Dom = x ：集合Aの配分に= x配される配分の集合
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n内部安定性　⇔　K ∩ Dom K =3D φ
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n外部安定性　⇔　K ∪ Dom K =3D A
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n安定集合　⇔　K =3D A −= Dom K を満たす集合 K⊂A
x∈A
The= orem
　ゲーム（N, v） の安定集合がただ1つの配分から成るための必= 要十分条件は，ゲームが非本質的であること．
The= orem
　ゲーム（N, v） のコアC および安= 闖W合 K が共に非空ならば
C ⊂ K．=
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投票ゲー=
n<= /span>投票ゲーム
–N人のプレイヤーによる投票で何らかの決定がなされるシス= テムを考える．
n<= /span>投票者の様々なグループ（Nの部分集合）＝提携（= coalition）
n= 法案の可決，など選択権を持つ提携＝勝利提携（= winning coalition）　= W
n<= /span>そうでない提携＝敗北提携（= losing coalition） L
n→　(N, W)：投票ゲーム（= voting game）=
n ただし，以下の性質を持つとする
n （１） <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N∈= W，φ∈L
n= （２） S∈W かつS⊆T　→　 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>T∈= W
n= （３） S∈W　→　N−S∈L
n =
–例：3つの政党 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N=3D{1,= 2,3} の議員で構成されている議会
– 　　定数<= /span>21で，各政= }の議席数 （10, 10, 1)．過半数で議案可決．
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n勝利提携 W =3D { {1, 2, 3}, {1, 2}, {1, 3}, {2, 3} }
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n敗北提携 L =3D { {1}, {2}, {3}, φ }
全員提携は勝利提携，空集合は敗北提携
勝利提携を含む提携は勝利提携
勝利提携の補集合は敗北提携
各投票者 N=3D{1,2,3} の
影響力（投票力指数）
はどの程度なのか= ？
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投票ゲー=
n投票力指数が満たすべき性質–[8] p.= 45〜
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
–<= span style=3D'mso-ascii-font-family:"Century Schoolbook";mso-hansi-font-family:= "Century Schoolbook"; display:none'>
n投票力指数
–シャープレイ・シュービック指数（Shapley-Shubik index） (1954)
–バンザフ指数（Banzhaf index）  (1965)
–ディーガン・パックル指数（Deegan-Packel index）  (1978)
–……
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(1, 2, 3)
提携に参加する順
投票ゲー=
n<= /span>投票力指数
–シャープレイ・シュービック指数（SS指数）
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n例：3人 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N=3D{1,= 2,3} の単純多数決ゲーム
–勝利提携 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>= W =3D { {1,2,3}, {1,2}, {2,3}, {3,1} }=
　協力ゲームの解の1つシャープレイ値を= C投票<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>者の影響力の評価に適= 用したもの．
全ての順列の生起確率が等しいと仮定したときの，各投票者のピヴォットとなる回数の期待値
(2, 3, 1),
(3, 1, 2),
(1, 3, 2),
(2, 1, 3),
(3, 2, 1)
ピヴ= ォット（pivot）
SS指数：
勝利提携
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φ
(1
(2
(3
(1, 2
(1, 3
(2, 3
(1, 2, 3
投票ゲー=
n<= /span>投票力指数
–バンザフ指数（絶対Bz指数）
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n例：4人 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N=3D{1,= 2,3,4} の単純多数決ゲーム
–勝利提携 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>= W =3D { {1,2,3,4}, {1,2,3}, {1,2,4}, {2,3,4} }
–&= #13;
–{1,2,3} の3人による全ての部分集合
全ての投票者が賛成・反対を表明しているとき，自らの投票態度を変更することによって結果を変えることの出来る投票者（スウィング）となる回数の期待値
絶対Bz指数：
勝利提携
,4 )
,4 )
,4 )
,4 )
,4 )
,4 )
,4 )
,4 )
+
勝利提携
勝利提携
勝利提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
敗北提携
勝利提携
スウ= ィング
（<= /span>swing）
正規Bz指数：
と正規化<= /span>
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投票ゲー=
n<= /span>投票力指数
–ディーガン・パックル指数（DP指数）
n= 投票者は「極小勝利提携Wm」に属しているとき，影響力を持つという考え
n= ただし，極小勝利提携に属す投票者は全て同じ影響力を持= つとする
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n投票者 i の= DP指数は，
n
<= span style=3D'font-family:"Century Schoolbook";mso-fareast-hint:yes'>n例：4人 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>N=3D{1,= 2,3,4} の単純多数決ゲーム
–勝利提携 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>= W =3D { {1,2,3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4} }
–極小勝利提携 <= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";mso-fareast-language:JA'>= Wm =3D { {1,2,3}, {1,2,4}, {1,3,4}, {= 2,3,4} }&= #13;
–極小勝利提携の全体 |= = Wm| =3D = 4
各極小勝利提携の生起確率が同じと仮定したときの，各投票者の影響力の割合
DP指数：
極小勝利提携
　勝利提携のうち，1人でも抜けると敗北提= gに<= span style=3D'font-family:"ＭＳ Ｐゴシック";mso-ascii-font-family:"Century Scho= olbook"; mso-fareast-font-family:"ＭＳ Ｐゴシック";mso-hansi-font-family:"Century S= choolbook"; font-size:89%;mso-fareast-hint:yes'>なってしまうもの．
<= ![if !ppt]>
∈
S
i
{1,2,3= } → (1/3, 1/3, 1/3,   0 )
{1,2,4= } → (1/3, 1/3,   0,  1/3)
{1,3,4= } → (1/3,   0,  1/3, 1/3)
{2,3,4= } → (  0,  1/3, 1/3, 1/3)
投票者1について= ﾌ和： 1
投票者2について= ﾌ和： 1
投票者3について= ﾌ和： 1
投票者4について= ﾌ和： 1
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投票ゲー=
n投票力指数の意味–例：定数20の議会，4政党所属議員で構成．過半数で議案可決．
構成比率
40%
35%
15%
10%
この比率が各党の力（議会発言力）なのか？
SS指数
Bz指数
DP指数
–例：定数が19に変化し，議席数が（8,7,3,1）となった．
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file:///C:/E17059D3/06dmt_5-3.files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="shift_jis" 意思決定科学： ゲーム理論3
投票ゲー=
n演習：
–以下の各投票ゲームにおけるSS指数， Bz指数，DP指数を計算しよう
–
= 211;（１）3人のプレイヤー N=3D{1,2,3} による単純多数決ゲームを考える．ただし，<= span style=3D'position: absolute;top:34.75%;left:10.29%;width:85.39%;height:4.75%'>プレイヤー1には拒否権がある．
R= 11;
= 211;（２）4つの政党がそれぞれ議席数（40, 30, 10, 5）を占めている議会において，2/3以上の賛成で議案を通すことが出来る．
R= 11;
= 211;（３）β社の株を5人の人が所有しており，その比率は（30%, 25%, 25%, 15%, 5%） である．株主総会において，過半数の意= ｩが通るとする．
投票力指数の説明と投票力指数を計算する，東大松井先生のWebサイト
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参考文献<= /span>
= n[1] 鈴木光男 「ゲーム理論入門」 共立出版（1981（新装版）= j
n[2] 鈴木光男 「新ゲーム理論」 勁草書房（1994）
n[3] 岡田章 「ゲーム理論」 有斐閣（1996）
n[4] 鈴木光男・武藤滋男 「協力ゲームの理論」 東京大学出版会(1985)
n[5] = 山幹夫・舟木由喜彦・武藤滋男 = uゲーム理論で解く」 有斐閣ブックス(2000)
n[6] = M木由喜彦 「エコノミックゲームセ= オリー」 サイエンス社n[7] 武藤滋男・小野理恵 「投票システムのゲーム分析」 = 科技連(1998)
n[8] 森雅夫・松井知己 「オペレーションズ・リサーチ」 朝倉書店(2004)
n[9] 松井知己 『投票力指数を計算する』=
nhttp://www.misojiro.t.u-tokyo.ac.jp/~tomomi/votin= g/voting.html
n[10] 毛利裕昭・岡本吉央 「離散最適化と協力ゲーム（１）（２）」 = Iペレーションズ・リサーチ
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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 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=3D44, SCRIPT_HREF=3D= "script.js", FULLSCR_HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0002.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("= slide0004.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("s= lide0008.htm",1,-1,1),new hrefList("slide0006.htm",1,-1,1),new hrefList("sl= ide0009.htm",1,-1,1),new hrefList("slide0011.htm",1,-1,1),new hrefList("sli= de0012.htm",1,-1,1),new hrefList("slide0013.htm",1,-1,1),new hrefList("slid= e0028.htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide= 0010.htm",1,-1,1),new hrefList("slide0015.htm",1,-1,1),new hrefList("slide0= 039.htm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("slide00= 40.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("slide004= 1.htm",1,-1,1),new hrefList("slide0018.htm",1,-1,1),new hrefList("slide0042= .htm",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("slide0020.= htm",1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("slide0024.h= tm",1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0026.ht= m",1,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0027.htm= ",1,-1,1),new hrefList("slide0043.htm",1,-1,1),new hrefList("slide0044.htm"= ,1,-1,1),new hrefList("slide0021.htm",1,-1,1),new hrefList("slide0045.htm",= 1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slide0029.htm",1= ,-1,1),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("slide0037.htm",1,-1,1),new hrefList("slide0038.htm",1,-1= ,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("slide0007.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" 意思決定科学： ゲーム理論3 ------=_NextPart_01C71EB2.74D88F70 Content-Location: file:///C:/E17059D3/06dmt_5-3.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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協力ゲー= の理論
n演習：
= 211;（３） 家購入ゲーム （[4] p.26 例3.4）=
1なら，1150万
2なら，1000万
=
1000万
= 900万
家を売りたい
家を買いたい
1なら，= 1070万
2なら，= 950万
player1
player2
player3
player4
評価額の差が最も大きくなるように売却し，その差の和で v を計算
交渉
N=3D{1,2,3,4}
v<= span lang=3DEN-US style=3D'font-family:"Century Schoolbook";mso-ascii-font-fami= ly:"Century Schoolbook"; mso-hansi-font-family:"Century Schoolbook";color:black;mso-fareast-languag= e: JA'>({1,2,3,4}) =3D 200,
v({1,2,3}) =3D 150, v({1,2,4}) =3D 70, v({1,3,4}) =3D 150, v({2,3,4}) =3D 100,
v({1,2}) =3D 0, v({1,3}) =3D 150, v({1,4}) =3D 70, v({2,3}) =3D 100, v({2,4}) =3D 50, v({3,4}) =3D 0,
v({1}) =3D v({2}) =3D v({3}) =3D v({4}) =3D v(φ) =3D 0
→ コア =
　　 C(v) =3D { x∈X |x1 = + x3 = =3D 150,  x2 + x4<= span style=3D'mso-spacerun:yes'>  =3D 50,  x1 = + x4 = ≧70,  x2 = + x3 = ≧ 100 }