Logic game (Pirates distribute gems)

Can't believe I haven't wrote anything for 3 years and came back to write something.... "Everyone should know how to invest" is still my belief though.

Ever heard of a logic game about "pirates distribute gem"? Five pirates would like to find a way to distribute 100 gems among them. Each pirate raises an idea about how to distribute in a randomly determined order. After one pirate raised his idea, the five of them can vote for or against the idea. This idea will only be accepted if the idea receives more vote for than against. If the idea is being rejected the pirate who suggests will be dumped to the sea for the sharks. The next pirate will suggests and they will go through the voting again, until a suggestion is accepted. Now, as the first pirate who is going to suggests, how would you suggest?

If you want to try to solve this yourself then sit back and enjoy the thinking before you read on. I'll try to go through the answer very quickly here. But my blog here is not about the answer, I will get to the point why I raise this topic later. Anyone who thinks they know the answer already can skip the answer part and read on.

Answer:
Think backward. Let's name the 5 pirates as A, B, C, D and E, with A as the first pirate to suggest, and E the last one in that alphabetical order. If you are D, you know regardless of how you suggest, you sure will get nothing because even a tie you lose, as E can always vote against you so you can never win. So if you are C, you know as long as you give D something he will vote for your suggestion. So C would suggest (99,1,0), or if D is scared E will vote against him and dump him into the sea, C can even suggest (100,0,0) and D will still vote for C's plan.

Let's assume the worst case for C so C will suggest (99,1,0). Now if you are B and you know if you got dumped into the sea, that will be what C is going to suggest, so E basically will get nothing and D at most will get 1. So if you are B you can simply suggest (97,0,2,1). So E will get 1, and D gets 1 more to 2, you should then have 3 votes to 1 and your plan will be accepted.

Finally if you are A, and you know if you got dumped into the sea, that will be what B is going to suggest. Now you know C will get nothing and as A you need only 3 votes. So A can suggest the following: (97,0,1,0,2)

so you can keep 97 gems. Not sure if this answer is very surprising to you.



Now you wonder why I tell this logic game in here, shouldn't this blog about investment?

Of course this is related to investment. Remember the financial tsunami? Financial institutions invested in too much highly-leveraged investment vehicles and when these vehicles defaulted, they got burned and the de-leveraging process brought the whole world's financial systems down with it. The US government, printed a lot of money by putting up tons of Treasury bonds as collateral with the Federal Reserve, tried to save the economy as many banks were simply insolvent.

What happened next was we saw many big investment banks (that still survived after the tsunami) paid historical high bonus to their employees as these banks made a lot of money by using the printed money from the government. These banks simply used the money the government printed to make those money. Can we say these people saved the financial system by using the government's money? Can we say these people made money by solving a problem that they created?

This made me thought of the logic game. These investment banks was the first pirate. They have the full control on how to distribute the gems, and they surely know very well how they should distribute. Since the government needed to inject the liquidity through these banks, these banks have the full control on how to distribute the money. And here you go, by going through similar logic, these banks for sure got the biggest chunk of the money and the people who could not have a say about how to distribute the money simply got almost nothing.

As you see, investment is not an easy game to play. As if you don't have a say about how to distribute the wealth, it's very difficult to play the game and earn a fortune.