You guys might know statistics but you sure don’t know the American mind. Based on all the game shows that get played in the US (think Deal or No Deal/Price is Right) I take Americans to be pretty stupid and you will definitely get that one idiot who will choose $1m, so I would just write down 999,999.99 and go home almost a millionaire.
Game theory has nothing to do with statistics…
Mobius Striptease Wrote: ------------------------------------------------------- > i agree with your own logic and explanation of > backward induction, because it makes sense, not > cause some professor says so. he might be the > brightest guy but there are also tons of dumba$$ > professors all over the place. proofs by > credentials and authority don’t apply I mostly did this to prove to myself that i remember how to use the education I paid for. I agree about the dumbass profs around the country but rarely see them in the hard sciences or mathematics fields, mostly in the opinion disciplines. Law for example has many subjective assumptions, whereas math just doesnt leave any room for subjective interpretation, at least at any level that i have taken it. This prof however is highly regarded and by the standards of Econ profs, being published in Econometrica or AER is regarded as the disciplines acceptance of your credibility. Which he has in both.
Here’s another game that might be of interest: There are five rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them. The Pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E. The Pirate world’s rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Pirates base their decisions on three factors. First of all, each pirate wants to survive. Secondly, each pirate wants to maximize the number of gold coins he receives. Thirdly, each pirate would prefer to throw another overboard, if all other results would otherwise be equal
I believe what happens is that A gets all coins minus two, and E and C get one coin each. You can solve it by working backwards from E to A and finding the Nash equilibrium at each step. You can say that this is the PIRATE-O efficient outcome. Get it??
Just by looking I am guessing the outcome is D ends up proposing 100 for him and voting yes while E no after the other 3 have been voted off and thrown overboard.
But Pirate A, who has first choice, will never choose an allocation that will result in himself being thrown over, unless this is the only outcome. So, unless A dies, the rest will never get to choose an allocation. This is how I figured it to work: E’s turn: E chooses to keep all. No brainer. D’s turn: D chooses to keep all, since E can vote for a tie at best. C’s turn: E will get zero if we progress to D’s turn. So, E’s vote can be bought by one coin. C will thus allocate 1 coin to E and keep the rest for himself. B’s turn: If we progress to C’s turn, C will get N-1, E will get 1 and D will get nothing. B only needs one vote in addition to his own. So, B will buy D’s vote with one coin and keep the rest for himself. A’s turn: If we progress to B’s turn, B will get N-1, D will get one coin, and C and E will get nothing. A needs two more votes in addition to his own. Thus, he buys C and E’s votes with one coin each, keeping the rest to himself.
> > You can say that this is the PIRATE-O efficient > outcome. Get it?? Well fine. I thought it was pretty funny…
It was but more Canadian funny.