game theory ( 经典例题），和几周前的“必答题”相似，提上来讨论

Country x is planning to attack country y, and country y is anticipating the attack. Country x can either attack by land or by sea. Country y can either prepare for a land defense or a sea defense. Both countries must choose either an all land or all sea strategy, they may not divide their forces. The following are the probabilities of a successful invasion according to both strategies used.

If x launches an attack by sea and y prepares a defense by sea the probability of a successful invasion is 80%.   If x launches an attack by sea and y prepares a defense by land the probability of a successful invasion is 100%. If x launches an attack by land and y prepares a defense by land the probability of a successful invasion is 60%. If x launches an attack by land and y prepares a defense by sea the probability of a successful invasion is 100%.

 

What should the strategy of country x be, assuming the goal is to maximize the probability of a successful invasion? Assume the goal of country y to be to minimize the probability of a successful invasion. What is the final probability of a successful invasion assuming both utilize an optimal strategy?

所有跟帖： 

• If X has spy 007,100% win. If Y...,60% lost. -jinjing- ♀ (84 bytes) () 11/12/2010 postreply 15:14:29

• If Y has spy 007, 60% lost. 这个未必吧？ -wushuihe- ♂ (0 bytes) () 11/15/2010 postreply 08:49:39

• 严谨得失去幽默,007定义为可左右对手策略的人. -jinjing- ♀ (0 bytes) () 11/17/2010 postreply 08:23:18

• 答案看楼下吧， 很经典的，值得一读， 有人愿意可以帮大家翻译一下 -guest007- ♂ (0 bytes) () 11/18/2010 postreply 07:51:25

• jinjing's answer,obviously, is incorrect -guest007- ♂ (0 bytes) () 11/15/2010 postreply 11:16:33

• 哈,我对. -jinjing- ♀ (0 bytes) () 11/17/2010 postreply 08:26:28

• 标准答案 13/15 -guest007- ♂ (1148 bytes) () 11/18/2010 postreply 07:48:46

• The writer is not qualified being my student. -jinjing- ♀ (283 bytes) () 11/18/2010 postreply 12:40:18

• The answer is right, but y=2/3 is wrong. The trick is that y be -jinjing- ♀ (58 bytes) () 11/19/2010 postreply 08:28:03