[passion]

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For all you game theorists out there.

Here is a simple game with two players, A and B. A is given $1000 and is able
to split it between he and B any way he chooses. B has the option to accept or
reject the offer. If he accepts the offer, the money is divided according to
A's split. If B rejects the offer, both players get nothing.

At face value, this game isn't interesting if played one time. B should always

accept. However, if this game is played 1000 times. it gets more interesting. Now consider that there will be 10 games going on at the same time with 10 different As and 10 different Bs. For the competition, the As are competing against the other As, not their actual opponent in the game.



What is A's optimal offer strategy? What is B's optimal strategy?

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I'm not sure the actual team competition matters to the game or at least you have not formalized how it matters. I am going to proceed by assuming that all As and Bs care about is their playoffs.

To solve these types of games it makes sense to start at the back and work forward.

What would happen in the 1000th period? A would offer B a the smallest possible share and B would accept.

What about the 999th period? Both players know that A will offer B the smallest share in the 1000th period and that B will accept. Knowing this, there is no reason for A to offer B anything but the smallest share in the 999th period.

What about the 998th period? Same thing - both players know A will offer B the smallest share in the last two periods and the B will accept - so in the 998th period A offers B the smallest share and B accepts.

Actually I think its the same thing for all prior periods.

When do you get someting different? If the game was played for an infinite (or indefinite) number of periods you would get different equillibrium strategies.

Passion