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Let me tell you how i discovered game theory. I read a riddle about five pirates – intelligent pirates – who want to split a treasure. I don’t want to present you with fancy formulas and mathematical explanations. Just try to solve the riddle yourself and enjoy the surprising solution. So here is the riddle:
Five pirates got their hand on 500 gold coins. Now they want to devide the treasure. But because they are intelligent pirates – like a sober captain sparrow - and not the stereotype pirates who would just betray and kill until there is only a last one standing. One after the other will make a suggestion how to split the coins among the pirates. If a suggestion doesn’t get at least half the votes it is declined and the pirate making the suggestion is killed by the others. If the suggestion gets half the votes - or more - it is accepted and the gold is split. The pirate making the suggestion can also vote. So if the first suggestions is not accepted – and the pirate killed - the second pirate only needs to persuade one companion to have the gold split the way he wants it to. So what is the accepted suggestion ? Each pirates wants to make as much as possible - of course - without dying - surprise, surprise.
I will post the solution and explanation as a comment within a couple of days.
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The answer is – unlike in reality – that nobody gets killed. And even more surprising the first pirate to make a suggestion will get most of the money. When i first read the puzzle i thought that either everyone gets killed or they will just give all the money to the last pirate. But because they are intelligent pirates who know game theory they found the surprising answer.
The first pirate suggest the distribution: 498 coins for himself, 1 coin for the third and 1 coin for the last pirate. And these pirates will vote for him and give him 3 to 2 voices. See the matrix below to understand how this solution can be found:
1.____2.____3.____4.____5._
dead__dead__dead__dead__500
dead__dead__dead___500____0
dead__dead___499_____0____1
dead___499_____0_____1____0
_498_____0_____1_____0____1
Well the first line is obvious and does not need any explaination. If there are only 2 pirates left the second to last will get all the money because his vote will be enough to accept his suggestion. The third pirate knows this problem of the last pirate. So for only a single coin he can buy the vote of the last pirate. From there on you just have to go further back to find this surprising solution.
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