More Game Theory

telerion
Posers and Puzzles 04 Oct '04 19:56
1. telerion
True X X Xian
04 Oct '04 19:56
Ok this one requires only a bit more mathematics then the last two. It is a classic example, introducing a concept called &quot;asymmetric information&quot;.

There are 2 players, P1 and P2.

P2 is considering buying the business. P2 values the business at 1.5V (Maybe P2 is a shrewder entrepenuer and thus can get more out of the business or P1 is subject to a 33% tax on earnings from which P2 is exempt).

Here's where asymmetric information comes in. Only P1 knows V. P2 only knows that V is uniformly distributed on the interval [0,1].

So P1 knows V.
P2 knows V~U(0,1).

Now P2 makes P1 a take-it-or-leave-it offer for the business. If the offer is greater than or equal to V, P1 will accept. If the offer is less than V, P1 will refuse.

What offer should P2 make to P1?
2. Acolyte
05 Oct '04 16:04
Does P2 know that P1 knows V? Does P1 know that, and so on ad infinitum?
3. 05 Oct '04 18:20
Originally posted by telerion
Ok this one requires only a bit more mathematics then the last two. It is a classic example, introducing a concept called "asymmetric information".

There are 2 players, P1 and P2.

P2 is considering buying the business. P2 values the business at 1.5V (Maybe P2 is a shrewder entrepenuer and thu ...[text shortened]... will accept. If the offer is less than V, P1 will refuse.

What offer should P2 make to P1?

what does V~U(0,1) mean. keep in mind that i read your entire post and still couldn't figure it out.
4. telerion
True X X Xian
05 Oct '04 19:15
Originally posted by Acolyte
Does P2 know that P1 knows V? Does P1 know that, and so on ad infinitum?
Uhm . . . yes. Yes I think we must go with that. I hesitate only because last time I let common knowledge out of her cage too early. This time though we must assume it from the start.
5. telerion
True X X Xian
05 Oct '04 19:17

what does V~U(0,1) mean. keep in mind that i read your entire post and still couldn't figure it out.
Now worries. V~U(0,1) is just notational form for &quot;V is distributed as uniform on the interval [0,1].&quot;
6. The Plumber
Leak-Proof
06 Oct '04 17:14
Originally posted by telerion
Now worries. V~U(0,1) is just notational form for "V is distributed as uniform on the interval [0,1]."
Some of us don't understand what &quot;distributed as uniform on the interval [0,1]&quot; means.
7. 06 Oct '04 17:29
Originally posted by The Plumber
Some of us don't understand what "distributed as uniform on the interval [0,1]" means.
If you have no idea what it means you should just leave this thread. It won't get any easier ðŸ˜€

Anyway, uniformly distributed means that all numbers in the interval have equal chance of being hit, or whatever the word is.
8. Acolyte
06 Oct '04 23:02

Suppose P1 offers to sell at price x. Then P2 knows that x is less than or equal to V, as P1 wouldn't sell at a loss. Therefore V must lie somewhere between 0 and x. Since this is a one-off transaction, P2 has no reason to believe that P1 is not trying to oversell the business, so from P2's p-o-v V~U[0,x] (or U[0,1] if x &gt; 1). The business therefore has a value to P2 of 3x/4 or 3/4, whichever is less, so he declines the offer.

=&gt; No transaction occurs at any price.
9. telerion
True X X Xian
07 Oct '04 00:24
You thinking along the correct lines. This is where you go astray just a bit.

Originally posted by Acolyte
Suppose P1 offers to sell at price x.

But notice from the OP that P2 is the player making the offer to P1. Amend your reasoning with this in mind, and I'm sure you will have it in a snap. Good work by the way.
10. Acolyte
07 Oct '04 08:17
Originally posted by telerion
You thinking along the correct lines. This is where you go astray just a bit.

Originally posted by Acolyte
[b]Suppose P1 offers to sell at price x.

But notice from the OP that P2 is the player making the offer to P1. Amend your reasoning with this in mind, and I'm sure you will have it in a snap. Good work by the way. [/b]