So the first-price auction is a classic trade off:

因此首价拍卖是一个经典的权衡
marginal benefit and marginal cost.

边际收入和边际支出
The marginal benefit of raising your bid is

你提高出价的边际收入
you increase the probability of winning.

是提升你获胜的几率
The marginal cost is you'll get less surplus if you win.

而边际支出是如果你赢了你会赢得少了
But in summary, in the second-price auction I bid "truthfully my value,"

简单地说在第二价格拍卖中我出价应等同价值
but if I win I only pay the second price.

但如果我赢了我只用付第二高的价
In the first price auction I bid less than my value

在首价拍卖中我出的价要比我的价值低
but I pay what I bid if I win.

但如果我赢了我要支付我的出价
That leads us to the natural question.

这就引出了一个本质的问题
Which of these two auctions, at least in expectation,

这两种拍卖起码看起来
is going to raise more money?

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