- dilemma del prigioniero e battaglia dei sessi - game form e gioco, in forma estesa e strategica
Appunti di Fioravante PATRONE
http://www.diptem.unige.it/patrone/default.htm Decisori (razionali) interagenti
versione del 1 aprile 2011
Finalit` a di queste note
Illustrare anche visivamente il caso pi` u semplice di gioco ripetuto, ovvero il caso a due soli stadi.
Avere a disposizione la forma estesa e quella strategica del gioco ripetuto offre la possibilit` a di cogliere pi` u direttamente alcuni aspetti interessanti.
Game form di un gioco ripetuto: forma estesa e forma strategica
𝐼
∖ ∖𝐼𝐼 L R
T 𝑥 𝑦
B 𝑧 𝑡
𝐼c 𝑇
𝐵 H
H H H H
H H H
H H s
@
@
@
@
@
s
@
@
@
@
@ 𝐼𝐼
𝐿 𝑅 𝐿 𝑅
s 𝐼
𝑇
1A A
A A
A 𝐵
1s𝐼
𝑇
2A A
A A
A 𝐵
2s 𝐼
𝑇
3A A
A A
A 𝐵
3s𝐼
𝑇
4A A
A A
A 𝐵
4s
𝐿
1s 𝑎
C C
C C
C 𝑅
1s 𝑏
s
𝐿
1s 𝑐
C C
C C
C 𝑅
1s 𝑑
𝐼𝐼 s
𝐿
2s 𝑒
C C
C C
Cs 𝑅
2𝑓
s
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2s 𝑔
C C
C C
C 𝑅
2s ℎ
𝐼𝐼 s
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3s 𝑖
C C
C C
C 𝑅
3s 𝑙
s
𝐿
3s 𝑚
C C
C C
C 𝑅
3s 𝑛
𝐼𝐼 s
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4s 𝑜
C C
C C
C 𝑅
4s 𝑝
s
𝐿
4s 𝑞
C C
C C
C 𝑅
4s
𝑟
𝐼𝐼
Game form di un gioco ripetuto: forma estesa e forma strategica
Pi` u espressiva ` e la game form seguente, in cui abbiamo evidenziato come gli esiti finali non siano altro che la “raccolta” degli esiti parziali ottenuti in ciascun stadio. Ad esempio, l’esito “(𝑦, 𝑡)” (le due coordinate sono poste in colonna, nella forma estesa, per ragioni tipografiche) indica che al primo stadio si ` e avuto l’esito 𝑥 e al secondo stadio l’esito 𝑡. Questo modo di denotare gli esiti ` e anche pi` u aderente all’idea di gioco ripetuto: ad ogni stadio si ottengono esiti “parziali”, che vanno a “comporre” l’esito finale. Questo significa anche che l’unica differenza tra (𝑥, 𝑦) ed (𝑦, 𝑥) sta nel fatto che c’` e una inversione temporale nell’ottenimento dei due esiti parziali 𝑥 ed 𝑦. Se vi fossero altre differenze, non ci troveremmo propriamente in un contesto di giochi ripetuti.
𝐼c 𝑇
𝐵 H H
H H H H
H H H H s
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s
@
@
@
@
@ 𝐼𝐼
𝐿 𝑅 𝐿 𝑅
s 𝐼
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1A A
A A
A 𝐵
1s𝐼
𝑇
2A A
A A
A 𝐵
2s 𝐼
𝑇
3A A
A A
A 𝐵
3s𝐼
𝑇
4A A
A A
A 𝐵
4s
𝐿
1s 𝑥 𝑥
C C
C C
C 𝑅
1s 𝑥 𝑦
s
𝐿
1s 𝑥 𝑧
C C
C C
C 𝑅
1s 𝑥 𝑡
𝐼𝐼 s
𝐿
2s 𝑦 𝑥
C C
C C
Cs 𝑅
2𝑦 𝑦
s
𝐿
2s 𝑦 𝑧
C C
C C
C 𝑅
2s 𝑦 𝑡
𝐼𝐼 s
𝐿
3s 𝑧 𝑥
C C
C C
C 𝑅
3s 𝑧 𝑦
s
𝐿
3s 𝑧 𝑧
C C
C C
C 𝑅
3s 𝑧 𝑡
𝐼𝐼 s
𝐿
4s 𝑡 𝑥
C C
C C
C 𝑅
4s 𝑡 𝑦
s
𝐿
4s 𝑡 𝑧
C C
C C
C 𝑅
4s
𝑡
𝑡
𝐼𝐼
I
∖
∖
∖
∖ 𝐼𝐼
𝐿 𝐿1 𝐿2 𝐿3 𝐿4
𝐿 𝐿1 𝐿2 𝐿3 𝑅4
𝐿 𝐿1 𝐿2 𝑅3 𝐿4
𝐿 𝐿1 𝐿2 𝑅3 𝑅4
𝐿 𝐿1 𝑅2 𝐿3 𝐿4
𝐿 𝐿1 𝑅2 𝐿3 𝑅4
𝐿 𝐿1 𝑅2 𝑅3 𝐿4
𝐿 𝐿1 𝑅2 𝑅3 𝑅4
𝐿 𝑅1 𝐿2 𝐿3 𝐿4
𝐿 𝑅1 𝐿2 𝐿3 𝑅4
𝐿 𝑅1 𝐿2 𝑅3 𝐿4
𝐿 𝑅1 𝐿2 𝑅3 𝑅4
𝐿 𝑅1 𝑅2 𝐿3 𝐿4
𝐿 𝑅1 𝑅2 𝐿3 𝑅4
𝐿 𝑅1 𝑅2 𝑅3 𝐿4 𝐿 𝑅1 𝑅2 𝑅3 𝑅4
𝑅 𝐿1 𝐿2 𝐿3 𝐿4
𝑅 𝐿1 𝐿2 𝐿3 𝑅4
𝑅 𝐿1 𝐿2 𝑅3 𝐿4
𝑅 𝐿1 𝐿2 𝑅3 𝑅4
𝑅 𝐿1 𝑅2 𝐿3 𝐿4
𝑅 𝐿1 𝑅2 𝐿3 𝑅4
𝑅 𝐿1 𝑅2 𝑅3 𝐿4
𝑅 𝐿1 𝑅2 𝑅3 𝑅4
𝑅 𝑅1 𝐿2 𝐿3 𝐿4
𝑅 𝑅1 𝐿2 𝐿3 𝑅4
𝑅 𝑅1 𝐿2 𝑅3 𝐿4
𝑅 𝑅1 𝐿2 𝑅3 𝑅4
𝑅 𝑅1 𝑅2 𝐿3 𝐿4
𝑅 𝑅1 𝑅2 𝐿3 𝑅4
𝑅 𝑅1 𝑅2 𝑅3 𝐿4
𝑅 𝑅1 𝑅2 𝑅3 𝑅4
𝑇 𝑇1𝑇2𝑇3𝑇4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝑇1𝑇2𝑇3𝐵4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝑇1𝑇2𝐵3𝑇4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝑇1𝑇2𝐵3𝐵4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝑇1𝐵2𝑇3𝑇4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝑇1𝐵2𝑇3𝐵4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝑇1𝐵2𝐵3𝑇4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝑇1𝐵2𝐵3𝐵4 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑏 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝐵1𝑇2𝑇3𝑇4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝐵1𝑇2𝑇3𝐵4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝐵1𝑇2𝐵3𝑇4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝐵1𝑇2𝐵3𝐵4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓 𝑒 𝑒 𝑒 𝑒 𝑓 𝑓 𝑓 𝑓
𝑇 𝐵1𝐵2𝑇3𝑇4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝐵1𝐵2𝑇3𝐵4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝐵1𝐵2𝐵3𝑇4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝑇 𝐵1𝐵2𝐵3𝐵4 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑐 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑑 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ 𝑔 𝑔 𝑔 𝑔 ℎ ℎ ℎ ℎ
𝐵𝑇1𝑇2𝑇3𝑇4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝑇1𝑇2𝑇3𝐵4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝑇1𝑇2𝐵3𝑇4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝑇1𝑇2𝐵3𝐵4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝑇1𝐵2𝑇3𝑇4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝑇1𝐵2𝑇3𝐵4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝑇1𝐵2𝐵3𝑇4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝑇1𝐵2𝐵3𝐵4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝐵1𝑇2𝑇3𝑇4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝐵1𝑇2𝑇3𝐵4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝐵1𝑇2𝐵3𝑇4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝐵1𝑇2𝐵3𝐵4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝐵1𝐵2𝑇3𝑇4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝐵1𝐵2𝑇3𝐵4 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑖 𝑖 𝑙 𝑙 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
𝐵𝐵1𝐵2𝐵3𝑇4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝 𝑜 𝑝
𝐵𝐵1𝐵2𝐵3𝐵4 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑚 𝑚 𝑛 𝑛 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟 𝑞 𝑟
Dilemma del prigioniero ripetuto: albero, forma strategica ed equilibri in strategie pure
𝐼
∖
∖𝐼𝐼 L R
T (3, 3) (0, 5) B (5, 0) (1, 1)
𝐼c 𝑇
𝐵 H H
H H H
H H H H s H
@
@
@
@
@
s
@
@
@
@
@ 𝐼𝐼
𝐿 𝑅 𝐿 𝑅
s 𝐼
𝑇
1A A
A A
A 𝐵
1s𝐼
𝑇
2A A
A A
A 𝐵
2s 𝐼
𝑇
3A A
A A
A 𝐵
3s𝐼
𝑇
4A A
A A
A 𝐵
4s
𝐿
1s 6 6
C C
C C
C 𝑅
1s 3 8
s
𝐿
1s 8 3
C C
C C
C 𝑅
1s 4 4
𝐼𝐼 s
𝐿
2s 3 8
C C
C C
Cs 𝑅
20 10
s
𝐿
2s 5 5
C C
C C
C 𝑅
2s 1 6
𝐼𝐼 s
𝐿
3s 8 3
C C
C C
C 𝑅
3s 5 5
s
𝐿
3s 10 0
C C
C C
C 𝑅
3s 6 1
𝐼𝐼 s
𝐿
4s 4 4
C C
C C
C 𝑅
4s 1 6
s
𝐿
4s 6 1
C C
C C
C 𝑅
4s 2 2 𝐼𝐼
Nella forma strategica, gli equilibri sono indicati con (x,y) , e l’unico SPE con (x,y)
I
∖
∖
∖
∖ 𝐼𝐼
𝐿 𝐿1 𝐿2 𝐿3 𝐿4
𝐿 𝐿1 𝐿2 𝐿3 𝑅4
𝐿 𝐿1 𝐿2 𝑅3 𝐿4
𝐿 𝐿1 𝐿2 𝑅3 𝑅4
𝐿 𝐿1 𝑅2 𝐿3 𝐿4
𝐿 𝐿1 𝑅2 𝐿3 𝑅4
𝐿 𝐿1 𝑅2 𝑅3 𝐿4
𝐿 𝐿1 𝑅2 𝑅3 𝑅4
𝐿 𝑅1 𝐿2 𝐿3 𝐿4
𝐿 𝑅1 𝐿2 𝐿3 𝑅4
𝐿 𝑅1 𝐿2 𝑅3 𝐿4
𝐿 𝑅1 𝐿2 𝑅3 𝑅4
𝐿 𝑅1 𝑅2 𝐿3 𝐿4
𝐿 𝑅1 𝑅2 𝐿3 𝑅4
𝐿 𝑅1 𝑅2 𝑅3 𝐿4
𝐿 𝑅1 𝑅2 𝑅3 𝑅4
𝑅 𝐿1 𝐿2 𝐿3 𝐿4
𝑅 𝐿1 𝐿2 𝐿3 𝑅4
𝑅 𝐿1 𝐿2 𝑅3 𝐿4
𝑅 𝐿1 𝐿2 𝑅3 𝑅4
𝑅 𝐿1 𝑅2 𝐿3 𝐿4
𝑅 𝐿1 𝑅2 𝐿3 𝑅4
𝑅 𝐿1 𝑅2 𝑅3 𝐿4
𝑅 𝐿1 𝑅2 𝑅3 𝑅4
𝑅 𝑅1 𝐿2 𝐿3 𝐿4
𝑅 𝑅1 𝐿2 𝐿3 𝑅4
𝑅 𝑅1 𝐿2 𝑅3 𝐿4
𝑅 𝑅1 𝐿2 𝑅3 𝑅4
𝑅 𝑅1 𝑅2 𝐿3 𝐿4
𝑅 𝑅1 𝑅2 𝐿3 𝑅4
𝑅 𝑅1 𝑅2 𝑅3 𝐿4
𝑅 𝑅1 𝑅2 𝑅3 𝑅4 𝑇 𝑇1𝑇2𝑇3𝑇4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝑇1𝑇2𝑇3𝐵4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝑇1𝑇2𝐵3𝑇4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝑇1𝑇2𝐵3𝐵4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝑇1𝐵2𝑇3𝑇4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝑇1𝐵2𝑇3𝐵4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝑇1𝐵2𝐵3𝑇4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝑇1𝐵2𝐵3𝐵4 (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (6, 6) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝐵1𝑇2𝑇3𝑇4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝐵1𝑇2𝑇3𝐵4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝐵1𝑇2𝐵3𝑇4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝐵1𝑇2𝐵3𝐵4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) (3, 8) (3, 8) (3, 8) (3, 8) (0, 10) (0, 10) (0, 10) (0, 10) 𝑇 𝐵1𝐵2𝑇3𝑇4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝐵1𝐵2𝑇3𝐵4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝐵1𝐵2𝐵3𝑇4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝑇 𝐵1𝐵2𝐵3𝐵4 (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (8, 3) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (4, 4) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) (5, 5) (5, 5) (5, 5) (5, 5) (1, 6) (1, 6) (1, 6) (1, 6) 𝐵𝑇1𝑇2𝑇3𝑇4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝑇1𝑇2𝑇3𝐵4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝑇1𝑇2𝐵3𝑇4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝑇1𝑇2𝐵3𝐵4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝑇1𝐵2𝑇3𝑇4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝑇1𝐵2𝑇3𝐵4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝑇1𝐵2𝐵3𝑇4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝑇1𝐵2𝐵3𝐵4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝐵1𝑇2𝑇3𝑇4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝐵1𝑇2𝑇3𝐵4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝐵1𝑇2𝐵3𝑇4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝐵1𝑇2𝐵3𝐵4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝐵1𝐵2𝑇3𝑇4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝐵1𝐵2𝑇3𝐵4 (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (8, 3) (8, 3) (5, 5) (5, 5) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) 𝐵𝐵1𝐵2𝐵3𝑇4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) (4, 4) (1, 6) 𝐵𝐵1𝐵2𝐵3𝐵4 (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (10, 0) (10, 0) (6, 1) (6, 1) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2) (6, 1) (2, 2)
Battaglia dei sessi ripetuta: albero, forma strategica e corrispondenza di miglior risposta in pure
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𝐿 𝐿1 𝐿2 𝐿3 𝐿4
𝐿 𝐿1 𝐿2 𝐿3 𝑅4
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𝑅 𝐿1 𝐿2 𝐿3 𝐿4
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𝑅 𝑅1 𝑅2 𝑅3 𝑅4 𝑇 𝑇1𝑇2𝑇3𝑇4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝑇1𝑇2𝑇3𝐵4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝑇1𝑇2𝐵3𝑇4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝑇1𝑇2𝐵3𝐵4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝑇1𝐵2𝑇3𝑇4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) 𝑇 𝑇1𝐵2𝑇3𝐵4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) 𝑇 𝑇1𝐵2𝐵3𝑇4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) 𝑇 𝑇1𝐵2𝐵3𝐵4 ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) ( 4 , 2 ) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (2, 1) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2 ) (1, 2 ) (1, 2 ) (1, 2 ) 𝑇 𝐵1𝑇2𝑇3𝑇4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝐵1𝑇2𝑇3𝐵4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝐵1𝑇2𝐵3𝑇4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝐵1𝑇2𝐵3𝐵4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) (2, 1) ( 2 , 1) (2, 1) ( 2 , 1) (0, 0) (0, 0) (0, 0) (0, 0) 𝑇 𝐵1𝐵2𝑇3𝑇4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) 𝑇 𝐵1𝐵2𝑇3𝐵4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) 𝑇 𝐵1𝐵2𝐵3𝑇4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) 𝑇 𝐵1𝐵2𝐵3𝐵4 (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) (1, 2) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) ( 3 , 3 ) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) (0, 0) (0, 0) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) (1, 2) 𝐵𝑇1𝑇2𝑇3𝑇4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝑇1𝑇2𝑇3𝐵4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝑇1𝑇2𝐵3𝑇4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝑇1𝑇2𝐵3𝐵4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝑇1𝐵2𝑇3𝑇4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝑇1𝐵2𝑇3𝐵4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝑇1𝐵2𝐵3𝑇4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝑇1𝐵2𝐵3𝐵4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝐵1𝑇2𝑇3𝑇4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝐵1𝑇2𝑇3𝐵4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝐵1𝑇2𝐵3𝑇4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝐵1𝑇2𝐵3𝐵4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝐵1𝐵2𝑇3𝑇4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝐵1𝐵2𝑇3𝐵4 (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (2, 1) (2, 1) (0, 0) (0, 0) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) 𝐵𝐵1𝐵2𝐵3𝑇4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) ( 3 , 3 ) (1, 2) 𝐵𝐵1𝐵2𝐵3𝐵4 (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (0, 0) (0, 0) (1, 2) (1, 2) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 ) (1, 2) ( 2 , 4 )