女人的年龄是由她自己决定的。

A woman has the age she deserves.

youdao

她带领我们参观了由她自己设计的工厂。

She showed us around the factory of her own designing.

youdao

她的婴儿是由她自己的医生给接生的。

Her baby was delivered by her own doctor.

youdao

So Player i's payoff "Ui," depends on all the choices in the class, in this case, including her own choice. Of course, a shorter way of writing that would be "Ui," it depends on the profile.

参与人i的收益Ui,由所有参与人的策略决定,当然也包括她自己的策略,简写应该是Ui,它由策略组合决定

耶鲁公开课 - 博弈论课程节选