Question: There is a million, a group of people to go to the auction, each time an integer multiple of price to 100, the highest bidder, but ranked second person bid will be confiscated. Assuming that only two people to participate in the auction, who have 10 million, and the two men are rational people, how much you can take this bid 10,000 yuan?
Thinking: this game once you start, the two sides in order to allow it to reduce their losses will continue to raise prices. E.g. first person offer 100 yuan 9900 yuan successful bid will get a second person to obtain 0. The second person in order to obtain greater benefits might bid $ 200, if the second person successful bid will receive 9800 yuan, this time not with the first person they would lose $ 100. . . . Here is the process of nesting dolls. The two sides will continue to increase in order to reduce losses to always have a final increase to 100,000 yuan. Then the auction ended.
So assuming that the outcome is a man A $ 100,000 for the end of the auction, then A will lose 90,000. A purpose of the hundreds of thousands to make themselves get more benefits, that is, the loss is even worse, when A loss of more than 90,000 yuan to 100,000 yuan he will be out of the auction. Ratio is more than 90,000 100 90,100. If, when A bid 90,100 yuan, if B continues to increase, then A fare increase to 10w can make him less of a loss, why? For example, a B 90200. If A does not increase, then A loss 90100, on the contrary A fare increase to just only 100,000 yuan losses 90,000 yuan. At this point you might be wondering, if B direct increase to 10,000 yuan? The answer is impossible, because before A bid 90,100 yuan, B bid certainly less than 90100, that is, up to this time bid 90,000 yuan B, at this time no matter a bid whether to continue, losses B certainly less 90,000 yuan, 100,000 yuan bid if B, then B will lose 90,000 yuan, 100,000 yuan bid then B does not reduce their losses so is not necessary. Then the sum can be launched when A bid 90,100 yuan, B does not make sense to continue to increase. Similarly it can launch a bid 80,200 yuan when the A, B does not make sense to continue to increase. . . . . A final push to 1000 yuan bid when B does not make sense to continue to increase. So the answer is $ 1,000.
