This is a discontinuous payoff function, so differentiating isn't going to get you very far.

这是一个不连续的收益函数,所以不会涉及太多微分的东西

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So this line represents the expected payoff of shooting to the middle as a function of the probability that the goal keeper dives to the right.

这条线表示从中路射门时罚球者的收益,是门将扑向右路概率的一个函数

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And here's my green line representing my expected payoff as the shooter, from shooting to the right, as a function of the probability that the goalie dives to the right.

这条绿线表示作为一个罚球球员,我从右路射门的收益,是门将扑向右路概率的一个函数

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So here's Player I's payoff as a function of what Player II chooses and what Player I chooses, so we have that already.

这个就是参与人I的收益的方程,它是参与人I和II策略的函数,我们已经得到了

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Find player I's payoff is a function of what player II's effort is.

参与人I的收益是参与人II付出的函数

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We have Player I's payoff as a function of the two efforts and now I want to find out what is Player I's best efforts given a particular choice of S2? Yeah.

参与人I的收益是两人付出的函数,那么对于某个给定的S2,怎么计算参与人I的最佳对策呢

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This is the payoff to Player I of choosing Middle against Right, and the line in between, this line here, is the expected payoff to Player I of choosing Middle as a function of the probability that other people choose Right.

这条表示对手选右时参与人选中的收益,两个端点中间的线段部分,表示参与人I选右的预期收益,它是对手选右概率的一个方程

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