(博奕論)北海道大學入學試題,1至100選最大數字

巴打係咪差唔多開估
定係太少人玩唔到

整緊

順帶一提，唔好諗住用simulation嘅outcome做prediction，你會死得好慘

根本不可predict

太長唔想用中文打

The strategy of choosing 100 is a weakly dominant strategy.

Consider a player, Alice. We only need to consider two cases:

Case 1: The largest number chosen by the rest of the group is strictly less than 100. Then, Alice can always win by choosing 100, but if she may lose if she chooses a number less than 100.

Case 2: The largest number chosen by the rest of the group is 100. Then, Alice will lose no matter which number she chooses, so she is indifferent between all possible strategies.

The conclusion means that all (rational) players should choose 100, leading to a Nash equilibrium outcome in which all players gain zero point.

多謝ching 今日畀人笑我傻仔揀100

我改咗RX-78-2段code再寫咗個simulation
link: https://pastebin.com/VwnHggRD
data主要係用之前所得嘅sample distribution模擬出來

Output:

[63, 52, 48, 62, 65, 63, 66, 63, 63, 63, 63, 65, 63, 44, 63, 52, 64, 63, 64, 63, 63, 65, 54, 50, 40, 65, 63, 48, 63, 56]
The mean of winning places for 1000 players is 59.3

[31, 27, 27, 63, 19, 18, 27, 6, 33, 52, 31, 21, 33, 46, 63, 15, 18, 31, 48, 63, 21, 31, 63, 31, 33, 52, 49, 28, 46, 14]
The mean of winning places for 2000 players is 34.6666666667

[27, 6, 14, 27, 28, nan, 12, nan, 28, 18, nan, 15, 21, 5, nan, 33, 28, 14, 11, nan, 31, nan, nan, 28, nan, 63, 33, 15, nan, 5]
The mean of winning places for 3000 players is 22.0

[11, 63, nan, nan, nan, nan, 63, nan, 8, nan, 33, nan, nan, 27, nan, 14, 21, 63, 31, nan, 0, nan, nan, 21, nan, 18, nan, 18, nan, nan]
The mean of winning places for 4000 players is 27.9285714286

[nan, nan, 8, nan, 0, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, 63, 31, 28, 31, nan, nan, nan, 11, 3, nan, nan, nan, nan, 8, nan]
The mean of winning places for 5000 players is 20.3333333333

[nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan]
No winning places

[Finished in 12.3s]

我前面話「如果有一萬人玩隻game，啲人重夠唔夠膽講60-70係合理範圍」係有少少根據嘅
每一條array有30個elements，分別代表30回合裡面每一場邊個數字贏咗
3000人嗰度你已經見到有好多nan，因為嗰一場裡面無人贏，所以我set咗winning position係nan

睇返上面output你就會見到愈多參賽者個winning number就會愈低
其實4000同5000個players出嘅sample mean唔係太靠得住，因為太多nan啦，拖低咗個sample size of non-missing data
去到6000個players就直情無人贏
背後原因我諗同birthday problem/pigeonhole principle有啲關係

呢條題目夠UG做一份功課

不過好玩過讀analysis

巴打係咪差唔多開估
定係太少人玩唔到

整緊

唔識整
呢度係個EXCEL表
有冇巴打幫幫手
https://docs.google.com/spreadsheets/d/1RdtMihlBQWSbcFqXzJKzX9rXkIR4nmFG89JGLBIKMaw/edit#gid=2079417308

8?
打橫係 ∞

巴打係咪差唔多開估
定係太少人玩唔到

整緊

唔識整
呢度係個EXCEL表
有冇巴打幫幫手
https://docs.google.com/spreadsheets/d/1RdtMihlBQWSbcFqXzJKzX9rXkIR4nmFG89JGLBIKMaw/edit#gid=2079417308

參與人數為 221人
目測結果
第二round 勝利者為 145

巴打係咪差唔多開估
定係太少人玩唔到

整緊

唔識整
呢度係個EXCEL表
有冇巴打幫幫手
https://docs.google.com/spreadsheets/d/1RdtMihlBQWSbcFqXzJKzX9rXkIR4nmFG89JGLBIKMaw/edit#gid=2079417308

參與人數為 221人
目測結果
第二round 勝利者為 145

因為個個俾第一次影響左 估到會好高

選項 150 [20
選項 149 [3
選項 148 [2
選項 147 [2
選項 146 [2
選項 145 [1
選項 144 [2
選項 143 [4
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選項 136 [2
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選項 104 [1
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選項 96 [1
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選項 51 [1
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選項 46 [2
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選項 42 [1
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選項 17 [2
選項 13 [1
選項 12 [1
選項 10 [1
選項 2 [2
選項 1 [3


總數 221人
勝利者為選項 145

上面嗰個唔係一千人咩，變咗二百人，成隻game唔同咗啦

上面嗰個唔係一千人咩，變咗二百人，成隻game唔同咗啦

無錯呀, 上限係一千人

用stat玩game theory game 冇咩意思。之前睇過本書講獎門人隻1-100。數學人正路就半分咁玩 下一個50，25/75咁 。但佢話如果我玩你我就會set51/49咁，再狗啲就53，47咁，其實一有對手就難搞好多

最尾會唔會出番解題/講返e題大概係點做

太長唔想用中文打

The strategy of choosing 100 is a weakly dominant strategy.

Consider a player, Alice. We only need to consider two cases:

Case 1: The largest number chosen by the rest of the group is strictly less than 100. Then, Alice can always win by choosing 100, but if she may lose if she chooses a number less than 100.

Case 2: The largest number chosen by the rest of the group is 100. Then, Alice will lose no matter which number she chooses, so she is indifferent between all possible strategies.

The conclusion means that all (rational) players should choose 100, leading to a Nash equilibrium outcome in which all players gain zero point.

多謝ching 今日畀人笑我傻仔揀100

佢個答案係答緊唔同既問題

其實話簡最大(100)係best strategy既人睇到兩個TEST 最大既號碼都係大比數咁輸, 有咩感想?

一早講左 個game 係玩唔同其他人撞為先 你愈有理由去分析點解一個答案係最佳既時候 果個答案就係一定係最差

你掉番轉問我叫我解釋點為63會赢 145會赢 我係解釋唔到 正正就係解釋唔到 所以佢係最好既答案

一早講左 個game 係玩唔同其他人撞為先 你愈有理由去分析點解一個答案係最佳既時候 果個答案就係一定係最差

你掉番轉問我叫我解釋點為63會赢 145會赢 我係解釋唔到 正正就係解釋唔到 所以佢係最好既答案

agger
題目都寫左係博奕論
呢題唔係數學題 而係econ題

係咪鬥背兀?

其實話簡最大(100)係best strategy既人睇到兩個TEST 最大既號碼都係大比數咁輸, 有咩感想?

best strategy唔係用嚟贏架

其實話簡最大(100)係best strategy既人睇到兩個TEST 最大既號碼都係大比數咁輸, 有咩感想?

best strategy唔係用嚟贏架

唔係要贏咁玩呢個Game為咩？
證明你嘅睇法好出類拔萃，只要無一個人同我諗嘅野一樣就一定我贏

其實話簡最大(100)係best strategy既人睇到兩個TEST 最大既號碼都係大比數咁輸, 有咩感想?

best strategy唔係用嚟贏架

如果你呢個best係理解為最用少時間黎決定嘅話咪係囉