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[1] 参与者1可能会考虑威胁要引爆手雷的对手不是个疯子。这种怀疑在模型中我们表示为不完全信息——参与者1对参与者2的收益函数并不确定。参见第3章。
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[2] 参与者2的可选择行动空间A2,可以允许依赖于参与者1的行动a1。这种依赖性可以表示为A2(a1),或者可以合并到参与者2的收益函数中,对那些给定a1时不可行的a2,令u1(a1,a2)=-∞。有时参与者1的某些行动甚至可以结束整个博弈,不给参与者2行动的机会,对这样的a1值,可行的行动空间A2(a1)中只有一个元素,令参与者2别无选择。
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[3] 回想我们在重复剔除严格劣战略的讨论时(在第1.1.B节),参与者是理性的是共同知识,如果所有参与者都是理性的,并且所有参与者都知道所有参与者都是理性的,并且所有参与者都知道所有参与者都知道所有参与者都是理性的,如此等等,以至无穷。
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[4] 正如“古诺均衡”和“贝特兰德均衡”一般是指古诺和贝特兰德博弈中的纳什均衡,提及“斯塔克尔贝里均衡”一般表示序贯行动博弈,用以和同时行动相区别。但如前一节提到过的,序贯行动博弈有时会有多个纳什均衡,只有一个是和博弈的逆向归纳解相关的,这样“斯塔克尔贝里均衡”就有了双重含义,既表示博弈的序贯行动特点,又用来表示比简单纳什均衡条件更强的解的概念。
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[5] 此例也说明了,我们在第l.1.A节中作出的一个结论:在标准式博弈中,参与者同时选择各自的战略,但这并不要求各方必须同时行动;只要每个人在选择自己的行动时不知道其他人的选择就足够了。关于这一点的进一步讨论参见第2.4.A节。
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[6] 后面一点只不过是L*(w)定义的另一种表述,即对给定的w,L*(w)使π(w,L)最大化。比如工会开价w’,则企业沿w=w’的水平线选择L,而企业选择的就业L能使可能的利润达到最高,从而使通过(L,w’)的等利润曲线与约束w=w’相切。
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