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So, by putting ourselves in Hannibal's shoes, we could figure out that his hard attack strategy was weakly dominated.
那么我们从汉尼拔的角度来考虑一下,我们发现崎岖之途是弱劣势策略
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If he meets your army, whichever pass he chooses, if he meets your army defending a pass, then he'll lose another battalion.
如果他碰巧遇到了你设防的途径,无论崎岖之途还是平坦之途,他还要再损失一个营的兵力
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Conversely, if he goes on the hard pass and you defend the easy pass, he's going to lose one of those battalions.
相反,如果他选择崎岖之途,而你却防守平坦之路,那么他仅仅损失一个营的兵力
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Again, easy pass here just means no mountains, we're not talking about something on the New Jersey Turnpike.
强调一下 平坦之途不用翻山越岭,我们说的不是新泽西收费公路
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Just check, that exactly corresponds to the easy and hard thing we just had before.
验证一下,这和我们之前,选择平坦之途还是崎岖之途是对应的
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And there are two passes you could defend: the easy pass or the hard pass.
你要选择两条途径中的一条设防,平坦之途的或崎岖之途
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But if the attacker was to attack through the hard pass, again not surprisingly, you do better if you defend the hard pass than the easy pass.
但如果入侵者选择崎岖之途,仍然是毫无疑问,选择防御崎岖之途要比平坦之途好
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It means by choosing the easy pass, he does at least as well, and sometimes better, than he would have done had he chosen the hard pass.
它意味着选择平坦之途,较选择崎岖之途而言,至少要同样的好,可能还稍微好些
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Now since we think that Hannibal, the attacker, is not going to play a weakly dominated strategy, we think Hannibal is not going to choose the hard pass.
好了,既然我们认为入侵者汉尼拔,不会选择弱劣势策略,我们认为汉尼拔不会选择崎岖之途
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And there's two you could use to attack through, easy or hard.
同样他也有两条路入侵途径,平坦之途和崎岖之途
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It isn't the case that defending easy dominates defending hard.
防守平坦之途并非优于防守崎岖之途
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How many of you think you should defend the easy pass?
有多少人选择防守平坦之途的
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And how many think you're going to defend the hard pass?
有多少人选择防守崎岖之途
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He's going to choose easy, so we should defend easy.
他会选择平坦之途,我们应该在此设防
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In fact, we could check that if the attacker attacks through the easy pass, not surprisingly, you do better if you defend the easy pass than the hard pass: 1 versus 0.
我们来分析一下,如果入侵者选择平坦之途,毫无疑问,如果你选平坦之途要比崎岖之途更好,1比0
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He's going to attack on the easy pass.
他会选择从平坦之途入侵
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Nevertheless, almost all of you chose easy.
然而大多数人都选择防守平坦之途了
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So if you defend the easy pass, from his point of view, it doesn't matter whether he chooses the easy pass and gets one in there or the hard pass, he gets one in there.
那么如果你防守平坦的路,从他的立场出发,无论怎么选择,选崎岖之途收益是1,而选择平坦之途的收益也是1
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If you were to defend the easy pass and he goes through the easy pass, he will get into your country with one battalion and that's the same as he would have got if he went through the hard pass.
如果你们都选择的是平坦之途,那么他攻入你的国家时他只剩一个营,这与他选择崎岖之途别无二致
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So just to give an example, if he goes through the hard pass and you defend the hard pass, he loses one of those battalions going over the mountains and the other one because he meets you.
举个例子吧,如果入侵者与你在崎岖之途上狭路相逢,他在翻越山岭时损失一营,与你交战再损失一营
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But if you were to defend the hard pass, if you were to defend the mountains, then if he chooses the easy pass, he gets both battalions in and if he chooses the hard pass, he gets no battalions in. So in this case, easy is better.
但是如果你选择防守崎岖之途,即你要低于高山巨岭,而他却选择的是平坦之途,他将兵力全存,而要是选崎岖之途,他将全军覆没,这样来看,选择平坦之途要好些
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