Problem:N人猜[1,100]内的整数,每个人都希望猜到所有数平均值的三倍,假设每个人足够理性,那么你应该猜多少?
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博弈三要素:
Players: N={1,2,...n},n>2;
Actions:选{1,2,...33},记ai为每个人的选择;
Profit / Payoff function: Ui
U(ai)=1, if ai 最接近所有人所猜数的average的3倍
U(ai)=0, if 有人比ai更接近average的3倍
U(ai)=1/k, if 有k个人都猜中了最接近average的3倍的这个数,而且ai在这k个人中
分析:
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看答案咯!
每个人选的最少为1,即average>=1, 如果average=2,则每个人都想选 3*average=6,这样average变成6;如果average=6,则每个人想选average*3=18...
……
iteration
……
所以最终每个人都按照最理智的方法选的话,结果是一个Nash equilibrium:每个人都选了100……