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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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If we have a small engine, and we have to pull the car up a steep hill,a difficult hill, the engine is more likely to collapse,to blow up.
如果我们用的引擎很小，想把车开上一个陡峭崎岖的山坡，引擎很容易损毁，爆炸。
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On the other hand, we've just argued that you don't have a dominant strategy here; it's not the case that easy dominates hard.
我们刚才说这里没有优势策略,平坦之途并不总是优于崎岖之途
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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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Is it the case that defending the easy pass dominates defending the hard pass?
防守平坦之途是否,到底是不是优于防守崎岖之途呢
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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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And how many of you think you're going to defend the hard pass?
那么有多少人选择防守崎岖之途
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If the invader chooses the hard pass he will lose one battalion of his army simply in getting over the mountains, simply in going through the hard pass.
如果侵略者选择崎岖的路,仅在穿越阿尔卑斯山的途中,他就要损失一个营的兵力,这就是选崎岖之路的代价
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Well if you're not defending the easy pass, he doesn't lose anyone, and if he attacks through the hard pass he's going to lose at least one battalion.
如果你没有在平坦之途设防他兵力不减,然而如果他从崎岖之途进军,那么他将至少损失一个营
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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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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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One of these passes is a hard pass. It goes over the Alps.
一条路崎岖,需要翻越阿尔卑斯山
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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 is the case -- to introduce some jargon -- it is the case that the easy pass for the attacker, weakly dominates the hard pass for the attacker.
对入侵者来说,我们再词引入术语,对入侵者而言,平坦之途,弱优于崎岖之途
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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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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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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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It's not the case that for Hannibal, choosing the easy pass to attack through, strictly dominates choosing the hard pass, but it is the case that there's a weak notion of domination here.
对汉尼拔而言,选择平坦之途入侵并不是,严格优于选择崎岖之途的,但是在这种情况下有一个弱优势
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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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